@inproceedings{6889,
abstract = {We study Markov decision processes and turn-based stochastic games with parity conditions. There are three qualitative winning criteria, namely, sure winning, which requires all paths to satisfy the condition, almost-sure winning, which requires the condition to be satisfied with probability 1, and limit-sure winning, which requires the condition to be satisfied with probability arbitrarily close to 1. We study the combination of two of these criteria for parity conditions, e.g., there are two parity conditions one of which must be won surely, and the other almost-surely. The problem has been studied recently by Berthon et al. for MDPs with combination of sure and almost-sure winning, under infinite-memory strategies, and the problem has been established to be in NP cap co-NP. Even in MDPs there is a difference between finite-memory and infinite-memory strategies. Our main results for combination of sure and almost-sure winning are as follows: (a) we show that for MDPs with finite-memory strategies the problem is in NP cap co-NP; (b) we show that for turn-based stochastic games the problem is co-NP-complete, both for finite-memory and infinite-memory strategies; and (c) we present algorithmic results for the finite-memory case, both for MDPs and turn-based stochastic games, by reduction to non-stochastic parity games. In addition we show that all the above complexity results also carry over to combination of sure and limit-sure winning, and results for all other combinations can be derived from existing results in the literature. Thus we present a complete picture for the study of combinations of two qualitative winning criteria for parity conditions in MDPs and turn-based stochastic games. },
author = {Chatterjee, Krishnendu and Piterman, Nir},
location = {Amsterdam, Netherlands},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Combinations of Qualitative Winning for Stochastic Parity Games}},
doi = {10.4230/LIPICS.CONCUR.2019.6},
volume = {140},
year = {2019},
}
@inproceedings{6942,
abstract = {Graph games and Markov decision processes (MDPs) are standard models in reactive synthesis and verification of probabilistic systems with nondeterminism. The class of 𝜔 -regular winning conditions; e.g., safety, reachability, liveness, parity conditions; provides a robust and expressive specification formalism for properties that arise in analysis of reactive systems. The resolutions of nondeterminism in games and MDPs are represented as strategies, and we consider succinct representation of such strategies. The decision-tree data structure from machine learning retains the flavor of decisions of strategies and allows entropy-based minimization to obtain succinct trees. However, in contrast to traditional machine-learning problems where small errors are allowed, for winning strategies in graph games and MDPs no error is allowed, and the decision tree must represent the entire strategy. In this work we propose decision trees with linear classifiers for representation of strategies in graph games and MDPs. We have implemented strategy representation using this data structure and we present experimental results for problems on graph games and MDPs, which show that this new data structure presents a much more efficient strategy representation as compared to standard decision trees.},
author = {Ashok, Pranav and Brázdil, Tomáš and Chatterjee, Krishnendu and Křetínský, Jan and Lampert, Christoph and Toman, Viktor},
booktitle = {16th International Conference on Quantitative Evaluation of Systems},
isbn = {9783030302801},
issn = {0302-9743},
location = {Glasgow, United Kingdom},
pages = {109--128},
publisher = {Springer Nature},
title = {{Strategy representation by decision trees with linear classifiers}},
doi = {10.1007/978-3-030-30281-8_7},
volume = {11785},
year = {2019},
}
@article{7014,
abstract = {We study the problem of developing efficient approaches for proving
worst-case bounds of non-deterministic recursive programs. Ranking functions
are sound and complete for proving termination and worst-case bounds of
nonrecursive programs. First, we apply ranking functions to recursion,
resulting in measure functions. We show that measure functions provide a sound
and complete approach to prove worst-case bounds of non-deterministic recursive
programs. Our second contribution is the synthesis of measure functions in
nonpolynomial forms. We show that non-polynomial measure functions with
logarithm and exponentiation can be synthesized through abstraction of
logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem
using linear programming. While previous methods obtain worst-case polynomial
bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$
as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present
experimental results to demonstrate that our approach can obtain efficiently
worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the
divide-and-conquer algorithm for the Closest-Pair problem, where we obtain
$\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for
polynomial multiplication and Strassen's algorithm for matrix multiplication,
where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and
close to the best-known bounds for the respective algorithms.},
author = {Chatterjee, Krishnendu and Fu, Hongfei and Goharshady, Amir Kafshdar},
journal = {ACM Transactions on Programming Languages and Systems},
number = {4},
publisher = {ACM},
title = {{Non-polynomial worst-case analysis of recursive programs}},
doi = {10.1145/3339984},
volume = {41},
year = {2019},
}
@article{7158,
abstract = {
Interprocedural analysis is at the heart of numerous applications in programming languages, such as alias analysis, constant propagation, and so on. 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, and so on. 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 an important algorithmic distinction between the resource usage of the one-time preprocessing vs for each individual query. The second aspect we consider is that the control flow graphs for most programs have constant treewidth.
