TY - JOUR
AB - Population structure can facilitate evolution of cooperation. In a structured population, cooperators can form clusters which resist exploitation by defectors. Recently, it was observed that a shift update rule is an extremely strong amplifier of cooperation in a one dimensional spatial model. For the shift update rule, an individual is chosen for reproduction proportional to fecundity; the offspring is placed next to the parent; a random individual dies. Subsequently, the population is rearranged (shifted) until all individual cells are again evenly spaced out. For large population size and a one dimensional population structure, the shift update rule favors cooperation for any benefit-to-cost ratio greater than one. But every attempt to generalize shift updating to higher dimensions while maintaining its strong effect has failed. The reason is that in two dimensions the clusters are fragmented by the movements caused by rearranging the cells. Here we introduce the natural phenomenon of a repulsive force between cells of different types. After a birth and death event, the cells are being rearranged minimizing the overall energy expenditure. If the repulsive force is sufficiently high, shift becomes a strong promoter of cooperation in two dimensions.
AU - Pavlogiannis, Andreas
AU - Chatterjee, Krishnendu
AU - Adlam, Ben
AU - Nowak, Martin
ID - 1624
JF - Scientific Reports
TI - Cellular cooperation with shift updating and repulsion
VL - 5
ER -
TY - CONF
AB - We study the pattern frequency vector for runs in probabilistic Vector Addition Systems with States (pVASS). Intuitively, each configuration of a given pVASS is assigned one of finitely many patterns, and every run can thus be seen as an infinite sequence of these patterns. The pattern frequency vector assigns to each run the limit of pattern frequencies computed for longer and longer prefixes of the run. If the limit does not exist, then the vector is undefined. We show that for one-counter pVASS, the pattern frequency vector is defined and takes one of finitely many values for almost all runs. Further, these values and their associated probabilities can be approximated up to an arbitrarily small relative error in polynomial time. For stable two-counter pVASS, we show the same result, but we do not provide any upper complexity bound. As a byproduct of our study, we discover counterexamples falsifying some classical results about stochastic Petri nets published in the 80s.
AU - Brázdil, Tomáš
AU - Kiefer, Stefan
AU - Kučera, Antonín
AU - Novotny, Petr
ID - 1660
TI - Long-run average behaviour of probabilistic vector addition systems
ER -
TY - CONF
AB - We consider parametric version of fixed-delay continuoustime Markov chains (or equivalently deterministic and stochastic Petri nets, DSPN) where fixed-delay transitions are specified by parameters, rather than concrete values. Our goal is to synthesize values of these parameters that, for a given cost function, minimise expected total cost incurred before reaching a given set of target states. We show that under mild assumptions, optimal values of parameters can be effectively approximated using translation to a Markov decision process (MDP) whose actions correspond to discretized values of these parameters. To this end we identify and overcome several interesting phenomena arising in systems with fixed delays.
AU - Brázdil, Tomáš
AU - Korenčiak, L'Uboš
AU - Krčál, Jan
AU - Novotny, Petr
AU - Řehák, Vojtěch
ID - 1667
TI - Optimizing performance of continuous-time stochastic systems using timeout synthesis
VL - 9259
ER -
TY - JOUR
AB - When a new mutant arises in a population, there is a probability it outcompetes the residents and fixes. The structure of the population can affect this fixation probability. Suppressing population structures reduce the difference between two competing variants, while amplifying population structures enhance the difference. Suppressors are ubiquitous and easy to construct, but amplifiers for the large population limit are more elusive and only a few examples have been discovered. Whether or not a population structure is an amplifier of selection depends on the probability distribution for the placement of the invading mutant. First, we prove that there exist only bounded amplifiers for adversarial placement-that is, for arbitrary initial conditions. Next, we show that the Star population structure, which is known to amplify for mutants placed uniformly at random, does not amplify for mutants that arise through reproduction and are therefore placed proportional to the temperatures of the vertices. Finally, we construct population structures that amplify for all mutational events that arise through reproduction, uniformly at random, or through some combination of the two.
AU - Adlam, Ben
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 1673
IS - 2181
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
TI - Amplifiers of selection
VL - 471
ER -
TY - JOUR
AB - Which genetic alterations drive tumorigenesis and how they evolve over the course of disease and therapy are central questions in cancer biology. Here we identify 44 recurrently mutated genes and 11 recurrent somatic copy number variations through whole-exome sequencing of 538 chronic lymphocytic leukaemia (CLL) and matched germline DNA samples, 278 of which were collected in a prospective clinical trial. These include previously unrecognized putative cancer drivers (RPS15, IKZF3), and collectively identify RNA processing and export, MYC activity, and MAPK signalling as central pathways involved in CLL. Clonality analysis of this large data set further enabled reconstruction of temporal relationships between driver events. Direct comparison between matched pre-treatment and relapse samples from 59 patients demonstrated highly frequent clonal evolution. Thus, large sequencing data sets of clinically informative samples enable the discovery of novel genes associated with cancer, the network of relationships between the driver events, and their impact on disease relapse and clinical outcome.
AU - Landau, Dan
AU - Tausch, Eugen
AU - Taylor Weiner, Amaro
AU - Stewart, Chip
AU - Reiter, Johannes
AU - Bahlo, Jasmin
AU - Kluth, Sandra
AU - Božić, Ivana
AU - Lawrence, Michael
AU - Böttcher, Sebastian
AU - Carter, Scott
AU - Cibulskis, Kristian
AU - Mertens, Daniel
AU - Sougnez, Carrie
AU - Rosenberg, Mara
AU - Hess, Julian
AU - Edelmann, Jennifer
AU - Kless, Sabrina
AU - Kneba, Michael
AU - Ritgen, Matthias
AU - Fink, Anna
AU - Fischer, Kirsten
AU - Gabriel, Stacey
AU - Lander, Eric
AU - Nowak, Martin
AU - Döhner, Hartmut
AU - Hallek, Michael
AU - Neuberg, Donna
AU - Getz, Gad
AU - Stilgenbauer, Stephan
AU - Wu, Catherine
ID - 1665
IS - 7574
JF - Nature
TI - Mutations driving CLL and their evolution in progression and relapse
VL - 526
ER -
TY - CONF
AB - We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. We demonstrate our approach on an illustrative case study.
