TY - JOUR
AB - Social dilemmas occur when incentives for individuals are misaligned with group interests 1-7 . According to the 'tragedy of the commons', these misalignments can lead to overexploitation and collapse of public resources. The resulting behaviours can be analysed with the tools of game theory 8 . The theory of direct reciprocity 9-15 suggests that repeated interactions can alleviate such dilemmas, but previous work has assumed that the public resource remains constant over time. Here we introduce the idea that the public resource is instead changeable and depends on the strategic choices of individuals. An intuitive scenario is that cooperation increases the public resource, whereas defection decreases it. Thus, cooperation allows the possibility of playing a more valuable game with higher payoffs, whereas defection leads to a less valuable game. We analyse this idea using the theory of stochastic games 16-19 and evolutionary game theory. We find that the dependence of the public resource on previous interactions can greatly enhance the propensity for cooperation. For these results, the interaction between reciprocity and payoff feedback is crucial: neither repeated interactions in a constant environment nor single interactions in a changing environment yield similar cooperation rates. Our framework shows which feedbacks between exploitation and environment - either naturally occurring or designed - help to overcome social dilemmas.
AU - Hilbe, Christian
AU - Šimsa, Štepán
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 157
IS - 7713
JF - Nature
TI - Evolution of cooperation in stochastic games
VL - 559
ER -
TY - JOUR
AB - 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.
AU - Hilbe, Christian
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 419
JF - Nature Human Behaviour
TI - Partners and rivals in direct reciprocity
VL - 2
ER -
TY - JOUR
AB - 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.
AU - Reiter, Johannes
AU - Hilbe, Christian
AU - Rand, David
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 454
IS - 1
JF - Nature Communications
TI - Crosstalk in concurrent repeated games impedes direct reciprocity and requires stronger levels of forgiveness
VL - 9
ER -
TY - CONF
AB - A model of computation that is widely used in the formal analysis of reactive systems is symbolic algorithms. In this model the access to the input graph is restricted to consist of symbolic operations, which are expensive in comparison to the standard RAM operations. We give lower bounds on the number of symbolic operations for basic graph problems such as the computation of the strongly connected components and of the approximate diameter as well as for fundamental problems in model checking such as safety, liveness, and coliveness. Our lower bounds are linear in the number of vertices of the graph, even for constant-diameter graphs. For none of these problems lower bounds on the number of symbolic operations were known before. The lower bounds show an interesting separation of these problems from the reachability problem, which can be solved with O(D) symbolic operations, where D is the diameter of the graph. Additionally we present an approximation algorithm for the graph diameter which requires Õ(n/D) symbolic steps to achieve a (1 +ϵ)-approximation for any constant > 0. This compares to O(n/D) symbolic steps for the (naive) exact algorithm and O(D) symbolic steps for a 2-approximation. Finally we also give a refined analysis of the strongly connected components algorithms of [15], showing that it uses an optimal number of symbolic steps that is proportional to the sum of the diameters of the strongly connected components.
AU - Chatterjee, Krishnendu
AU - Dvorák, Wolfgang
AU - Henzinger, Monika
AU - Loitzenbauer, Veronika
ID - 310
TI - Lower bounds for symbolic computation on graphs: Strongly connected components, liveness, safety and diameter
ER -
TY - CONF
AB - Probabilistic programs extend classical imperative programs with real-valued random variables and random branching. The most basic liveness property for such programs is the termination property. The qualitative (aka almost-sure) termination problem asks whether a given program program terminates with probability 1. While ranking functions provide a sound and complete method for non-probabilistic programs, the extension of them to probabilistic programs is achieved via ranking supermartingales (RSMs). Although deep theoretical results have been established about RSMs, their application to probabilistic programs with nondeterminism has been limited only to programs of restricted control-flow structure. For non-probabilistic programs, lexicographic ranking functions provide a compositional and practical approach for termination analysis of real-world programs. In this work we introduce lexicographic RSMs and show that they present a sound method for almost-sure termination of probabilistic programs with nondeterminism. We show that lexicographic RSMs provide a tool for compositional reasoning about almost-sure termination, and for probabilistic programs with linear arithmetic they can be synthesized efficiently (in polynomial time). We also show that with additional restrictions even asymptotic bounds on expected termination time can be obtained through lexicographic RSMs. Finally, we present experimental results on benchmarks adapted from previous work to demonstrate the effectiveness of our approach.