Our main contributions are simple and implementable algorithms that support multiple 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 algorithmic solutions for interprocedural dataflow analysis. We have also implemented our algorithms and evaluated their performance for performing on-demand interprocedural dataflow analysis on various domains, such as for live variable analysis and reaching definitions, on a standard benchmark set. Our experimental results align with our theoretical statements and show that after a lightweight preprocessing, on-demand queries are answered much faster than the standard existing algorithmic approaches.
},
author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Goyal, Prateesh and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
issn = {0164-0925},
journal = {ACM Transactions on Programming Languages and Systems},
number = {4},
publisher = {ACM},
title = {{Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth}},
doi = {10.1145/3363525},
volume = {41},
year = {2019},
}
@inproceedings{7183,
abstract = {A probabilistic vector addition system with states (pVASS) is a finite state Markov process augmented with non-negative integer counters that can be incremented or decremented during each state transition, blocking any behaviour that would cause a counter to decrease below zero. The pVASS can be used as abstractions of probabilistic programs with many decidable properties. The use of pVASS as abstractions requires the presence of nondeterminism in the model. In this paper, we develop techniques for checking fast termination of pVASS with nondeterminism. That is, for every initial configuration of size n, we consider the worst expected number of transitions needed to reach a configuration with some counter negative (the expected termination time). We show that the problem whether the asymptotic expected termination time is linear is decidable in polynomial time for a certain natural class of pVASS with nondeterminism. Furthermore, we show the following dichotomy: if the asymptotic expected termination time is not linear, then it is at least quadratic, i.e., in Ω(n2).},
author = {Brázdil, Tomás and Chatterjee, Krishnendu and Kucera, Antonín and Novotný, Petr and Velan, Dominik},
booktitle = {International Symposium on Automated Technology for Verification and Analysis},
isbn = {9783030317836},
issn = {16113349},
location = {Taipei, Taiwan},
pages = {462--478},
publisher = {Springer Nature},
title = {{Deciding fast termination for probabilistic VASS with nondeterminism}},
doi = {10.1007/978-3-030-31784-3_27},
volume = {11781},
year = {2019},
}
@article{7210,
abstract = {The rate of biological evolution depends on the fixation probability and on the fixation time of new mutants. Intensive research has focused on identifying population structures that augment the fixation probability of advantageous mutants. But these amplifiers of natural selection typically increase fixation time. Here we study population structures that achieve a tradeoff between fixation probability and time. First, we show that no amplifiers can have an asymptotically lower absorption time than the well-mixed population. Then we design population structures that substantially augment the fixation probability with just a minor increase in fixation time. Finally, we show that those structures enable higher effective rate of evolution than the well-mixed population provided that the rate of generating advantageous mutants is relatively low. Our work sheds light on how population structure affects the rate of evolution. Moreover, our structures could be useful for lab-based, medical, or industrial applications of evolutionary optimization.},
author = {Tkadlec, Josef and Pavlogiannis, Andreas and Chatterjee, Krishnendu and Nowak, Martin A.},
issn = {2399-3642},
journal = {Communications Biology},
publisher = {Springer Nature},
title = {{Population structure determines the tradeoff between fixation probability and fixation time}},
doi = {10.1038/s42003-019-0373-y},
volume = {2},
year = {2019},
}
@inproceedings{7402,
abstract = {Graph planning gives rise to fundamental algorithmic questions such as shortest path, traveling salesman problem, etc. A classical problem in discrete planning is to consider a weighted graph and construct a path that maximizes the sum of weights for a given time horizon T. However, in many scenarios, the time horizon is not fixed, but the stopping time is chosen according to some distribution such that the expected stopping time is T. If the stopping time distribution is not known, then to ensure robustness, the distribution is chosen by an adversary, to represent the worst-case scenario. A stationary plan for every vertex always chooses the same outgoing edge. For fixed horizon or fixed stopping-time distribution, stationary plans are not sufficient for optimality. Quite surprisingly we show that when an adversary chooses the stopping-time distribution with expected stopping time T, then stationary plans are sufficient. While computing optimal stationary plans for fixed horizon is NP-complete, we show that computing optimal stationary plans under adversarial stopping-time distribution can be achieved in polynomial time. Consequently, our polynomial-time algorithm for adversarial stopping time also computes an optimal plan among all possible plans.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
booktitle = {34th Annual ACM/IEEE Symposium on Logic in Computer Science},
isbn = {9781728136080},
location = {Vancouver, BC, Canada},
pages = {1--13},
publisher = {IEEE},
title = {{Graph planning with expected finite horizon}},
doi = {10.1109/lics.2019.8785706},
year = {2019},
}
@unpublished{7950,
abstract = {The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results:
1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan.
