@inproceedings{3316,
abstract = {In addition to being correct, a system should be robust, that is, it should behave reasonably even after receiving unexpected inputs. In this paper, we summarize two formal notions of robustness that we have introduced previously for reactive systems. One of the notions is based on assigning costs for failures on a user-provided notion of incorrect transitions in a specification. Here, we define a system to be robust if a finite number of incorrect inputs does not lead to an infinite number of incorrect outputs. We also give a more refined notion of robustness that aims to minimize the ratio of output failures to input failures. The second notion is aimed at liveness. In contrast to the previous notion, it has no concept of recovery from an error. Instead, it compares the ratio of the number of liveness constraints that the system violates to the number of liveness constraints that the environment violates.},
author = {Bloem, Roderick and Chatterjee, Krishnendu and Greimel, Karin and Henzinger, Thomas A and Jobstmann, Barbara},
booktitle = {6th IEEE International Symposium on Industrial and Embedded Systems},
location = {Vasteras, Sweden},
pages = {176 -- 185},
publisher = {IEEE},
title = {{Specification-centered robustness}},
doi = {10.1109/SIES.2011.5953660},
year = {2011},
}
@article{3318,
abstract = {Parvalbumin is thought to act in a manner similar to EGTA, but how a slow Ca2+ buffer affects nanodomain-coupling regimes at GABAergic synapses is unclear. Direct measurements of parvalbumin concentration and paired recordings in rodent hippocampus and cerebellum revealed that parvalbumin affects synaptic dynamics only when expressed at high levels. Modeling suggests that, in high concentrations, parvalbumin may exert BAPTA-like effects, modulating nanodomain coupling via competition with local saturation of endogenous fixed buffers.},
author = {Eggermann, Emmanuel and Jonas, Peter M},
journal = {Nature Neuroscience},
pages = {20 -- 22},
publisher = {Nature Publishing Group},
title = {{How the “slow” Ca(2+) buffer parvalbumin affects transmitter release in nanodomain coupling regimes at GABAergic synapses}},
doi = {10.1038/nn.3002},
volume = {15},
year = {2011},
}
@article{3320,
abstract = {Powerful statistical models that can be learned efficiently from large amounts of data are currently revolutionizing computer vision. These models possess a rich internal structure reflecting task-specific relations and constraints. This monograph introduces the reader to the most popular classes of structured models in computer vision. Our focus is discrete undirected graphical models which we cover in detail together with a description of algorithms for both probabilistic inference and maximum a posteriori inference. We discuss separately recently successful techniques for prediction in general structured models. In the second part of this monograph we describe methods for parameter learning where we distinguish the classic maximum likelihood based methods from the more recent prediction-based parameter learning methods. We highlight developments to enhance current models and discuss kernelized models and latent variable models. To make the monograph more practical and to provide links to further study we provide examples of successful application of many methods in the computer vision literature.},
author = {Nowozin, Sebastian and Lampert, Christoph},
journal = {Foundations and Trends in Computer Graphics and Vision},
number = {3-4},
pages = {185 -- 365},
publisher = {now},
title = {{Structured learning and prediction in computer vision}},
doi = {10.1561/0600000033},
volume = {6},
year = {2011},
}
@inproceedings{3324,
abstract = {Automated termination provers often use the following schema to prove that a program terminates: construct a relational abstraction of the program's transition relation and then show that the relational abstraction is well-founded. The focus of current tools has been on developing sophisticated techniques for constructing the abstractions while relying on known decidable logics (such as linear arithmetic) to express them. We believe we can significantly increase the class of programs that are amenable to automated termination proofs by identifying more expressive decidable logics for reasoning about well-founded relations. We therefore present a new decision procedure for reasoning about multiset orderings, which are among the most powerful orderings used to prove termination. We show that, using our decision procedure, one can automatically prove termination of natural abstractions of programs.},
author = {Piskac, Ruzica and Wies, Thomas},
editor = {Jhala, Ranjit and Schmidt, David},
location = {Texas, USA},
pages = {371 -- 386},
publisher = {Springer},
title = {{Decision procedures for automating termination proofs}},
doi = {10.1007/978-3-642-18275-4_26},
volume = {6538},
year = {2011},
}
@inproceedings{3326,