AU - Agrawal, Sheshansh
AU - Chatterjee, Krishnendu
AU - Novotny, Petr
ID - 325
IS - POPL
TI - Lexicographic ranking supermartingales: an efficient approach to termination of probabilistic programs
VL - 2
ER -
TY - CONF
AB - Partially observable Markov decision processes (POMDPs) are widely used in probabilistic planning problems in which an agent interacts with an environment using noisy and imprecise sensors. We study a setting in which the sensors are only partially defined and the goal is to synthesize “weakest” additional sensors, such that in the resulting POMDP, there is a small-memory policy for the agent that almost-surely (with probability 1) satisfies a reachability objective. We show that the problem is NP-complete, and present a symbolic algorithm by encoding the problem into SAT instances. We illustrate trade-offs between the amount of memory of the policy and the number of additional sensors on a simple example. We have implemented our approach and consider three classical POMDP examples from the literature, and show that in all the examples the number of sensors can be significantly decreased (as compared to the existing solutions in the literature) without increasing the complexity of the policies.
AU - Chatterjee, Krishnendu
AU - Chemlík, Martin
AU - Topcu, Ufuk
ID - 34
TI - Sensor synthesis for POMDPs with reachability objectives
VL - 2018
ER -
TY - CONF
AB - We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an adversarial environment. We consider two planning problems where there are k different target sets, and the problems are as follows: (a) the coverage problem asks whether there is a plan for each individual target set; and (b) the sequential target reachability problem asks whether the targets can be reached in sequence. For the coverage problem, we present a linear-time algorithm for graphs, and quadratic conditional lower bound for MDPs and games on graphs. For the sequential target problem, we present a linear-time algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic conditional lower bound for games on graphs. Our results with conditional lower bounds establish (i) model-separation results showing that for the coverage problem MDPs and games on graphs are harder than graphs and for the sequential reachability problem games on graphs are harder than MDPs and graphs; and (ii) objective-separation results showing that for MDPs the coverage problem is harder than the sequential target problem.
AU - Chatterjee, Krishnendu
AU - Dvorák, Wolfgang
AU - Henzinger, Monika
AU - Svozil, Alexander
ID - 35
T2 - 28th International Conference on Automated Planning and Scheduling
TI - Algorithms and conditional lower bounds for planning problems
ER -
TY - CONF
AB - We present a secure approach for maintaining andreporting credit history records on the Blockchain. Our ap-proach removes third-parties such as credit reporting agen-cies from the lending process and replaces them with smartcontracts. This allows customers to interact directly with thelenders or banks while ensuring the integrity, unmalleabilityand privacy of their credit data. Additionally, each customerhas full control over complete or selective disclosure of hercredit records, eliminating the risk of privacy violations or databreaches. Moreover, our approach provides strong guaranteesfor the lenders as well. A lender can check both correctness andcompleteness of the credit data disclosed to her. This is the firstapproach that can perform all credit reporting tasks withouta central authority or changing the financial mechanisms*.