2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2.
3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved.},
author = {Biniaz, Ahmad and Jain, Kshitij and Lubiw, Anna and Masárová, Zuzana and Miltzow, Tillmann and Mondal, Debajyoti and Naredla, Anurag Murty and Tkadlec, Josef and Turcotte, Alexi},
booktitle = {arXiv:1903.06981},
pages = {41},
publisher = {ArXiv},
title = {{Token swapping on trees}},
year = {2019},
}
@article{6836,
abstract = {Direct reciprocity is a powerful mechanism for the evolution of cooperation on the basis of repeated interactions1,2,3,4. It requires that interacting individuals are sufficiently equal, such that everyone faces similar consequences when they cooperate or defect. Yet inequality is ubiquitous among humans5,6 and is generally considered to undermine cooperation and welfare7,8,9,10. Most previous models of reciprocity do not include inequality11,12,13,14,15. These models assume that individuals are the same in all relevant aspects. Here we introduce a general framework to study direct reciprocity among unequal individuals. Our model allows for multiple sources of inequality. Subjects can differ in their endowments, their productivities and in how much they benefit from public goods. We find that extreme inequality prevents cooperation. But if subjects differ in productivity, some endowment inequality can be necessary for cooperation to prevail. Our mathematical predictions are supported by a behavioural experiment in which we vary the endowments and productivities of the subjects. We observe that overall welfare is maximized when the two sources of heterogeneity are aligned, such that more productive individuals receive higher endowments. By contrast, when endowments and productivities are misaligned, cooperation quickly breaks down. Our findings have implications for policy-makers concerned with equity, efficiency and the provisioning of public goods.},
author = {Hauser, Oliver P. and Hilbe, Christian and Chatterjee, Krishnendu and Nowak, Martin A.},
issn = {14764687},
journal = {Nature},
number = {7770},
pages = {524--527},
publisher = {Springer Nature},
title = {{Social dilemmas among unequals}},
doi = {10.1038/s41586-019-1488-5},
volume = {572},
year = {2019},
}
@article{198,
abstract = {We consider a class of students learning a language from a teacher. The situation can be interpreted as a group of child learners receiving input from the linguistic environment. The teacher provides sample sentences. The students try to learn the grammar from the teacher. In addition to just listening to the teacher, the students can also communicate with each other. The students hold hypotheses about the grammar and change them if they receive counter evidence. The process stops when all students have converged to the correct grammar. We study how the time to convergence depends on the structure of the classroom by introducing and evaluating various complexity measures. We find that structured communication between students, although potentially introducing confusion, can greatly reduce some of the complexity measures. Our theory can also be interpreted as applying to the scientific process, where nature is the teacher and the scientists are the students.},
author = {Ibsen-Jensen, Rasmus and Tkadlec, Josef and Chatterjee, Krishnendu and Nowak, Martin},
journal = {Journal of the Royal Society Interface},
number = {140},
publisher = {Royal Society},
title = {{Language acquisition with communication between learners}},
doi = {10.1098/rsif.2018.0073},
volume = {15},
year = {2018},
}
@inproceedings{24,
abstract = {Partially-observable Markov decision processes (POMDPs) with discounted-sum payoff are a standard framework to model a wide range of problems related to decision making under uncertainty. Traditionally, the goal has been to obtain policies that optimize the expectation of the discounted-sum payoff. A key drawback of the expectation measure is that even low probability events with extreme payoff can significantly affect the expectation, and thus the obtained policies are not necessarily risk-averse. An alternate approach is to optimize the probability that the payoff is above a certain threshold, which allows obtaining risk-averse policies, but ignores optimization of the expectation. We consider the expectation optimization with probabilistic guarantee (EOPG) problem, where the goal is to optimize the expectation ensuring that the payoff is above a given threshold with at least a specified probability. We present several results on the EOPG problem, including the first algorithm to solve it.},