AU - Svoreňová, Mária
AU - Kretinsky, Jan
AU - Chmelik, Martin
AU - Chatterjee, Krishnendu
AU - Cěrná, Ivana
AU - Belta, Cǎlin
ID - 1689
T2 - Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control
TI - Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games
ER -
TY - CONF
AB - We consider a case study of the problem of deploying an autonomous air vehicle in a partially observable, dynamic, indoor environment from a specification given as a linear temporal logic (LTL) formula over regions of interest. We model the motion and sensing capabilities of the vehicle as a partially observable Markov decision process (POMDP). We adapt recent results for solving POMDPs with parity objectives to generate a control policy. We also extend the existing framework with a policy minimization technique to obtain a better implementable policy, while preserving its correctness. The proposed techniques are illustrated in an experimental setup involving an autonomous quadrotor performing surveillance in a dynamic environment.
AU - Svoreňová, Mária
AU - Chmelik, Martin
AU - Leahy, Kevin
AU - Eniser, Hasan
AU - Chatterjee, Krishnendu
AU - Cěrná, Ivana
AU - Belta, Cǎlin
ID - 1691
T2 - Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control
TI - Temporal logic motion planning using POMDPs with parity objectives: Case study paper
ER -
TY - JOUR
AB -
We introduce quantitative timed refinement and timed simulation (directed) metrics, incorporating zenoness checks, for timed systems. These metrics assign positive real numbers which quantify the timing mismatches between two timed systems, amongst non-zeno runs. We quantify timing mismatches in three ways: (1) the maximal timing mismatch that can arise, (2) the “steady-state” maximal timing mismatches, where initial transient timing mismatches are ignored; and (3) the (long-run) average timing mismatches amongst two systems. These three kinds of mismatches constitute three important types of timing differences. Our event times are the global times, measured from the start of the system execution, not just the time durations of individual steps. We present algorithms over timed automata for computing the three quantitative simulation distances to within any desired degree of accuracy. In order to compute the values of the quantitative simulation distances, we use a game theoretic formulation. We introduce two new kinds of objectives for two player games on finite-state game graphs: (1) eventual debit-sum level objectives, and (2) average debit-sum level objectives. We present algorithms for computing the optimal values for these objectives in graph games, and then use these algorithms to compute the values of the timed simulation distances over timed automata.
AU - Chatterjee, Krishnendu
AU - Prabhu, Vinayak
ID - 1694
IS - 9
JF - IEEE Transactions on Automatic Control
TI - Quantitative temporal simulation and refinement distances for timed systems
VL - 60
ER -
TY - JOUR
AB - In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Multi-mean-payoff and multi-energy games replace individual weights by tuples, and the limit average (resp., running sum) of each coordinate must be (resp., remain) nonnegative. We prove finite-memory determinacy of multi-energy games and show inter-reducibility of multi-mean-payoff and multi-energy games for finite-memory strategies. We improve the computational complexity for solving both classes with finite-memory strategies: we prove coNP-completeness improving the previous known EXPSPACE bound. For memoryless strategies, we show that deciding the existence of a winning strategy for the protagonist is NP-complete. We present the first solution of multi-mean-payoff games with infinite-memory strategies: we show that mean-payoff-sup objectives can be decided in NP∩coNP, whereas mean-payoff-inf objectives are coNP-complete.
AU - Velner, Yaron
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
AU - Rabinovich, Alexander
AU - Raskin, Jean
ID - 1698
IS - 4
JF - Information and Computation
TI - The complexity of multi-mean-payoff and multi-energy games
VL - 241
ER -
TY - JOUR
AB - In many social situations, individuals endeavor to find the single best possible partner, but are constrained to evaluate the candidates in sequence. Examples include the search for mates, economic partnerships, or any other long-term ties where the choice to interact involves two parties. Surprisingly, however, previous theoretical work on mutual choice problems focuses on finding equilibrium solutions, while ignoring the evolutionary dynamics of decisions. Empirically, this may be of high importance, as some equilibrium solutions can never be reached unless the population undergoes radical changes and a sufficient number of individuals change their decisions simultaneously. To address this question, we apply a mutual choice sequential search problem in an evolutionary game-theoretical model that allows one to find solutions that are favored by evolution. As an example, we study the influence of sequential search on the evolutionary dynamics of cooperation. For this, we focus on the classic snowdrift game and the prisoner’s dilemma game.
AU - Priklopil, Tadeas
AU - Chatterjee, Krishnendu
ID - 1681
IS - 4
JF - Games
TI - Evolution of decisions in population games with sequentially searching individuals
VL - 6
ER -
TY - JOUR
AB - The competition for resources among cells, individuals or species is a fundamental characteristic of evolution. Biological all-pay auctions have been used to model situations where multiple individuals compete for a single resource. However, in many situations multiple resources with various values exist and single reward auctions are not applicable. We generalize the model to multiple rewards and study the evolution of strategies. In biological all-pay auctions the bid of an individual corresponds to its strategy and is equivalent to its payment in the auction. The decreasingly ordered rewards are distributed according to the decreasingly ordered bids of the participating individuals. The reproductive success of an individual is proportional to its fitness given by the sum of the rewards won minus its payments. Hence, successful bidding strategies spread in the population. We find that the results for the multiple reward case are very different from the single reward case. While the mixed strategy equilibrium in the single reward case with more than two players consists of mostly low-bidding individuals, we show that the equilibrium can convert to many high-bidding individuals and a few low-bidding individuals in the multiple reward case. Some reward values lead to a specialization among the individuals where one subpopulation competes for the rewards and the other subpopulation largely avoids costly competitions. Whether the mixed strategy equilibrium is an evolutionarily stable strategy (ESS) depends on the specific values of the rewards.
