@inproceedings{3839, abstract = {We present a loop property generation method for loops iterating over multi-dimensional arrays. When used on matrices, our method is able to infer their shapes (also called types), such as upper-triangular, diagonal, etc. To gen- erate loop properties, we first transform a nested loop iterating over a multi- dimensional array into an equivalent collection of unnested loops. Then, we in- fer quantified loop invariants for each unnested loop using a generalization of a recurrence-based invariant generation technique. These loop invariants give us conditions on matrices from which we can derive matrix types automatically us- ing theorem provers. Invariant generation is implemented in the software package Aligator and types are derived by theorem provers and SMT solvers, including Vampire and Z3. When run on the Java matrix package JAMA, our tool was able to infer automatically all matrix types describing the matrix shapes guaranteed by JAMA’s API.}, author = {Henzinger, Thomas A and Hottelier, Thibaud and Kovács, Laura and Voronkov, Andrei}, location = {Madrid, Spain}, pages = {163 -- 179}, publisher = {Springer}, title = {{Invariant and type inference for matrices}}, doi = {10.1007/978-3-642-11319-2_14}, volume = {5944}, year = {2010}, } @inproceedings{3840, abstract = {Classical formalizations of systems and properties are boolean: given a system and a property, the property is either true or false of the system. Correspondingly, classical methods for system analysis determine the truth value of a property, preferably giving a proof if the property is true, and a counterexample if the property is false; classical methods for system synthesis construct a system for which a property is true; classical methods for system transformation, composition, and abstraction aim to preserve the truth of properties. The boolean view is prevalent even if the system, the property, or both refer to numerical quantities, such as the times or probabilities of events. For example, a timed automaton either satisfies or violates a formula of a real-time logic; a stochastic process either satisfies or violates a formula of a probabilistic logic. The classical black-and-white view partitions the world into "correct" and "incorrect" systems, offering few nuances. In reality, of several systems that satisfy a property in the boolean sense, often some are more desirable than others, and of the many systems that violate a property, usually some are less objectionable than others. For instance, among the systems that satisfy the response property that every request be granted, we may prefer systems that grant requests quickly (the quicker, the better), or we may prefer systems that issue few unnecessary grants (the fewer, the better); and among the systems that violate the response property, we may prefer systems that serve many initial requests (the more, the better), or we may prefer systems that serve many requests in the long run (the greater the fraction of served to unserved requests, the better). Formally, while a boolean notion of correctness is given by a preorder on systems and properties, a quantitative notion of correctness is defined by a directed metric on systems and properties, where the distance between a system and a property provides a measure of "fit" or "desirability." There are many ways how such distances can be defined. In a linear-time framework, one assigns numerical values to individual behaviors before assigning values to systems and properties, which are sets of behaviors. For example, the value of a single behavior may be a discounted value, which is largely determined by a prefix of the behavior, e.g., by the number of requests that are granted before the first request that is not granted; or a limit value, which is independent of any finite prefix. A limit value may be an average, such as the average response time over an infinite sequence of requests and grants, or a supremum, such as the worst-case response time. Similarly, the value of a set of behaviors may be an extremum or an average across the values of all behaviors in the set: in this way one can measure the worst of all possible average-case response times, or the average of all possible worst-case response times, etc. Accordingly, the distance between two sets of behaviors may be defined as the worst or average difference between the values of corresponding behaviors. In summary, we propagate replacing boolean specifications for the correctness of systems with quantitative measures for the desirability of systems. In quantitative analysis, the aim is to compute the distance between a system and a property (or between two systems, or two properties); in quantitative synthesis, the objective is to construct a system that has minimal distance from a given property. Multiple quantitative measures can be prioritized (e.g., combined lexicographically into a single measure) or studied along the Pareto curve. Quantitative transformations, compositions, and abstractions of systems are useful if they allow us to bound the induced change in distance from a property. We present some initial results in some of these directions. We also give some potential applications, which not only generalize tradiditional correctness concerns in the functional, timed, and probabilistic domains, but also capture such system measures as resource use, performance, cost, reliability, and robustness.