author = {Chatterjee, Krishnendu and Elgyütt, Adrian and Novotny, Petr and Rouillé, Owen},
location = {Stockholm, Sweden},
pages = {4692 -- 4699},
publisher = {IJCAI},
title = {{Expectation optimization with probabilistic guarantees in POMDPs with discounted-sum objectives}},
doi = {10.24963/ijcai.2018/652},
volume = {2018},
year = {2018},
}
@inproceedings{25,
abstract = {Partially observable Markov decision processes (POMDPs) are the standard models for planning under uncertainty with both finite and infinite horizon. Besides the well-known discounted-sum objective, indefinite-horizon objective (aka Goal-POMDPs) is another classical objective for POMDPs. In this case, given a set of target states and a positive cost for each transition, the optimization objective is to minimize the expected total cost until a target state is reached. In the literature, RTDP-Bel or heuristic search value iteration (HSVI) have been used for solving Goal-POMDPs. Neither of these algorithms has theoretical convergence guarantees, and HSVI may even fail to terminate its trials. We give the following contributions: (1) We discuss the challenges introduced in Goal-POMDPs and illustrate how they prevent the original HSVI from converging. (2) We present a novel algorithm inspired by HSVI, termed Goal-HSVI, and show that our algorithm has convergence guarantees. (3) We show that Goal-HSVI outperforms RTDP-Bel on a set of well-known examples.},
author = {Horák, Karel and Bošanský, Branislav and Chatterjee, Krishnendu},
booktitle = {Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence},
location = {Stockholm, Sweden},
pages = {4764 -- 4770},
publisher = {IJCAI},
title = {{Goal-HSVI: Heuristic search value iteration for goal-POMDPs}},
doi = {10.24963/ijcai.2018/662},
volume = {2018-July},
year = {2018},
}
@article{419,
abstract = {Reciprocity is a major factor in human social life and accounts for a large part of cooperation in our communities. Direct reciprocity arises when repeated interactions occur between the same individuals. The framework of iterated games formalizes this phenomenon. Despite being introduced more than five decades ago, the concept keeps offering beautiful surprises. Recent theoretical research driven by new mathematical tools has proposed a remarkable dichotomy among the crucial strategies: successful individuals either act as partners or as rivals. Rivals strive for unilateral advantages by applying selfish or extortionate strategies. Partners aim to share the payoff for mutual cooperation, but are ready to fight back when being exploited. Which of these behaviours evolves depends on the environment. Whereas small population sizes and a limited number of rounds favour rivalry, partner strategies are selected when populations are large and relationships stable. Only partners allow for evolution of cooperation, while the rivals’ attempt to put themselves first leads to defection. Hilbe et al. synthesize recent theoretical work on zero-determinant and ‘rival’ versus ‘partner’ strategies in social dilemmas. They describe the environments under which these contrasting selfish or cooperative strategies emerge in evolution.},
author = {Hilbe, Christian and Chatterjee, Krishnendu and Nowak, Martin},
journal = {Nature Human Behaviour},
pages = {469–477},
publisher = {Nature Publishing Group},
title = {{Partners and rivals in direct reciprocity}},
doi = {10.1038/s41562-018-0320-9},
volume = {2},
year = {2018},
}
@article{454,
abstract = {Direct reciprocity is a mechanism for cooperation among humans. Many of our daily interactions are repeated. We interact repeatedly with our family, friends, colleagues, members of the local and even global community. In the theory of repeated games, it is a tacit assumption that the various games that a person plays simultaneously have no effect on each other. Here we introduce a general framework that allows us to analyze “crosstalk” between a player’s concurrent games. In the presence of crosstalk, the action a person experiences in one game can alter the person’s decision in another. We find that crosstalk impedes the maintenance of cooperation and requires stronger levels of forgiveness. The magnitude of the effect depends on the population structure. In more densely connected social groups, crosstalk has a stronger effect. A harsh retaliator, such as Tit-for-Tat, is unable to counteract crosstalk. The crosstalk framework provides a unified interpretation of direct and upstream reciprocity in the context of repeated games.},