AU - Goharshady, Amir Kafshdar
AU - Behrouz, Ali
AU - Chatterjee, Krishnendu
ID - 6340
SN - 978-1-5386-7975-3
T2 - Proceedings of the IEEE International Conference on Blockchain
TI - Secure Credit Reporting on the Blockchain
ER -
TY - JOUR
AB - We study algorithmic questions wrt algebraic path properties in concurrent systems, where the transitions of the system are labeled from a complete, closed semiring. 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 Kafshdar
AU - Pavlogiannis, Andreas
ID - 6009
IS - 3
JF - ACM Transactions on Programming Languages and Systems
SN - 0164-0925
TI - Algorithms for algebraic path properties in concurrent systems of constant treewidth components
VL - 40
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Fu, Hongfei
AU - Goharshady, Amir
AU - Okati, Nastaran
ID - 5977
SN - 10450823
T2 - Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
TI - Computational approaches for stochastic shortest path on succinct MDPs
VL - 2018
ER -
TY - CONF
AB - Crypto-currencies are digital assets designed to work as a medium of exchange, e.g., Bitcoin, but they are susceptible to attacks (dishonest behavior of participants). A framework for the analysis of attacks in crypto-currencies requires (a) modeling of game-theoretic aspects to analyze incentives for deviation from honest behavior; (b) concurrent interactions between participants; and (c) analysis of long-term monetary gains. Traditional game-theoretic approaches for the analysis of security protocols consider either qualitative temporal properties such as safety and termination, or the very special class of one-shot (stateless) games. However, to analyze general attacks on protocols for crypto-currencies, both stateful analysis and quantitative objectives are necessary. In this work our main contributions are as follows: (a) we show how a class of concurrent mean-payo games, namely ergodic games, can model various attacks that arise naturally in crypto-currencies; (b) we present the first practical implementation of algorithms for ergodic games that scales to model realistic problems for crypto-currencies; and (c) we present experimental results showing that our framework can handle games with thousands of states and millions of transitions.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir
AU - Ibsen-Jensen, Rasmus
AU - Velner, Yaron
ID - 66
SN - 978-3-95977-087-3
TI - Ergodic mean-payoff games for the analysis of attacks in crypto-currencies
VL - 118
ER -
TY - CONF
AB - Smart contracts are computer programs that are executed by a network of mutually distrusting agents, without the need of an external trusted authority. Smart contracts handle and transfer assets of considerable value (in the form of crypto-currency like Bitcoin). Hence, it is crucial that their implementation is bug-free. We identify the utility (or expected payoff) of interacting with such smart contracts as the basic and canonical quantitative property for such contracts. We present a framework for such quantitative analysis of smart contracts. Such a formal framework poses new and novel research challenges in programming languages, as it requires modeling of game-theoretic aspects to analyze incentives for deviation from honest behavior and modeling utilities which are not specified as standard temporal properties such as safety and termination. While game-theoretic incentives have been analyzed in the security community, their analysis has been restricted to the very special case of stateless games. However, to analyze smart contracts, stateful analysis is required as it must account for the different program states of the protocol. Our main contributions are as follows: we present (i)~a simplified programming language for smart contracts; (ii)~an automatic translation of the programs to state-based games; (iii)~an abstraction-refinement approach to solve such games; and (iv)~experimental results on real-world-inspired smart contracts.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir
AU - Velner, Yaron
ID - 311
TI - Quantitative analysis of smart contracts
VL - 10801
ER -
TY - THES
AB - This dissertation focuses on algorithmic aspects of program verification, and presents modeling and complexity advances on several problems related to the
static analysis of programs, the stateless model checking of concurrent programs, and the competitive analysis of real-time scheduling algorithms.
Our contributions can be broadly grouped into five categories.
Our first contribution is a set of new algorithms and data structures for the quantitative and data-flow analysis of programs, based on the graph-theoretic notion of treewidth.
It has been observed that the control-flow graphs of typical programs have special structure, and are characterized as graphs of small treewidth.
We utilize this structural property to provide faster algorithms for the quantitative and data-flow analysis of recursive and concurrent programs.
In most cases we make an algebraic treatment of the considered problem,
where several interesting analyses, such as the reachability, shortest path, and certain kind of data-flow analysis problems follow as special cases.
We exploit the constant-treewidth property to obtain algorithmic improvements for on-demand versions of the problems,
and provide data structures with various tradeoffs between the resources spent in the preprocessing and querying phase.
We also improve on the algorithmic complexity of quantitative problems outside the algebraic path framework,
namely of the minimum mean-payoff, minimum ratio, and minimum initial credit for energy problems.
Our second contribution is a set of algorithms for Dyck reachability with applications to data-dependence analysis and alias analysis.
In particular, we develop an optimal algorithm for Dyck reachability on bidirected graphs, which are ubiquitous in context-insensitive, field-sensitive points-to analysis.
Additionally, we develop an efficient algorithm for context-sensitive data-dependence analysis via Dyck reachability,
where the task is to obtain analysis summaries of library code in the presence of callbacks.