AU - Reiter, Johannes
AU - Kanodia, Ayush
AU - Gupta, Raghav
AU - Nowak, Martin
AU - Chatterjee, Krishnendu
ID - 1709
IS - 1812
JF - Proceedings of the Royal Society of London Series B Biological Sciences
TI - Biological auctions with multiple rewards
VL - 282
ER -
TY - CONF
AB - We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objec- tive we study asks to minimize the expected total cost till the target set is reached, while ensuring that the target set is reached almost-surely (with probability 1). We show that for integer costs approximating the optimal cost is undecidable. For positive costs, our results are as follows: (i) we establish matching lower and upper bounds for the optimal cost and the bound is double exponential; (ii) we show that the problem of approximating the optimal cost is decidable and present ap- proximation algorithms developing on the existing algorithms for POMDPs with finite-horizon objectives. While the worst- case running time of our algorithm is double exponential, we present efficient stopping criteria for the algorithm and show experimentally that it performs well in many examples.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 1820
T2 - Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence
TI - Optimal cost almost-sure reachability in POMDPs
VL - 5
ER -
TY - JOUR
AB - Modal transition systems (MTS) is a well-studied specification formalism of reactive systems supporting a step-wise refinement methodology. Despite its many advantages, the formalism as well as its currently known extensions are incapable of expressing some practically needed aspects in the refinement process like exclusive, conditional and persistent choices. We introduce a new model called parametric modal transition systems (PMTS) together with a general modal refinement notion that overcomes many of the limitations. We investigate the computational complexity of modal and thorough refinement checking on PMTS and its subclasses and provide a direct encoding of the modal refinement problem into quantified Boolean formulae, allowing us to employ state-of-the-art QBF solvers for modal refinement checking. The experiments we report on show that the feasibility of refinement checking is more influenced by the degree of nondeterminism rather than by the syntactic restrictions on the types of formulae allowed in the description of the PMTS.
AU - Beneš, Nikola
AU - Kretinsky, Jan
AU - Larsen, Kim
AU - Möller, Mikael
AU - Sickert, Salomon
AU - Srba, Jiří
ID - 1846
IS - 2-3
JF - Acta Informatica
TI - Refinement checking on parametric modal transition systems
VL - 52
ER -
TY - JOUR
AB - We consider mating strategies for females who search for males sequentially during a season of limited length. We show that the best strategy rejects a given male type if encountered before a time-threshold but accepts him after. For frequency-independent benefits, we obtain the optimal time-thresholds explicitly for both discrete and continuous distributions of males, and allow for mistakes being made in assessing the correct male type. When the benefits are indirect (genes for the offspring) and the population is under frequency-dependent ecological selection, the benefits depend on the mating strategy of other females as well. This case is particularly relevant to speciation models that seek to explore the stability of reproductive isolation by assortative mating under frequency-dependent ecological selection. We show that the indirect benefits are to be quantified by the reproductive values of couples, and describe how the evolutionarily stable time-thresholds can be found. We conclude with an example based on the Levene model, in which we analyze the evolutionarily stable assortative mating strategies and the strength of reproductive isolation provided by them.
AU - Priklopil, Tadeas
AU - Kisdi, Eva
AU - Gyllenberg, Mats
ID - 1851
IS - 4
JF - Evolution
TI - Evolutionarily stable mating decisions for sequentially searching females and the stability of reproductive isolation by assortative mating
VL - 69
ER -
TY - CONF
AB - Synthesis of program parts is particularly useful for concurrent systems. However, most approaches do not support common design tasks, like modifying a single process without having to re-synthesize or verify the whole system. Assume-guarantee synthesis (AGS) provides robustness against modifications of system parts, but thus far has been limited to the perfect information setting. This means that local variables cannot be hidden from other processes, which renders synthesis results cumbersome or even impossible to realize.We resolve this shortcoming by defining AGS under partial information. We analyze the complexity and decidability in different settings, showing that the problem has a high worstcase complexity and is undecidable in many interesting cases. Based on these observations, we present a pragmatic algorithm based on bounded synthesis, and demonstrate its practical applicability on several examples.
AU - Bloem, Roderick
AU - Chatterjee, Krishnendu
AU - Jacobs, Swen
AU - Könighofer, Robert
ID - 1838
TI - Assume-guarantee synthesis for concurrent reactive programs with partial information
VL - 9035
ER -
TY - CONF
AB - We present MultiGain, a tool to synthesize strategies for Markov decision processes (MDPs) with multiple mean-payoff objectives. Our models are described in PRISM, and our tool uses the existing interface and simulator of PRISM. Our tool extends PRISM by adding novel algorithms for multiple mean-payoff objectives, and also provides features such as (i) generating strategies and exploring them for simulation, and checking them with respect to other properties; and (ii) generating an approximate Pareto curve for two mean-payoff objectives. In addition, we present a new practical algorithm for the analysis of MDPs with multiple mean-payoff objectives under memoryless strategies.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Forejt, Vojtěch
AU - Kučera, Antonín
ID - 1839
TI - Multigain: A controller synthesis tool for MDPs with multiple mean-payoff objectives
VL - 9035
ER -
TY - JOUR
AB - We consider partially observable Markov decision processes (POMDPs) with limit-average payoff, where a reward value in the interval [0,1] is associated with every transition, and the payoff of an infinite path is the long-run average of the rewards. We consider two types of path constraints: (i) a quantitative constraint defines the set of paths where the payoff is at least a given threshold λ1ε(0,1]; and (ii) a qualitative constraint which is a special case of the quantitative constraint with λ1=1. We consider the computation of the almost-sure winning set, where the controller needs to ensure that the path constraint is satisfied with probability 1. Our main results for qualitative path constraints are as follows: (i) the problem of deciding the existence of a finite-memory controller is EXPTIME-complete; and (ii) the problem of deciding the existence of an infinite-memory controller is undecidable. For quantitative path constraints we show that the problem of deciding the existence of a finite-memory controller is undecidable. We also present a prototype implementation of our EXPTIME algorithm and experimental results on several examples.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
ID - 1873
JF - Artificial Intelligence
TI - POMDPs under probabilistic semantics
VL - 221
ER -
TY - CONF
AB - We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear various types of quantitative information. Throughout the design process the actions can be further refined and the information made more precise. We show how to compute the results of standard operations on the systems, including the quotient (residual), which has not been previously considered for quantitative non-deterministic systems. Our quantitative framework has close connections to the modal nu-calculus and is compositional with respect to general notions of distances between systems and the standard operations.