author = {Reiter, Johannes and Hilbe, Christian and Rand, David and Chatterjee, Krishnendu and Nowak, Martin},
journal = {Nature Communications},
number = {1},
publisher = {Nature Publishing Group},
title = {{Crosstalk in concurrent repeated games impedes direct reciprocity and requires stronger levels of forgiveness}},
doi = {10.1038/s41467-017-02721-8},
volume = {9},
year = {2018},
}
@inproceedings{5679,
abstract = {We study the almost-sure termination problem for probabilistic programs. First, we show that supermartingales with lower bounds on conditional absolute difference provide a sound approach for the almost-sure termination problem. Moreover, using this approach we can obtain explicit optimal bounds on tail probabilities of non-termination within a given number of steps. Second, we present a new approach based on Central Limit Theorem for the almost-sure termination problem, and show that this approach can establish almost-sure termination of programs which none of the existing approaches can handle. Finally, we discuss algorithmic approaches for the two above methods that lead to automated analysis techniques for almost-sure termination of probabilistic programs.},
author = {Huang, Mingzhang and Fu, Hongfei and Chatterjee, Krishnendu},
editor = {Ryu, Sukyoung},
isbn = {9783030027674},
issn = {03029743},
location = {Wellington, New Zealand},
pages = {181--201},
publisher = {Springer},
title = {{New approaches for almost-sure termination of probabilistic programs}},
doi = {10.1007/978-3-030-02768-1_11},
volume = {11275},
year = {2018},
}
@article{5751,
abstract = {Because of the intrinsic randomness of the evolutionary process, a mutant with a fitness advantage has some chance to be selected but no certainty. Any experiment that searches for advantageous mutants will lose many of them due to random drift. It is therefore of great interest to find population structures that improve the odds of advantageous mutants. Such structures are called amplifiers of natural selection: they increase the probability that advantageous mutants are selected. Arbitrarily strong amplifiers guarantee the selection of advantageous mutants, even for very small fitness advantage. Despite intensive research over the past decade, arbitrarily strong amplifiers have remained rare. Here we show how to construct a large variety of them. Our amplifiers are so simple that they could be useful in biotechnology, when optimizing biological molecules, or as a diagnostic tool, when searching for faster dividing cells or viruses. They could also occur in natural population structures.},
author = {Pavlogiannis, Andreas and Tkadlec, Josef and Chatterjee, Krishnendu and Nowak, Martin A.},
issn = {2399-3642},
journal = {Communications Biology},
number = {1},
publisher = {Springer Nature},
title = {{Construction of arbitrarily strong amplifiers of natural selection using evolutionary graph theory}},
doi = {10.1038/s42003-018-0078-7},
volume = {1},
year = {2018},
}
@inbook{59,
abstract = {Graph-based games are an important tool in computer science. They have applications in synthesis, verification, refinement, and far beyond. We review graphbased games with objectives on infinite plays. We give definitions and algorithms to solve the games and to give a winning strategy. The objectives we consider are mostly Boolean, but we also look at quantitative graph-based games and their objectives. Synthesis aims to turn temporal logic specifications into correct reactive systems. We explain the reduction of synthesis to graph-based games (or equivalently tree automata) using synthesis of LTL specifications as an example. We treat the classical approach that uses determinization of parity automata and more modern approaches.},
author = {Bloem, Roderick and Chatterjee, Krishnendu and Jobstmann, Barbara},
booktitle = {Handbook of Model Checking},
editor = {Henzinger, Thomas A and Clarke, Edmund M. and Veith, Helmut and Bloem, Roderick},
isbn = {978-3-319-10574-1},
pages = {921 -- 962},
publisher = {Springer},
title = {{Graph games and reactive synthesis}},
doi = {10.1007/978-3-319-10575-8_27},
year = {2018},
}
@inproceedings{5967,
abstract = {The Big Match is a multi-stage two-player game. In each stage Player 1 hides one or two pebbles in his hand, and his opponent has to guess that number; Player 1 loses a point if Player 2 is correct, and otherwise he wins a point. As soon as Player 1 hides one pebble, the players cannot change their choices in any future stage.