abstract = {Weighted automata map input words to numerical values. Ap- plications of weighted automata include formal verification of quantitative properties, as well as text, speech, and image processing. A weighted au- tomaton is defined with respect to a semiring. For the tropical semiring, the weight of a run is the sum of the weights of the transitions taken along the run, and the value of a word is the minimal weight of an accepting run on it. In the 90’s, Krob studied the decidability of problems on rational series defined with respect to the tropical semiring. Rational series are strongly related to weighted automata, and Krob’s results apply to them. In par- ticular, it follows from Krob’s results that the universality problem (that is, deciding whether the values of all words are below some threshold) is decidable for weighted automata defined with respect to the tropical semir- ing with domain ∪ {∞}, and that the equality problem is undecidable when the domain is ∪ {∞}. In this paper we continue the study of the borders of decidability in weighted automata, describe alternative and direct proofs of the above results, and tighten them further. Unlike the proofs of Krob, which are algebraic in their nature, our proofs stay in the terrain of state machines, and the reduction is from the halting problem of a two-counter machine. This enables us to significantly simplify Krob’s reasoning, make the un- decidability result accessible to the automata-theoretic community, and strengthen it to apply already to a very simple class of automata: all the states are accepting, there are no initial nor final weights, and all the weights on the transitions are from the set {−1, 0, 1}. The fact we work directly with the automata enables us to tighten also the decidability re- sults and to show that the universality problem for weighted automata defined with respect to the tropical semiring with domain ∪ {∞}, and in fact even with domain ≥0 ∪ {∞}, is PSPACE-complete. Our results thus draw a sharper picture about the decidability of decision problems for weighted automata, in both the front of containment vs. universality and the front of the ∪ {∞} vs. the ∪ {∞} domains.},
author = {Almagor, Shaull and Boker, Udi and Kupferman, Orna},
location = {Taipei, Taiwan},
pages = {482 -- 491},
publisher = {Springer},
title = {{What’s decidable about weighted automata }},
doi = {10.1007/978-3-642-24372-1_37},
volume = {6996},
year = {2011},
}
@inproceedings{3328,
abstract = {We report on a generic uni- and bivariate algebraic kernel that is publicly available with CGAL 3.7. It comprises complete, correct, though efficient state-of-the-art implementations on polynomials, roots of polynomial systems, and the support to analyze algebraic curves defined by bivariate polynomials. The kernel design is generic, that is, various number types and substeps can be exchanged. It is accompanied with a ready-to-use interface to enable arrangements induced by algebraic curves, that have already been used as basis for various geometric applications, as arrangements on Dupin cyclides or the triangulation of algebraic surfaces. We present two novel applications: arrangements of rotated algebraic curves and Boolean set operations on polygons bounded by segments of algebraic curves. We also provide experiments showing that our general implementation is competitive and even often clearly outperforms existing implementations that are explicitly tailored for specific types of non-linear curves that are available in CGAL.},
author = {Berberich, Eric and Hemmer, Michael and Kerber, Michael},
location = {Paris, France},
pages = {179 -- 186},
publisher = {ACM},
title = {{A generic algebraic kernel for non linear geometric applications}},
doi = {10.1145/1998196.1998224},
year = {2011},
}
@inproceedings{3329,
abstract = {We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance µ in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution shape P; then, P's offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(n log n)-time exact decision algorithm that handles any polygonal shape, assuming the real-RAM model of computation. An alternative algorithm, based purely on rational arithmetic, answers the same deconstruction problem, up to an uncertainty parameter, and its running time depends on the parameter δ (in addition to the other input parameters: n, δ and the radius of the disk). If the input shape is found to be approximable, the rational-arithmetic algorithm also computes an approximate solution shape for the problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution shape P with at most one more vertex than a vertex-minimal one. Our study is motivated by applications from two different domains. However, since the offset operation has numerous uses, we anticipate that the reverse question that we study here will be still more broadly applicable. We present results obtained with our implementation of the rational-arithmetic algorithm.},
author = {Berberich, Eric and Halperin, Dan and Kerber, Michael and Pogalnikova, Roza},