Our algorithm preprocesses libraries in almost linear time, after which the contribution of the library in the complexity of the client analysis is (i)~linear in the number of call sites and (ii)~only logarithmic in the size of the whole library, as opposed to linear in the size of the whole library.
Finally, we prove that Dyck reachability is Boolean Matrix Multiplication-hard in general, and the hardness also holds for graphs of constant treewidth.
This hardness result strongly indicates that there exist no combinatorial algorithms for Dyck reachability with truly subcubic complexity.
Our third contribution is the formalization and algorithmic treatment of the Quantitative Interprocedural Analysis framework.
In this framework, the transitions of a recursive program are annotated as good, bad or neutral, and receive a weight which measures
the magnitude of their respective effect.
The Quantitative Interprocedural Analysis problem asks to determine whether there exists an infinite run of the program where the long-run ratio of the bad weights over the good weights is above a given threshold.
We illustrate how several quantitative problems related to static analysis of recursive programs can be instantiated in this framework,
and present some case studies to this direction.
Our fourth contribution is a new dynamic partial-order reduction for the stateless model checking of concurrent programs. Traditional approaches rely on the standard Mazurkiewicz equivalence between traces, by means of partitioning the trace space into equivalence classes, and attempting to explore a few representatives from each class.
We present a new dynamic partial-order reduction method called the Data-centric Partial Order Reduction (DC-DPOR).
Our algorithm is based on a new equivalence between traces, called the observation equivalence.
DC-DPOR explores a coarser partitioning of the trace space than any exploration method based on the standard Mazurkiewicz equivalence.
Depending on the program, the new partitioning can be even exponentially coarser.
Additionally, DC-DPOR spends only polynomial time in each explored class.
Our fifth contribution is the use of automata and game-theoretic verification techniques in the competitive analysis and synthesis of real-time scheduling algorithms for firm-deadline tasks.
On the analysis side, we leverage automata on infinite words to compute the competitive ratio of real-time schedulers subject to various environmental constraints.
On the synthesis side, we introduce a new instance of two-player mean-payoff partial-information games, and show
how the synthesis of an optimal real-time scheduler can be reduced to computing winning strategies in this new type of games.
AU - Pavlogiannis, Andreas
ID - 821
TI - Algorithmic advances in program analysis and their applications
ER -
TY - JOUR
AB - Two-player games on graphs are central in many problems in formal verification and program analysis, such as synthesis and verification of open systems. In this work, we consider solving recursive game graphs (or pushdown game graphs) that model the control flow of sequential programs with recursion.While pushdown games have been studied before with qualitative objectives-such as reachability and ?-regular objectives- in this work, we study for the first time such games with the most well-studied quantitative objective, the mean-payoff objective. In pushdown games, two types of strategies are relevant: (1) global strategies, which depend on the entire global history; and (2) modular strategies, which have only local memory and thus do not depend on the context of invocation but rather only on the history of the current invocation of the module. Our main results are as follows: (1) One-player pushdown games with mean-payoff objectives under global strategies are decidable in polynomial time. (2) Two-player pushdown games with mean-payoff objectives under global strategies are undecidable. (3) One-player pushdown games with mean-payoff objectives under modular strategies are NP-hard. (4) Two-player pushdown games with mean-payoff objectives under modular strategies can be solved in NP (i.e., both one-player and two-player pushdown games with mean-payoff objectives under modular strategies are NP-complete). We also establish the optimal strategy complexity by showing that global strategies for mean-payoff objectives require infinite memory even in one-player pushdown games and memoryless modular strategies are sufficient in two-player pushdown games. Finally, we also show that all the problems have the same complexity if the stack boundedness condition is added, where along with the mean-payoff objective the player must also ensure that the stack height is bounded.