}, author = {Henzinger, Thomas A}, location = {Madrid, Spain}, number = {1}, pages = {157 -- 158}, publisher = {ACM}, title = {{From boolean to quantitative notions of correctness}}, doi = {10.1145/1706299.1706319}, volume = {45}, year = {2010}, } @article{3842, abstract = {Within systems biology there is an increasing interest in the stochastic behavior of biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous-time Markov chain (CTMC). The uniformization technique is an efficient method to compute probability distributions of a CTMC if the number of states is manageable. However, the size of a CTMC that represents a biochemical reaction network is usually far beyond what is feasible. In this paper we present an on-the-fly variant of uniformization, where we improve the original algorithm at the cost of a small approximation error. By means of several examples, we show that our approach is particularly well-suited for biochemical reaction networks.}, author = {Didier, Frédéric and Henzinger, Thomas A and Mateescu, Maria and Wolf, Verena}, journal = {IET Systems Biology}, number = {6}, pages = {441 -- 452}, publisher = {Institution of Engineering and Technology}, title = {{Fast adaptive uniformization of the chemical master equation}}, doi = {10.1049/iet-syb.2010.0005}, volume = {4}, year = {2010}, } @inproceedings{3845, abstract = {This paper presents Aligators, a tool for the generation of universally quantified array invariants. Aligators leverages recurrence solving and algebraic techniques to carry out inductive reasoning over array content. The Aligators’ loop extraction module allows treatment of multi-path loops by exploiting their commutativity and serializability properties. Our experience in applying Aligators on a collection of loops from open source software projects indicates the applicability of recurrence and algebraic solving techniques for reasoning about arrays.}, author = {Henzinger, Thomas A and Hottelier, Thibaud and Kovács, Laura and Rybalchenko, Andrey}, location = {Yogyakarta, Indonesia}, pages = {348 -- 356}, publisher = {Springer}, title = {{Aligators for arrays}}, doi = {10.1007/978-3-642-16242-8_25}, volume = {6397}, year = {2010}, } @inproceedings{3847, abstract = {The importance of stochasticity within biological systems has been shown repeatedly during the last years and has raised the need for efficient stochastic tools. We present SABRE, a tool for stochastic analysis of biochemical reaction networks. SABRE implements fast adaptive uniformization (FAU), a direct numerical approximation algorithm for computing transient solutions of biochemical reaction networks. Biochemical reactions networks represent biological systems studied at a molecular level and these reactions can be modeled as transitions of a Markov chain. SABRE accepts as input the formalism of guarded commands, which it interprets either as continuous-time or as discrete-time Markov chains. Besides operating in a stochastic mode, SABRE may also perform a deterministic analysis by directly computing a mean-field approximation of the system under study. We illustrate the different functionalities of SABRE by means of biological case studies.}, author = {Didier, Frédéric and Henzinger, Thomas A and Mateescu, Maria and Wolf, Verena}, location = {Williamsburg, USA}, pages = {193 -- 194}, publisher = {IEEE}, title = {{SABRE: A tool for the stochastic analysis of biochemical reaction networks}}, doi = {10.1109/QEST.2010.33}, year = {2010}, } @inproceedings{3848, abstract = {We define the robustness of a level set homology class of a function f:XR as the magnitude of a perturbation necessary to kill the class. Casting this notion into a group theoretic framework, we compute the robustness for each class, using a connection to extended persistent homology. The special case X=R3 has ramifications in medical imaging and scientific visualization.}, author = {Bendich, Paul and Edelsbrunner, Herbert and Morozov, Dmitriy and Patel, Amit}, location = {Liverpool, UK}, pages = {1 -- 10}, publisher = {Springer}, title = {{The robustness of level sets}}, doi = {10.1007/978-3-642-15775-2_1}, volume = {6346}, year = {2010}, } @inproceedings{3849, abstract = {Using ideas from persistent homology, the robustness of a level set of a real-valued function is defined in terms of the magnitude of the perturbation necessary to kill the classes. Prior work has shown that the homology and robustness information can be read off the extended persistence diagram of the function. This paper extends these results to a non-uniform error model in which perturbations vary in their magnitude across the domain.