booktitle = {Proceedings of the twenty-seventh annual symposium on Computational geometry},
location = {Paris, France},
pages = {187 -- 196},
publisher = {ACM},
title = {{Deconstructing approximate offsets}},
doi = {10.1145/1998196.1998225},
year = {2011},
}
@inproceedings{3330,
abstract = {We consider the problem of approximating all real roots of a square-free polynomial f. Given isolating intervals, our algorithm refines each of them to a width at most 2-L, that is, each of the roots is approximated to L bits after the binary point. Our method provides a certified answer for arbitrary real polynomials, only requiring finite approximations of the polynomial coefficient and choosing a suitable working precision adaptively. In this way, we get a correct algorithm that is simple to implement and practically efficient. Our algorithm uses the quadratic interval refinement method; we adapt that method to be able to cope with inaccuracies when evaluating f, without sacrificing its quadratic convergence behavior. We prove a bound on the bit complexity of our algorithm in terms of degree, coefficient size and discriminant. Our bound improves previous work on integer polynomials by a factor of deg f and essentially matches best known theoretical bounds on root approximation which are obtained by very sophisticated algorithms.},
author = {Kerber, Michael and Sagraloff, Michael},
location = {California, USA},
pages = {209 -- 216},
publisher = {Springer},
title = {{Root refinement for real polynomials}},
doi = {10.1145/1993886.1993920},
year = {2011},
}
@article{3332,
abstract = {Given an algebraic hypersurface O in ℝd, how many simplices are necessary for a simplicial complex isotopic to O? We address this problem and the variant where all vertices of the complex must lie on O. We give asymptotically tight worst-case bounds for algebraic plane curves. Our results gradually improve known bounds in higher dimensions; however, the question for tight bounds remains unsolved for d ≥ 3.},
author = {Kerber, Michael and Sagraloff, Michael},
journal = {Graphs and Combinatorics},
number = {3},
pages = {419 -- 430},
publisher = {Springer},
title = {{A note on the complexity of real algebraic hypersurfaces}},
doi = {10.1007/s00373-011-1020-7},
volume = {27},
year = {2011},
}
@inbook{3335,
abstract = {We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology, they extend the information beyond conventional cosmological studies of topology in terms of genus and Euler characteristic. The richer information content of Betti numbers goes along the availability of fast algorithms to compute them. For continuous density fields, we determine the scale-dependence of Betti numbers by invoking the cosmologically familiar filtration of sublevel or superlevel sets defined by density thresholds. For the discrete galaxy distribution, however, the analysis is based on the alpha shapes of the particles. These simplicial complexes constitute an ordered sequence of nested subsets of the Delaunay tessellation, a filtration defined by the scale parameter, α. As they are homotopy equivalent to the sublevel sets of the distance field, they are an excellent tool for assessing the topological structure of a discrete point distribution. In order to develop an intuitive understanding for the behavior of Betti numbers as a function of α, and their relation to the morphological patterns in the Cosmic Web, we first study them within the context of simple heuristic Voronoi clustering models. These can be tuned to consist of specific morphological elements of the Cosmic Web, i.e. clusters, filaments, or sheets. To elucidate the relative prominence of the various Betti numbers in different stages of morphological evolution, we introduce the concept of alpha tracks. Subsequently, we address the topology of structures emerging in the standard LCDM scenario and in cosmological scenarios with alternative dark energy content. The evolution of the Betti numbers is shown to reflect the hierarchical evolution of the Cosmic Web. We also demonstrate that the scale-dependence of the Betti numbers yields a promising measure of cosmological parameters, with a potential to help in determining the nature of dark energy and to probe primordial non-Gaussianities. We also discuss the expected Betti numbers as a function of the density threshold for superlevel sets of a Gaussian random field. Finally, we introduce the concept of persistent homology. It measures scale levels of the mass distribution and allows us to separate small from large scale features. Within the context of the hierarchical cosmic structure formation, persistence provides a natural formalism for a multiscale topology study of the Cosmic Web.},
author = {Van De Weygaert, Rien and Vegter, Gert and Edelsbrunner, Herbert and Jones, Bernard and Pranav, Pratyush and Park, Changbom and Hellwing, Wojciech and Eldering, Bob and Kruithof, Nico and Bos, Patrick and Hidding, Johan and Feldbrugge, Job and Ten Have, Eline and Van Engelen, Matti and Caroli, Manuel and Teillaud, Monique},