AU - Chatterjee, Krishnendu
AU - Velner, Yaron
ID - 716
IS - 5
JF - Journal of the ACM
SN - 00045411
TI - The complexity of mean-payoff pushdown games
VL - 64
ER -
TY - JOUR
AB - We consider finite-state and recursive game graphs with multidimensional mean-payoff objectives. In recursive games two types of strategies are relevant: global strategies and modular strategies. Our contributions are: (1) We show that finite-state multidimensional mean-payoff games can be solved in polynomial time if the number of dimensions and the maximal absolute value of weights are fixed; whereas for arbitrary dimensions the problem is coNP-complete. (2) We show that one-player recursive games with multidimensional mean-payoff objectives can be solved in polynomial time. Both above algorithms are based on hyperplane separation technique. (3) For recursive games we show that under modular strategies the multidimensional problem is undecidable. We show that if the number of modules, exits, and the maximal absolute value of the weights are fixed, then one-dimensional recursive mean-payoff games under modular strategies can be solved in polynomial time, whereas for unbounded number of exits or modules the problem is NP-hard.
AU - Chatterjee, Krishnendu
AU - Velner, Yaron
ID - 717
JF - Journal of Computer and System Sciences
TI - Hyperplane separation technique for multidimensional mean-payoff games
VL - 88
ER -
TY - JOUR
AB - The ubiquity of computation in modern machines and devices imposes a need to assert the correctness of their behavior. Especially in the case of safety-critical systems, their designers need to take measures that enforce their safe operation. Formal methods has emerged as a research field that addresses this challenge: by rigorously proving that all system executions adhere to their specifications, the correctness of an implementation under concern can be assured. To achieve this goal, a plethora of techniques are nowadays available, all of which are optimized for different system types and application domains.
AU - Chatterjee, Krishnendu
AU - Ehlers, Rüdiger
ID - 719
IS - 6
JF - Acta Informatica
SN - 00015903
TI - Special issue: Synthesis and SYNT 2014
VL - 54
ER -
TY - JOUR
AB - In evolutionary game theory interactions between individuals are often assumed obligatory. However, in many real-life situations, individuals can decide to opt out of an interaction depending on the information they have about the opponent. We consider a simple evolutionary game theoretic model to study such a scenario, where at each encounter between two individuals the type of the opponent (cooperator/defector) is known with some probability, and where each individual either accepts or opts out of the interaction. If the type of the opponent is unknown, a trustful individual accepts the interaction, whereas a suspicious individual opts out of the interaction. If either of the two individuals opt out both individuals remain without an interaction. We show that in the prisoners dilemma optional interactions along with suspicious behaviour facilitates the emergence of trustful cooperation.
AU - Priklopil, Tadeas
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 744
JF - Journal of Theoretical Biology
SN - 00225193
TI - Optional interactions and suspicious behaviour facilitates trustful cooperation in prisoners dilemma
VL - 433
ER -
TY - JOUR
AB - The computation of the winning set for parity objectives and for Streett objectives in 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-formedness of specifications, and the synthesis of reactive systems. We show how to compute the winning set on n vertices for (1) parity-3 (aka one-pair Streett) objectives in game graphs in time O(n5/2) and for (2) k-pair Streett objectives in graphs in time O(n2+nklogn). For both problems this gives faster algorithms for dense graphs and represents the first improvement in asymptotic running time in 15 years.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
AU - Loitzenbauer, Veronika
ID - 464
IS - 3
JF - Logical Methods in Computer Science
SN - 18605974
TI - Improved algorithms for parity and Streett objectives
VL - 13
ER -
TY - JOUR
AB - The edit distance between two words w 1 , w 2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w 1 to w 2 . The edit distance generalizes to languages L 1 , L 2 , where the edit distance from L 1 to L 2 is the minimal number k such that for every word from L 1 there exists a word in L 2 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 the following problems: (1) deciding whether, for a given threshold k , the edit distance from a pushdown automaton to a finite automaton is at most k , and (2) deciding whether the edit distance from a pushdown automaton to a finite automaton is finite.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Ibsen-Jensen, Rasmus
AU - Otop, Jan
ID - 465
IS - 3
JF - Logical Methods in Computer Science
SN - 18605974
TI - Edit distance for pushdown automata
VL - 13
ER -
TY - JOUR
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 - Křetínská, Zuzana
AU - Kretinsky, Jan
ID - 466
IS - 2
JF - Logical Methods in Computer Science
SN - 18605974
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
VL - 13
ER -