AU - Fahrenberg, Uli
AU - Kretinsky, Jan
AU - Legay, Axel
AU - Traonouez, Louis
ID - 1882
TI - Compositionality for quantitative specifications
VL - 8997
ER -
TY - JOUR
AB - Opacity is a generic security property, that has been defined on (non-probabilistic) transition systems and later on Markov chains with labels. For a secret predicate, given as a subset of runs, and a function describing the view of an external observer, the value of interest for opacity is a measure of the set of runs disclosing the secret. We extend this definition to the richer framework of Markov decision processes, where non-deterministicchoice is combined with probabilistic transitions, and we study related decidability problems with partial or complete observation hypotheses for the schedulers. We prove that all questions are decidable with complete observation and ω-regular secrets. With partial observation, we prove that all quantitative questions are undecidable but the question whether a system is almost surely non-opaquebecomes decidable for a restricted class of ω-regular secrets, as well as for all ω-regular secrets under finite-memory schedulers.
AU - Bérard, Béatrice
AU - Chatterjee, Krishnendu
AU - Sznajder, Nathalie
ID - 2034
IS - 1
JF - Information Processing Letters
TI - Probabilistic opacity for Markov decision processes
VL - 115
ER -
TY - JOUR
AB - We consider Markov decision processes (MDPs) with specifications given as Büchi (liveness) objectives, and examine the problem of computing the set of almost-sure winning vertices such that the objective can be ensured with probability 1 from these vertices. We study for the first time the average-case complexity of the classical algorithm for computing the set of almost-sure winning vertices for MDPs with Büchi objectives. Our contributions are as follows: First, we show that for MDPs with constant out-degree the expected number of iterations is at most logarithmic and the average-case running time is linear (as compared to the worst-case linear number of iterations and quadratic time complexity). Second, for the average-case analysis over all MDPs we show that the expected number of iterations is constant and the average-case running time is linear (again as compared to the worst-case linear number of iterations and quadratic time complexity). Finally we also show that when all MDPs are equally likely, the probability that the classical algorithm requires more than a constant number of iterations is exponentially small.
AU - Chatterjee, Krishnendu
AU - Joglekar, Manas
AU - Shah, Nisarg
ID - 1598
IS - 3
JF - Theoretical Computer Science
TI - Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives
VL - 573
ER -
TY - THES
AB - Cancer results from an uncontrolled growth of abnormal cells. Sequentially accumulated genetic and epigenetic alterations decrease cell death and increase cell replication. We used mathematical models to quantify the effect of driver gene mutations. The recently developed targeted therapies can lead to dramatic regressions. However, in solid cancers, clinical responses are often short-lived because resistant cancer cells evolve. We estimated that approximately 50 different mutations can confer resistance to a typical targeted therapeutic agent. We find that resistant cells are likely to be present in expanded subclones before the start of the treatment. The dominant strategy to prevent the evolution of resistance is combination therapy. Our analytical results suggest that in most patients, dual therapy, but not monotherapy, can result in long-term disease control. However, long-term control can only occur if there are no possible mutations in the genome that can cause cross-resistance to both drugs. Furthermore, we showed that simultaneous therapy with two drugs is much more likely to result in long-term disease control than sequential therapy with the same drugs. To improve our understanding of the underlying subclonal evolution we reconstruct the evolutionary history of a patient's cancer from next-generation sequencing data of spatially-distinct DNA samples. Using a quantitative measure of genetic relatedness, we found that pancreatic cancers and their metastases demonstrated a higher level of relatedness than that expected for any two cells randomly taken from a normal tissue. This minimal amount of genetic divergence among advanced lesions indicates that genetic heterogeneity, when quantitatively defined, is not a fundamental feature of the natural history of untreated pancreatic cancers. Our newly developed, phylogenomic tool Treeomics finds evidence for seeding patterns of metastases and can directly be used to discover rules governing the evolution of solid malignancies to transform cancer into a more predictable disease.
AU - Reiter, Johannes
ID - 1400
TI - The subclonal evolution of cancer
ER -
TY - CONF
AB - The computation of the winning set for one-pair Streett objectives and for k-pair Streett objectives in (standard) graphs as well as in game graphs are central problems in computer-aided verification, with application to the verification of closed systems with strong fairness conditions, the verification of open systems, checking interface compatibility, well-formed ness of specifications, and the synthesis of reactive systems. We give faster algorithms for the computation of the winning set for (1) one-pair Streett objectives (aka parity-3 problem) in game graphs and (2) for k-pair Streett objectives in graphs. For both problems this represents the first improvement in asymptotic running time in 15 years.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
AU - Loitzenbauer, Veronika
ID - 1661
T2 - Proceedings - Symposium on Logic in Computer Science
TI - Improved algorithms for one-pair and k-pair Streett objectives
VL - 2015-July
ER -
TY - JOUR
AB - We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (both players interact simultaneously); and (b) turn-based (both players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. In this work we present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Gimbert, Hugo
AU - Henzinger, Thomas A
ID - 1731
IS - 12
JF - Information and Computation
TI - Randomness for free
VL - 245
ER -
TY - JOUR
AB - The traditional synthesis question given a specification asks for the automatic construction of a system that satisfies the specification, whereas often there exists a preference order among the different systems that satisfy the given specification. Under a probabilistic assumption about the possible inputs, such a preference order is naturally expressed by a weighted automaton, which assigns to each word a value, such that a system is preferred if it generates a higher expected value. We solve the following optimal synthesis problem: given an omega-regular specification, a Markov chain that describes the distribution of inputs, and a weighted automaton that measures how well a system satisfies the given specification under the input assumption, synthesize a system that optimizes the measured value. For safety specifications and quantitative measures that are defined by mean-payoff automata, the optimal synthesis problem reduces to finding a strategy in a Markov decision process (MDP) that is optimal for a long-run average reward objective, which can be achieved in polynomial time. For general omega-regular specifications along with mean-payoff automata, the solution rests on a new, polynomial-time algorithm for computing optimal strategies in MDPs with mean-payoff parity objectives. Our algorithm constructs optimal strategies that consist of two memoryless strategies and a counter. The counter is in general not bounded. To obtain a finite-state system, we show how to construct an ε-optimal strategy with a bounded counter, for all ε > 0. Furthermore, we show how to decide in polynomial time if it is possible to construct an optimal finite-state system (i.e., a system without a counter) for a given specification. We have implemented our approach and the underlying algorithms in a tool that takes qualitative and quantitative specifications and automatically constructs a system that satisfies the qualitative specification and optimizes the quantitative specification, if such a system exists. We present some experimental results showing optimal systems that were automatically generated in this way.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Jobstmann, Barbara