}, author = {Bendich, Paul and Edelsbrunner, Herbert and Kerber, Michael and Patel, Amit}, location = {Brno, Czech Republic}, pages = {12 -- 23}, publisher = {Springer}, title = {{Persistent homology under non-uniform error}}, doi = {10.1007/978-3-642-15155-2_2}, volume = {6281}, year = {2010}, } @article{385, abstract = {Scanning tunneling spectroscopy studies on high-quality Bi2Te3 crystals exhibit perfect correspondence to angle-resolved photoemission spectroscopy data, hence enabling identification of different regimes measured in the local density of states (LDOS). Oscillations of LDOS near a step are analyzed. Within the main part of the surface band oscillations are strongly damped, supporting the hypothesis of topological protection. At higher energies, as the surface band becomes concave, oscillations appear, dispersing with a wave vector that may result from a hexagonal warping term. }, author = {Alpichshev, Zhanybek and Analytis, James and Chu, Jiunhaw and Fisher, Ian and Chen, Yulin and Shen, Zhixun and Fang, Aiping and Kapitulnik, Aharon}, journal = {Physical Review Letters}, number = {1}, publisher = {American Physical Society}, title = {{STM imaging of electronic waves on the surface of Bi2Te3 Topologically protected surface states and hexagonal warping effects}}, doi = {10.1103/PhysRevLett.104.016401}, volume = {104}, year = {2010}, } @inproceedings{3850, abstract = {Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance ε in Hausdorff distance, as the Minkowski sum of another polygonal shape with a disk of fixed radius? If it does, we also seek a preferably simple solution shape P;P’s offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give a decision algorithm for fixed radius in O(nlogn) time that handles any polygonal shape. For convex shapes, the complexity 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.}, author = {Berberich, Eric and Halperin, Dan and Kerber, Michael and Pogalnikova, Roza}, location = {Dortmund, Germany}, pages = {12 -- 23}, publisher = {TU Dortmund}, title = {{Polygonal reconstruction from approximate offsets}}, year = {2010}, } @inproceedings{3851, abstract = {Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of energy in the game) must remain positive. Beside their own interest in the design and synthesis of resource-constrained omega-regular specifications, energy parity games provide one of the simplest model of games with combined qualitative and quantitative objective. Our main results are as follows: (a) exponential memory is sufficient and may be necessary for winning strategies in energy parity games; (b) the problem of deciding the winner in energy parity games can be solved in NP ∩ coNP; and (c) we give an algorithm to solve energy parity by reduction to energy games. We also show that the problem of deciding the winner in energy parity games is polynomially equivalent to the problem of deciding the winner in mean-payoff parity games, which can thus be solved in NP ∩ coNP. As a consequence we also obtain a conceptually simple algorithm to solve mean-payoff parity games.}, author = {Chatterjee, Krishnendu and Doyen, Laurent}, location = {Bordeaux, France}, pages = {599 -- 610}, publisher = {Springer}, title = {{Energy parity games}}, doi = {10.1007/978-3-642-14162-1_50}, volume = {6199}, year = {2010}, } @inproceedings{3852, abstract = {We introduce two-level discounted games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted game and the lower level game is an undiscounted reachability game. Two-level games model hierarchical and sequential decision making under uncertainty across different time scales. We show the existence of pure memoryless optimal strategies for both players and an ordered field property for such games. We show that if there is only one player (Markov decision processes), then the values can be computed in polynomial time. It follows that whether the value of a player is equal to a given rational constant in two-level discounted games can be decided in NP intersected coNP. We also give an alternate strategy improvement algorithm to compute the value. }, author = {Chatterjee, Krishnendu and Majumdar, Ritankar}, location = {Minori, Italy}, pages = {22 -- 29}, publisher = {EPTCS}, title = {{Discounting in games across time scales}}, doi = {10.4204/EPTCS.25.6}, volume = {25}, year = {2010}, } @inproceedings{3853, abstract = {Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the transition weights. When the mode of branching of the automaton is deterministic, nondeterministic, or alternating, the corresponding class of quantitative languages is not robust as it is not closed under the pointwise operations of max, min, sum, and numerical complement. Nondeterministic and alternating mean-payoff automata are not decidable either, as the quantitative generalization of the problems of universality and language inclusion is undecidable. We introduce a new class of quantitative languages, defined by mean-payoff automaton expressions, which is robust and decidable: it is closed under the four pointwise operations, and we show that all decision problems are decidable for this class. Mean-payoff automaton expressions subsume deterministic meanpayoff automata, and we show that they have expressive power incomparable to nondeterministic and alternating mean-payoff automata. We also present for the first time an algorithm to compute distance between two quantitative languages, and in our case the quantitative languages are given as mean-payoff automaton expressions.