Blackwell and Ferguson (1968) give an ε-optimal strategy for Player 1 that hides, in each stage, one pebble with a probability that depends on the entire past history. Any strategy that depends just on the clock or on a finite memory is worthless. The long-standing natural open problem has been whether every strategy that depends just on the clock and a finite memory is worthless. We prove that there is such a strategy that is ε-optimal. In fact, we show that just two states of memory are sufficient.
},
author = {Hansen, Kristoffer Arnsfelt and Ibsen-Jensen, Rasmus and Neyman, Abraham},
booktitle = {Proceedings of the 2018 ACM Conference on Economics and Computation - EC '18},
isbn = {9781450358293},
location = {Ithaca, NY, United States},
pages = {149--150},
publisher = {ACM Press},
title = {{The Big Match with a clock and a bit of memory}},
doi = {10.1145/3219166.3219198},
year = {2018},
}
@inproceedings{5977,
abstract = {We consider the stochastic shortest path (SSP)problem for succinct Markov decision processes(MDPs), where the MDP consists of a set of vari-ables, and a set of nondeterministic rules that up-date the variables. First, we show that several ex-amples from the AI literature can be modeled assuccinct MDPs. Then we present computationalapproaches for upper and lower bounds for theSSP problem: (a) for computing upper bounds, ourmethod is polynomial-time in the implicit descrip-tion of the MDP; (b) for lower bounds, we present apolynomial-time (in the size of the implicit descrip-tion) reduction to quadratic programming. Our ap-proach is applicable even to infinite-state MDPs.Finally, we present experimental results to demon-strate the effectiveness of our approach on severalclassical examples from the AI literature.},
author = {Chatterjee, Krishnendu and Fu, Hongfei and Goharshady, Amir and Okati, Nastaran},
booktitle = {Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence},
isbn = {978-099924112-7},
issn = {10450823},
location = {Stockholm, Sweden},
pages = {4700--4707},
publisher = {IJCAI},
title = {{Computational approaches for stochastic shortest path on succinct MDPs}},
doi = {10.24963/ijcai.2018/653},
volume = {2018},
year = {2018},
}
@article{5993,
abstract = {In this article, we consider the termination problem of probabilistic programs with real-valued variables. Thequestions concerned are: qualitative ones that ask (i) whether the program terminates with probability 1(almost-sure termination) and (ii) whether the expected termination time is finite (finite termination); andquantitative ones that ask (i) to approximate the expected termination time (expectation problem) and (ii) tocompute a boundBsuch that the probability not to terminate afterBsteps decreases exponentially (con-centration problem). To solve these questions, we utilize the notion of ranking supermartingales, which isa powerful approach for proving termination of probabilistic programs. In detail, we focus on algorithmicsynthesis of linear ranking-supermartingales over affine probabilistic programs (Apps) with both angelic anddemonic non-determinism. An important subclass of Apps is LRApp which is defined as the class of all Appsover which a linear ranking-supermartingale exists.Our main contributions are as follows. Firstly, we show that the membership problem of LRApp (i) canbe decided in polynomial time for Apps with at most demonic non-determinism, and (ii) isNP-hard and inPSPACEfor Apps with angelic non-determinism. Moreover, theNP-hardness result holds already for Appswithout probability and demonic non-determinism. Secondly, we show that the concentration problem overLRApp can be solved in the same complexity as for the membership problem of LRApp. Finally, we show thatthe expectation problem over LRApp can be solved in2EXPTIMEand isPSPACE-hard even for Apps withoutprobability and non-determinism (i.e., deterministic programs). Our experimental results demonstrate theeffectiveness of our approach to answer the qualitative and quantitative questions over Apps with at mostdemonic non-determinism.},
author = {Chatterjee, Krishnendu and Fu, Hongfei and Novotný, Petr and Hasheminezhad, Rouzbeh},
issn = {0164-0925},
journal = {ACM Transactions on Programming Languages and Systems},
number = {2},
publisher = {Association for Computing Machinery (ACM)},
title = {{Algorithmic analysis of qualitative and quantitative termination problems for affine probabilistic programs}},
doi = {10.1145/3174800},
volume = {40},
year = {2018},
}