AU - Singh, Rohit
ID - 1856
IS - 1
JF - Journal of the ACM
TI - Measuring and synthesizing systems in probabilistic environments
VL - 62
ER -
TY - JOUR
AB - We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives coincide, we show that in contrast to multi-dimensional mean-payoff games that are known to be coNP-complete, multi-dimensional total-payoff games are undecidable. We introduce conservative approximations of these objectives, where the payoff is considered over a local finite window sliding along a play, instead of the whole play. For single dimension, we show that (i) if the window size is polynomial, deciding the winner takes polynomial time, and (ii) the existence of a bounded window can be decided in NP ∩ coNP, and is at least as hard as solving mean-payoff games. For multiple dimensions, we show that (i) the problem with fixed window size is EXPTIME-complete, and (ii) there is no primitive-recursive algorithm to decide the existence of a bounded window.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Randour, Mickael
AU - Raskin, Jean
ID - 523
IS - 6
JF - Information and Computation
TI - Looking at mean-payoff and total-payoff through windows
VL - 242
ER -
TY - JOUR
AB - We consider concurrent games played by two players on a finite-state graph, where in every round the players simultaneously choose a move, and the current state along with the joint moves determine the successor state. We study the most fundamental objective for concurrent games, namely, mean-payoff or limit-average objective, where a reward is associated to each transition, and the goal of player 1 is to maximize the long-run average of the rewards, and the objective of player 2 is strictly the opposite (i.e., the games are zero-sum). The path constraint for player 1 could be qualitative, i.e., the mean-payoff is the maximal reward, or arbitrarily close to it; or quantitative, i.e., a given threshold between the minimal and maximal reward. We consider the computation of the almost-sure (resp. positive) winning sets, where player 1 can ensure that the path constraint is satisfied with probability 1 (resp. positive probability). Almost-sure winning with qualitative constraint exactly corresponds to the question of whether there exists a strategy to ensure that the payoff is the maximal reward of the game. Our main results for qualitative path constraints are as follows: (1) we establish qualitative determinacy results that show that for every state either player 1 has a strategy to ensure almost-sure (resp. positive) winning against all player-2 strategies, or player 2 has a spoiling strategy to falsify almost-sure (resp. positive) winning against all player-1 strategies; (2) we present optimal strategy complexity results that precisely characterize the classes of strategies required for almost-sure and positive winning for both players; and (3) we present quadratic time algorithms to compute the almost-sure and the positive winning sets, matching the best known bound of the algorithms for much simpler problems (such as reachability objectives). For quantitative constraints we show that a polynomial time solution for the almost-sure or the positive winning set would imply a solution to a long-standing open problem (of solving the value problem of turn-based deterministic mean-payoff games) that is not known to be solvable in polynomial time.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
ID - 524
IS - 6
JF - Information and Computation
TI - Qualitative analysis of concurrent mean payoff games
VL - 242
ER -
TY - CONF
AB - Simple board games, like Tic-Tac-Toe and CONNECT-4, play an important role not only in the development of mathematical and logical skills, but also in the emotional and social development. In this paper, we address the problem of generating targeted starting positions for such games. This can facilitate new approaches for bringing novice players to mastery, and also leads to discovery of interesting game variants. We present an approach that generates starting states of varying hardness levels for player 1 in a two-player board game, given rules of the board game, the desired number of steps required for player 1 to win, and the expertise levels of the two players. Our approach leverages symbolic methods and iterative simulation to efficiently search the extremely large state space. We present experimental results that include discovery of states of varying hardness levels for several simple grid-based board games. The presence of such states for standard game variants like 4×4 Tic-Tac-Toe opens up new games to be played that have never been played as the default start state is heavily biased.
AU - Ahmed, Umair
AU - Chatterjee, Krishnendu
AU - Gulwani, Sumit
ID - 1481
T2 - Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence
TI - Automatic generation of alternative starting positions for simple traditional board games
VL - 2
ER -
TY - CONF
AB - We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 1732
TI - Qualitative analysis of POMDPs with temporal logic specifications for robotics applications
ER -
TY - GEN
AB - We consider finite-state concurrent stochastic games, played by k>=2 players for an infinite number of rounds, where in every round, each player simultaneously and independently of the other players chooses an action, whereafter the successor state is determined by a probability distribution given by the current state and the chosen actions. We consider reachability objectives that given a target set of states require that some state in the target set is visited, and the dual safety objectives that given a target set require that only states in the target set are visited. We are interested in the complexity of stationary strategies measured by their patience, which is defined as the inverse of the smallest non-zero probability employed.
Our main results are as follows: We show that in two-player zero-sum concurrent stochastic games (with reachability objective for one player and the complementary safety objective for the other player): (i) the optimal bound on the patience of optimal and epsilon-optimal strategies, for both players is doubly exponential; and (ii) even in games with a single non-absorbing state exponential (in the number of actions) patience is necessary. In general we study the class of non-zero-sum games admitting epsilon-Nash equilibria. We show that if there is at least one player with reachability objective, then doubly-exponential patience is needed in general for epsilon-Nash equilibrium strategies, whereas in contrast if all players have safety objectives, then the optimal bound on patience for epsilon-Nash equilibrium strategies is only exponential.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Hansen, Kristoffer
ID - 5431
SN - 2664-1690
TI - The patience of concurrent stochastic games with safety and reachability objectives
ER -
TY - GEN
AB - Recently there has been a significant effort to handle quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, some basic system properties such as average response time cannot be expressed using weighted automata, nor in any other know decidable formalism. In this work, we introduce nested weighted automata as a natural extension of weighted automata which makes it possible to express important quantitative properties such as average response time.