booktitle = {Transactions on Computational Science XIV},
editor = {Gavrilova, Marina and Tan, Kenneth and Mostafavi, Mir},
pages = {60 -- 101},
publisher = {Springer},
title = {{Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web}},
doi = {10.1007/978-3-642-25249-5_3},
volume = {6970},
year = {2011},
}
@unpublished{3338,
abstract = {We consider 2-player games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves inde- pendently and simultaneously; the current state and the two moves determine the successor state. We study concurrent games with ω-regular winning conditions specified as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respec- tively. In general the almost-sure and limit-sure winning strategies require both infinite-memory as well as infinite-precision (to describe probabilities). We study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set for player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision or infinite- precision; and in terms of memory, strategies can be memoryless, finite-memory or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as power- ful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in O(n2d+3) time, where n is the size of the game structure and 2d is the number of priorities (or colors), and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP ∩ coNP. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms, that are obtained by characterization of the winning sets as μ-calculus formulas, are considerably more involved than those for turn-based games.},
author = {Chatterjee, Krishnendu},
booktitle = {arXiv},
pages = {1 -- 51},
publisher = {ArXiv},
title = {{Bounded rationality in concurrent parity games}},
year = {2011},
}
@unpublished{3339,
abstract = {Turn-based stochastic games and its important subclass Markov decision processes (MDPs) provide models for systems with both probabilistic and nondeterministic behaviors. We consider turn-based stochastic games with two classical quantitative objectives: discounted-sum and long-run average objectives. The game models and the quantitative objectives are widely used in probabilistic verification, planning, optimal inventory control, network protocol and performance analysis. Games and MDPs that model realistic systems often have very large state spaces, and probabilistic abstraction techniques are necessary to handle the state-space explosion. The commonly used full-abstraction techniques do not yield space-savings for systems that have many states with similar value, but does not necessarily have similar transition structure. A semi-abstraction technique, namely Magnifying-lens abstractions (MLA), that clusters states based on value only, disregarding differences in their transition relation was proposed for qualitative objectives (reachability and safety objectives). In this paper we extend the MLA technique to solve stochastic games with discounted-sum and long-run average objectives. We present the MLA technique based abstraction-refinement algorithm for stochastic games and MDPs with discounted-sum objectives. For long-run average objectives, our solution works for all MDPs and a sub-class of stochastic games where every state has the same value. },
author = {Chatterjee, Krishnendu and De Alfaro, Luca and Pritam, Roy},
booktitle = {arXiv},
pages = {17},
publisher = {ArXiv},
title = {{Magnifying lens abstraction for stochastic games with discounted and long-run average objectives}},
year = {2011},
}
@inproceedings{3342,
abstract = {We consider Markov decision processes (MDPs) with ω-regular specifications given as parity objectives. We consider the problem of computing the set of almost-sure winning states from where the objective can be ensured with probability 1. The algorithms for the computation of the almost-sure winning set for parity objectives iteratively use the solutions for the almost-sure winning set for Büchi objectives (a special case of parity objectives). Our contributions are as follows: First, we present the first subquadratic symbolic algorithm to compute the almost-sure winning set for MDPs with Büchi objectives; our algorithm takes O(nm) symbolic steps as compared to the previous known algorithm that takes O(n 2) symbolic steps, where n is the number of states and m is the number of edges of the MDP. In practice MDPs often have constant out-degree, and then our symbolic algorithm takes O(nn) symbolic steps, as compared to the previous known O(n 2) symbolic steps algorithm. Second, we present a new algorithm, namely win-lose algorithm, with the following two properties: (a) the algorithm iteratively computes subsets of the almost-sure winning set and its complement, as compared to all previous algorithms that discover the almost-sure winning set upon termination; and (b) requires O(nK) symbolic steps, where K is the maximal number of edges of strongly connected components (scc’s) of the MDP. The win-lose algorithm requires symbolic computation of scc’s. Third, we improve the algorithm for symbolic scc computation; the previous known algorithm takes linear symbolic steps, and our new algorithm improves the constants associated with the linear number of steps. In the worst case the previous known algorithm takes 5·n symbolic steps, whereas our new algorithm takes 4 ·n symbolic steps.},