In nested weighted automata, a master automaton spins off and collects results from weighted slave automata, each of which computes a quantity along a finite portion of an infinite word. Nested weighted automata can be viewed as the quantitative analogue of monitor automata, which are used in run-time verification. We establish an almost complete decidability picture for the basic decision problems about nested weighted automata, and illustrate their applicability in several domains. In particular, nested weighted automata can be used to decide average response time properties.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 5436
SN - 2664-1690
TI - Nested weighted automata
ER -
TY - CONF
AB - We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives. There exist two different views: (i) ~the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) ~the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector. We consider optimization with respect to both objectives at once, thus unifying the existing semantics. Precisely, the goal is to optimize the expectation while ensuring the satisfaction constraint. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., Ensure certain probabilistic guarantee). Our main results are as follows: First, we present algorithms for the decision problems, which are always polynomial in the size of the MDP. We also show that an approximation of the Pareto curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Second, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.
AU - Chatterjee, Krishnendu
AU - Komárková, Zuzana
AU - Kretinsky, Jan
ID - 1657
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
ER -
TY - CONF
AB - Recently there has been a significant effort to handle quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, some basic system properties such as average response time cannot be expressed using weighted automata, nor in any other know decidable formalism. In this work, we introduce nested weighted automata as a natural extension of weighted automata which makes it possible to express important quantitative properties such as average response time. In nested weighted automata, a master automaton spins off and collects results from weighted slave automata, each of which computes a quantity along a finite portion of an infinite word. Nested weighted automata can be viewed as the quantitative analogue of monitor automata, which are used in run-time verification. We establish an almost complete decidability picture for the basic decision problems about nested weighted automata, and illustrate their applicability in several domains. In particular, nested weighted automata can be used to decide average response time properties.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 1656
T2 - Proceedings - Symposium on Logic in Computer Science
TI - Nested weighted automata
VL - 2015-July
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives.
There have been two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector.
We consider the problem where the goal is to optimize the expectation under the constraint that the satisfaction semantics is ensured, and thus consider a generalization that unifies the existing semantics.
Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensures certain probabilistic guarantee).
Our main results are algorithms for the decision problem which are always polynomial in the size of the MDP. We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions.
Finally, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.
AU - Chatterjee, Krishnendu
AU - Komarkova, Zuzana
AU - Kretinsky, Jan
ID - 5429
SN - 2664-1690
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives.
There have been two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector.
We consider the problem where the goal is to optimize the expectation under the constraint that the satisfaction semantics is ensured, and thus consider a generalization that unifies the existing semantics. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensures certain probabilistic guarantee).
Our main results are algorithms for the decision problem which are always polynomial in the size of the MDP.
We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Finally, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.
AU - Chatterjee, Krishnendu
AU - Komarkova, Zuzana
AU - Kretinsky, Jan
ID - 5435
SN - 2664-1690
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
ER -
TY - CONF
AB - The edit distance between two words w1, w2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w1 to w2. The edit distance generalizes to languages L1,L2, where the edit distance is the minimal number k such that for every word from L1 there exists a word in L2 with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses. The problem of computing edit distance to pushdown automata is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Ibsen-Jensen, Rasmus
AU - Otop, Jan
ID - 1610
IS - Part II
TI - Edit distance for pushdown automata
VL - 9135
ER -
TY - GEN
AB - We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean- payoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let n denote the number of nodes of a graph, m the number of edges (for constant treewidth graphs m = O ( n ) ) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a mul- tiplicative factor of ∊ in time O ( n · log( n/∊ )) and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time O ( n · log( | a · b · n | )) = O ( n · log( n · W )) , when the output is a b , as compared to the previously best known algorithm with running time O ( n 2 · log( n · W )) . Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O ( n 2 · m ) time and the associated decision problem can be solved in O ( n · m ) time, improving the previous known O ( n 3 · m · log( n · W )) and O ( n 2 · m ) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O ( n · log n ) time, improving the previous known O ( n 4 · log( n · W )) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 5430
SN - 2664-1690
TI - Faster algorithms for quantitative verification in constant treewidth graphs
ER -
TY - GEN
AB - We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff property, the ratio property, and the minimum initial credit for energy property.
The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let $n$ denote the number of nodes of a graph, $m$ the number of edges (for constant treewidth graphs $m=O(n)$) and $W$ the largest absolute value of the weights.
Our main theoretical results are as follows.
First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a multiplicative factor of $\epsilon$ in time $O(n \cdot \log (n/\epsilon))$ and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time $O(n \cdot \log (|a\cdot b|))=O(n\cdot\log (n\cdot W))$, when the output is $\frac{a}{b}$, as compared to the previously best known algorithm with running time $O(n^2 \cdot \log (n\cdot W))$. Third, for the minimum initial credit problem we show that (i)~for general graphs the problem can be solved in $O(n^2\cdot m)$ time and the associated decision problem can be solved in $O(n\cdot m)$ time, improving the previous known $O(n^3\cdot m\cdot \log (n\cdot W))$ and $O(n^2 \cdot m)$ bounds, respectively; and (ii)~for constant treewidth graphs we present an algorithm that requires $O(n\cdot \log n)$ time, improving the previous known $O(n^4 \cdot \log (n \cdot W))$ bound.
We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 5437
SN - 2664-1690
TI - Faster algorithms for quantitative verification in constant treewidth graphs
ER -
TY - GEN
AB - The edit distance between two words w1, w2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w1 to w2. The edit distance generalizes to languages L1, L2, where the edit distance is the minimal number k such that for every word from L1 there exists a word in L2 with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses.
The problem of computing edit distance to a pushdown automaton is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Ibsen-Jensen, Rasmus
AU - Otop, Jan
ID - 5438
SN - 2664-1690
TI - Edit distance for pushdown automata
ER -
TY - GEN
AB - Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom in the context of evolution.The replacement graph specifies who competes with whom for reproduction.
The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability.
Our main results are:
(1) We show that the qualitative question is NP-complete and the quantitative approximation question is #P-hard in the special case when the interaction and the replacement graphs coincide and even with the restriction that the resident individuals do not reproduce (which corresponds to an invading population taking over an empty structure).
(2) We show that in general the qualitative question is PSPACE-complete and the quantitative approximation question is PSPACE-hard and can be solved in exponential time.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Nowak, Martin
ID - 5432
SN - 2664-1690
TI - The complexity of evolutionary games on graphs
ER -
TY - GEN
AB - Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom for payoff in the context of evolution. The replacement graph specifies who competes with whom for reproduction. The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. The fitness (or the reproductive rate) is a non-negative number, and depends on the payoff. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. Our main results are as follows: First, we consider a special case of the general problem, where the residents do not reproduce. We show that the qualitative question is NP-complete, and the quantitative approximation question is #P-complete, and the hardness results hold even in the special case where the interaction and the replacement graphs coincide. Second, we show that in general both the qualitative and the quantitative approximation questions are PSPACE-complete. The PSPACE-hardness result for quantitative approximation holds even when the fitness is always positive.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Nowak, Martin
ID - 5440
SN - 2664-1690
TI - The complexity of evolutionary games on graphs
ER -
TY - GEN
AB - POMDPs are standard models for probabilistic planning problems, where an agent interacts with an uncertain environment. We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIME-complete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. We report experimental results demonstrating the scalability of our symbolic (SAT-based) approach.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Davies, Jessica
ID - 5443
SN - 2664-1690
TI - A symbolic SAT-based algorithm for almost-sure reachability with small strategies in POMDPs
ER -
TY - GEN
AB - A comprehensive understanding of the clonal evolution of cancer is critical for understanding neoplasia. Genome-wide sequencing data enables evolutionary studies at unprecedented depth. However, classical phylogenetic methods often struggle with noisy sequencing data of impure DNA samples and fail to detect subclones that have different evolutionary trajectories. We have developed a tool, called Treeomics, that allows us to reconstruct the phylogeny of a cancer with commonly available sequencing technologies. Using Bayesian inference and Integer Linear Programming, robust phylogenies consistent with the biological processes underlying cancer evolution were obtained for pancreatic, ovarian, and prostate cancers. Furthermore, Treeomics correctly identified sequencing artifacts such as those resulting from low statistical power; nearly 7% of variants were misclassified by conventional statistical methods. These artifacts can skew phylogenies by creating illusory tumor heterogeneity among distinct samples. Importantly, we show that the evolutionary trees generated with Treeomics are mathematically optimal.
AU - Reiter, Johannes
AU - Makohon-Moore, Alvin
AU - Gerold, Jeffrey
AU - Bozic, Ivana
AU - Chatterjee, Krishnendu
AU - Iacobuzio-Donahue, Christine
AU - Vogelstein, Bert
AU - Nowak, Martin
ID - 5444
SN - 2664-1690
TI - Reconstructing robust phylogenies of metastatic cancers
ER -
TY - DATA
AB - This repository contains the experimental part of the CAV 2015 publication Counterexample Explanation by Learning Small Strategies in Markov Decision Processes.
We extended the probabilistic model checker PRISM to represent strategies of Markov Decision Processes as Decision Trees.
The archive contains a java executable version of the extended tool (prism_dectree.jar) together with a few examples of the PRISM benchmark library.
To execute the program, please have a look at the README.txt, which provides instructions and further information on the archive.
The archive contains scripts that (if run often enough) reproduces the data presented in the publication.
AU - Fellner, Andreas
ID - 5549
KW - Markov Decision Process
KW - Decision Tree
KW - Probabilistic Verification
KW - Counterexample Explanation
TI - Experimental part of CAV 2015 publication: Counterexample Explanation by Learning Small Strategies in Markov Decision Processes
ER -
TY - CONF
AB - For deterministic systems, a counterexample to a property can simply be an error trace, whereas counterexamples in probabilistic systems are necessarily more complex. For instance, a set of erroneous traces with a sufficient cumulative probability mass can be used. Since these are too large objects to understand and manipulate, compact representations such as subchains have been considered. In the case of probabilistic systems with non-determinism, the situation is even more complex. While a subchain for a given strategy (or scheduler, resolving non-determinism) is a straightforward choice, we take a different approach. Instead, we focus on the strategy itself, and extract the most important decisions it makes, and present its succinct representation.
The key tools we employ to achieve this are (1) introducing a concept of importance of a state w.r.t. the strategy, and (2) learning using decision trees. There are three main consequent advantages of our approach. Firstly, it exploits the quantitative information on states, stressing the more important decisions. Secondly, it leads to a greater variability and degree of freedom in representing the strategies. Thirdly, the representation uses a self-explanatory data structure. In summary, our approach produces more succinct and more explainable strategies, as opposed to e.g. binary decision diagrams. Finally, our experimental results show that we can extract several rules describing the strategy even for very large systems that do not fit in memory, and based on the rules explain the erroneous behaviour.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Fellner, Andreas
AU - Kretinsky, Jan
ID - 1603
TI - Counterexample explanation by learning small strategies in Markov decision processes
VL - 9206
ER -
TY - GEN
AB - We study algorithmic questions for concurrent systems where the transitions are labeled from a complete, closed semiring, and path properties are algebraic with semiring operations. The algebraic path properties can model dataflow analysis problems, the shortest path problem, and many other natural problems that arise in program analysis. We consider that each component of the concurrent system is a graph with constant treewidth, a property satisfied by the controlflow graphs of most programs. We allow for multiple possible queries, which arise naturally in demand driven dataflow analysis. The study of multiple queries allows us to consider the tradeoff between the resource usage of the one-time preprocessing and for each individual query. The traditional approach constructs the product graph of all components and applies the best-known graph algorithm on the product. In this approach, even the answer to a single query requires the transitive closure (i.e., the results of all possible queries), which provides no room for tradeoff between preprocessing and query time. Our main contributions are algorithms that significantly improve the worst-case running time of the traditional approach, and provide various tradeoffs depending on the number of queries. For example, in a concurrent system of two components, the traditional approach requires hexic time in the worst case for answering one query as well as computing the transitive closure, whereas we show that with one-time preprocessing in almost cubic time, each subsequent query can be answered in at most linear time, and even the transitive closure can be computed in almost quartic time. Furthermore, we establish conditional optimality results showing that the worst-case running time of our algorithms cannot be improved without achieving major breakthroughs in graph algorithms (i.e., improving the worst-case bound for the shortest path problem in general graphs). Preliminary experimental results show that our algorithms perform favorably on several benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Goharshady, Amir