author = {Chatterjee, Krishnendu and Henzinger, Monika and Joglekar, Manas and Nisarg, Shah},
editor = {Gopalakrishnan, Ganesh and Qadeer, Shaz},
location = {Snowbird, USA},
pages = {260 -- 276},
publisher = {Springer},
title = {{Symbolic algorithms for qualitative analysis of Markov decision processes with Büchi objectives}},
doi = {10.1007/978-3-642-22110-1_21},
volume = {6806},
year = {2011},
}
@inproceedings{3343,
abstract = {We present faster and dynamic algorithms for the following problems arising in probabilistic verification: Computation of the maximal end-component (mec) decomposition of Markov decision processes (MDPs), and of the almost sure winning set for reachability and parity objectives in MDPs. We achieve the following running time for static algorithms in MDPs with graphs of n vertices and m edges: (1) O(m · min{ √m, n2/3 }) for the mec decomposition, improving the longstanding O(m·n) bound; (2) O(m·n2/3) for reachability objectives, improving the previous O(m · √m) bound for m > n4/3; and (3) O(m · min{ √m, n2/3 } · log(d)) for parity objectives with d priorities, improving the previous O(m · √m · d) bound. We also give incremental and decremental algorithms in linear time for mec decomposition and reachability objectives and O(m · log d) time for parity ob jectives.},
author = {Chatterjee, Krishnendu and Henzinger, Monika},
location = {San Francisco, USA},
pages = {1318 -- 1336},
publisher = {SIAM},
title = {{Faster and dynamic algorithms for maximal end component decomposition and related graph problems in probabilistic verification}},
doi = {10.1137/1.9781611973082.101},
year = {2011},
}
@inproceedings{3345,
abstract = {We consider Markov Decision Processes (MDPs) with mean-payoff parity and energy parity objectives. In system design, the parity objective is used to encode ω-regular specifications, and the mean-payoff and energy objectives can be used to model quantitative resource constraints. The energy condition re- quires that the resource level never drops below 0, and the mean-payoff condi- tion requires that the limit-average value of the resource consumption is within a threshold. While these two (energy and mean-payoff) classical conditions are equivalent for two-player games, we show that they differ for MDPs. We show that the problem of deciding whether a state is almost-sure winning (i.e., winning with probability 1) in energy parity MDPs is in NP ∩ coNP, while for mean- payoff parity MDPs, the problem is solvable in polynomial time, improving a recent PSPACE bound.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
location = {Warsaw, Poland},
pages = {206 -- 218},
publisher = {Springer},
title = {{Energy and mean-payoff parity Markov Decision Processes}},
doi = {10.1007/978-3-642-22993-0_21},
volume = {6907},
year = {2011},
}
@inproceedings{3346,
abstract = {We study Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) functions. We consider two different objectives, namely, expectation and satisfaction objectives. Given an MDP with k reward functions, in the expectation objective the goal is to maximize the expected limit-average value, and in the satisfaction objective the goal is to maximize the probability of runs such that the limit-average value stays above a given vector. We show that under the expectation objective, in contrast to the single-objective case, both randomization and memory are necessary for strategies, and that finite-memory randomized strategies are sufficient. Under the satisfaction objective, in contrast to the single-objective case, infinite memory is necessary for strategies, and that randomized memoryless strategies are sufficient for epsilon-approximation, for all epsilon>;0. We further prove that the decision problems for both expectation and satisfaction objectives can be solved in polynomial time and the trade-off curve (Pareto curve) can be epsilon-approximated in time polynomial in the size of the MDP and 1/epsilon, and exponential in the number of reward functions, for all epsilon>;0. Our results also reveal flaws in previous work for MDPs with multiple mean-payoff functions under the expectation objective, correct the flaws and obtain improved results.},
author = {Brázdil, Tomáš and Brožek, Václav and Chatterjee, Krishnendu and Forejt, Vojtěch and Kučera, Antonín},
location = {Toronto, Canada},
publisher = {IEEE},
title = {{Two views on multiple mean payoff objectives in Markov Decision Processes}},
doi = {10.1109/LICS.2011.10},
year = {2011},
}
@inproceedings{3347,