AU - Pavlogiannis, Andreas
ID - 5441
SN - 2664-1690
TI - Algorithms for algebraic path properties in concurrent systems of constant treewidth components
ER -
TY - JOUR
AB - Interprocedural analysis is at the heart of numerous applications in programming languages, such as alias analysis, constant propagation, etc. Recursive state machines (RSMs) are standard models for interprocedural analysis. We consider a general framework with RSMs where the transitions are labeled from a semiring, and path properties are algebraic with semiring operations. RSMs with algebraic path properties can model interprocedural dataflow analysis problems, the shortest path problem, the most probable path problem, etc. The traditional algorithms for interprocedural analysis focus on path properties where the starting point is fixed as the entry point of a specific method. In this work, we consider possible multiple queries as required in many applications such as in alias analysis. The study of multiple queries allows us to bring in a very important algorithmic distinction between the resource usage of the one-time preprocessing vs for each individual query. The second aspect that we consider is that the control flow graphs for most programs have constant treewidth. Our main contributions are simple and implementable algorithms that supportmultiple queries for algebraic path properties for RSMs that have constant treewidth. Our theoretical results show that our algorithms have small additional one-time preprocessing, but can answer subsequent queries significantly faster as compared to the current best-known solutions for several important problems, such as interprocedural reachability and shortest path. We provide a prototype implementation for interprocedural reachability and intraprocedural shortest path that gives a significant speed-up on several benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
AU - Goyal, Prateesh
ID - 1602
IS - 1
JF - ACM SIGPLAN Notices
TI - Faster algorithms for algebraic path properties in recursive state machines with constant treewidth
VL - 50
ER -
TY - JOUR
AB - We consider the quantitative analysis problem for interprocedural control-flow graphs (ICFGs). The input consists of an ICFG, a positive weight function that assigns every transition a positive integer-valued number, and a labelling of the transitions (events) as good, bad, and neutral events. The weight function assigns to each transition a numerical value that represents ameasure of how good or bad an event is. The quantitative analysis problem asks whether there is a run of the ICFG where the ratio of the sum of the numerical weights of good events versus the sum of weights of bad events in the long-run is at least a given threshold (or equivalently, to compute the maximal ratio among all valid paths in the ICFG). The quantitative analysis problem for ICFGs can be solved in polynomial time, and we present an efficient and practical algorithm for the problem. We show that several problems relevant for static program analysis, such as estimating the worst-case execution time of a program or the average energy consumption of a mobile application, can be modeled in our framework. We have implemented our algorithm as a tool in the Java Soot framework. We demonstrate the effectiveness of our approach with two case studies. First, we show that our framework provides a sound approach (no false positives) for the analysis of inefficiently-used containers. Second, we show that our approach can also be used for static profiling of programs which reasons about methods that are frequently invoked. Our experimental results show that our tool scales to relatively large benchmarks, and discovers relevant and useful information that can be used to optimize performance of the programs.
AU - Chatterjee, Krishnendu
AU - Pavlogiannis, Andreas
AU - Velner, Yaron
ID - 1604
IS - 1
JF - Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT
SN - 978-1-4503-3300-9
TI - Quantitative interprocedural analysis
VL - 50
ER -
TY - CONF
AB - We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let n denote the number of nodes of a graph, m the number of edges (for constant treewidth graphs m=O(n)) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a multiplicative factor of ϵ in time O(n⋅log(n/ϵ)) and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time O(n⋅log(|a⋅b|))=O(n⋅log(n⋅W)), when the output is ab, as compared to the previously best known algorithm with running time O(n2⋅log(n⋅W)). Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O(n2⋅m) time and the associated decision problem can be solved in O(n⋅m) time, improving the previous known O(n3⋅m⋅log(n⋅W)) and O(n2⋅m) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O(n⋅logn) time, improving the previous known O(n4⋅log(n⋅W)) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 1607
TI - Faster algorithms for quantitative verification in constant treewidth graphs
VL - 9206
ER -
TY - CONF
AB - We present a flexible framework for the automated competitive analysis of on-line scheduling algorithms for firm-deadline real-time tasks based on multi-objective graphs: Given a task set and an on-line scheduling algorithm specified as a labeled transition system, along with some optional safety, liveness, and/or limit-average constraints for the adversary, we automatically compute the competitive ratio of the algorithm w.r.t. A clairvoyant scheduler. We demonstrate the flexibility and power of our approach by comparing the competitive ratio of several on-line algorithms, including Dover, that have been proposed in the past, for various task sets. Our experimental results reveal that none of these algorithms is universally optimal, in the sense that there are task sets where other schedulers provide better performance. Our framework is hence a very useful design tool for selecting optimal algorithms for a given application.
AU - Chatterjee, Krishnendu
AU - Pavlogiannis, Andreas
AU - Kößler, Alexander
AU - Schmid, Ulrich
ID - 1714
IS - January
T2 - Real-Time Systems Symposium
TI - A framework for automated competitive analysis of on-line scheduling of firm-deadline tasks
VL - 2015
ER -
TY - JOUR
AB - We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1) First we show that the algorithmic question is reducible to the problem of a logarithmic number of min-plus matrix multiplications of n×n-matrices, where n is the number of vertices of the graph. (2) Second, when the weights are nonnegative, we present the first (1+ε)-approximation algorithm for the problem and the running time of our algorithm is Õ(nωlog3(nW/ε)/ε),1 where O(nω) is the time required for the classic n×n-matrix multiplication and W is the maximum value of the weights. With an additional O(log(nW/ε)) factor in space a cycle with approximately optimal weight can be computed within the same time bound.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
AU - Krinninger, Sebastian
AU - Loitzenbauer, Veronika
AU - Raskin, Michael
ID - 1375
IS - C
JF - Theoretical Computer Science
TI - Approximating the minimum cycle mean
VL - 547
ER -