abstract = {The class of omega-regular languages provides a robust specification language in verification. Every omega-regular condition can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens "eventually". Finitary liveness was proposed by Alur and Henzinger as a stronger formulation of liveness. It requires that there exists an unknown, fixed bound b such that something good happens within b transitions. In this work we consider automata with finitary acceptance conditions defined by finitary Buchi, parity and Streett languages. We study languages expressible by such automata: we give their topological complexity and present a regular-expression characterization. We compare the expressive power of finitary automata and give optimal algorithms for classical decisions questions. We show that the finitary languages are Sigma 2-complete; we present a complete picture of the expressive power of various classes of automata with finitary and infinitary acceptance conditions; we show that the languages defined by finitary parity automata exactly characterize the star-free fragment of omega B-regular languages; and we show that emptiness is NLOGSPACE-complete and universality as well as language inclusion are PSPACE-complete for finitary parity and Streett automata.},
author = {Chatterjee, Krishnendu and Fijalkow, Nathanaël},
location = {Tarragona, Spain},
pages = {216 -- 226},
publisher = {Springer},
title = {{Finitary languages}},
doi = {10.1007/978-3-642-21254-3_16},
volume = {6638},
year = {2011},
}
@inproceedings{3348,
abstract = {We study synthesis of controllers for real-time systems, where the objective is to stay in a given safe set. The problem is solved by obtaining winning strategies in the setting of concurrent two-player timed automaton games with safety objectives. To prevent a player from winning by blocking time, we restrict each player to strategies that ensure that the player cannot be responsible for causing a zeno run. We construct winning strategies for the controller which require access only to (1) the system clocks (thus, controllers which require their own internal infinitely precise clocks are not necessary), and (2) a linear (in the number of clocks) number of memory bits. Precisely, we show that for safety objectives, a memory of size (3 · |C|+lg(|C|+1)) bits suffices for winning controller strategies, where C is the set of clocks of the timed automaton game, significantly improving the previous known exponential bound. We also settle the open question of whether winning region controller strategies require memory for safety objectives by showing with an example the necessity of memory for region strategies to win for safety objectives.},
author = {Chatterjee, Krishnendu and Prabhu, Vinayak},
location = {Chicago, USA},
pages = {221 -- 230},
publisher = {Springer},
title = {{Synthesis of memory efficient real time controllers for safety objectives}},
doi = {10.1145/1967701.1967734},
year = {2011},
}
@inproceedings{3349,
abstract = {Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model various open systems in computer science, as for instance turn-based or concurrent moves, and deterministic or stochastic transitions. In this paper, we are interested in turn-based games, and specifically in deterministic parity games and stochastic reachability games (also known as simple stochastic games). We present a simple, direct and efficient reduction from deterministic parity games to simple stochastic games: it yields an arena whose size is linear up to a logarithmic factor in size of the original arena.},
author = {Chatterjee, Krishnendu and Fijalkow, Nathanaël},
location = {Minori, Italy},
pages = {74 -- 86},
publisher = {EPTCS},
title = {{A reduction from parity games to simple stochastic games}},
doi = {10.4204/EPTCS.54.6},
volume = {54},
year = {2011},
}
@inproceedings{3351,
abstract = {In two-player games on graph, the players construct an infinite path through the game graph and get a reward computed by a payoff function over infinite paths. Over weighted graphs, the typical and most studied payoff functions compute the limit-average or the discounted sum of the rewards along the path. Besides their simple definition, these two payoff functions enjoy the property that memoryless optimal strategies always exist. In an attempt to construct other simple payoff functions, we define a class of payoff functions which compute an (infinite) weighted average of the rewards. This new class contains both the limit-average and the discounted sum functions, and we show that they are the only members of this class which induce memoryless optimal strategies, showing that there is essentially no other simple payoff functions.},
author = {Chatterjee, Krishnendu and Doyen, Laurent and Singh, Rohit},
editor = {Owe, Olaf and Steffen, Martin and Telle, Jan Arne},
location = {Oslo, Norway},
pages = {148 -- 159},
publisher = {Springer},
title = {{On memoryless quantitative objectives}},
doi = {10.1007/978-3-642-22953-4_13},
volume = {6914},
year = {2011},
}