}, author = {Chatterjee, Krishnendu and Doyen, Laurent and Edelsbrunner, Herbert and Henzinger, Thomas A and Rannou, Philippe}, location = {Paris, France}, pages = {269 -- 283}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Mean-payoff automaton expressions}}, doi = {10.1007/978-3-642-15375-4_19}, volume = {6269}, year = {2010}, } @inproceedings{3854, abstract = {Graph games of infinite length provide a natural model for open reactive systems: one player (Eve) represents the controller and the other player (Adam) represents the environment. The evolution of the system depends on the decisions of both players. The specification for the system is usually given as an ω-regular language L over paths and Eve’s goal is to ensure that the play belongs to L irrespective of Adam’s behaviour. The classical notion of winning strategies fails to capture several interesting scenarios. For example, strong fairness (Streett) conditions are specified by a number of request-grant pairs and require every pair that is requested infinitely often to be granted infinitely often: Eve might win just by preventing Adam from making any new request, but a “better” strategy would allow Adam to make as many requests as possible and still ensure fairness. To address such questions, we introduce the notion of obliging games, where Eve has to ensure a strong condition Φ, while always allowing Adam to satisfy a weak condition Ψ. We present a linear time reduction of obliging games with two Muller conditions Φ and Ψ to classical Muller games. We consider obliging Streett games and show they are co-NP complete, and show a natural quantitative optimisation problem for obliging Streett games is in FNP. We also show how obliging games can provide new and interesting semantics for multi-player games.}, author = {Chatterjee, Krishnendu and Horn, Florian and Löding, Christof}, location = {Paris, France}, pages = {284 -- 296}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Obliging games}}, doi = {10.1007/978-3-642-15375-4_20}, volume = {6269}, year = {2010}, } @inproceedings{3855, abstract = {We study observation-based strategies for partially-observable Markov decision processes (POMDPs) with parity objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past sequence of observations. We consider qualitative analysis problems: given a POMDP with a parity objective, decide whether there exists an observation-based strategy to achieve the objective with probability 1 (almost-sure winning), or with positive probability (positive winning). Our main results are twofold. First, we present a complete picture of the computational complexity of the qualitative analysis problem for POMDPs with parity objectives and its subclasses: safety, reachability, Büchi, and coBüchi objectives. We establish several upper and lower bounds that were not known in the literature. Second, we give optimal bounds (matching upper and lower bounds) for the memory required by pure and randomized observation-based strategies for each class of objectives.}, author = {Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A}, location = {Brno, Czech Republic}, pages = {258 -- 269}, publisher = {Springer}, title = {{Qualitative analysis of partially-observable Markov Decision Processes}}, doi = {10.1007/978-3-642-15155-2_24}, volume = {6281}, year = {2010}, } @inproceedings{3856, abstract = {We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (players interact simultaneously); and (b) turn-based (players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. We present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function (probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games. }, author = {Chatterjee, Krishnendu and Doyen, Laurent and Gimbert, Hugo and Henzinger, Thomas A}, location = {Brno, Czech Republic}, pages = {246 -- 257}, publisher = {Springer}, title = {{Randomness for free}}, doi = {10.1007/978-3-642-15155-2_23}, volume = {6281}, year = {2010}, } @inproceedings{3857, abstract = {We consider probabilistic automata on infinite words with acceptance defined by safety, reachability, Büchi, coBüchi, and limit-average conditions. We consider quantitative and qualitative decision problems. We present extensions and adaptations of proofs for probabilistic finite automata and present an almost complete characterization of the decidability and undecidability frontier of the quantitative and qualitative decision problems for probabilistic automata on infinite words.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A}, location = {Singapore, Singapore}, pages = {1 -- 16}, publisher = {Springer}, title = {{Probabilistic Automata on infinite words: decidability and undecidability results}}, doi = {10.1007/978-3-642-15643-4_1}, volume = {6252}, year = {2010}, } @inproceedings{3858, abstract = {We consider two-player zero-sum games on graphs. On the basis of the information available to the players these games can be classified as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided partial-observation (one player has partial-observation and the other player has complete-observation); and (c) complete-observation (both players have com- plete view of the game). We survey the complexity results for the problem of de- ciding the winner in various classes of partial-observation games with ω-regular winning conditions specified as parity objectives. We present a reduction from the class of parity objectives that depend on sequence of states of the game to the sub-class of parity objectives that only depend on the sequence of observations. We also establish that partial-observation acyclic games are PSPACE-complete.}, author = {Chatterjee, Krishnendu and Doyen, Laurent}, location = {Yogyakarta, Indonesia}, pages = {1 -- 14}, publisher = {Springer}, title = {{The complexity of partial-observation parity games}}, doi = {10.1007/978-3-642-16242-8_1}, volume = {6397}, year = {2010}, } @proceedings{3859, abstract = {This book constitutes the proceedings of the 8th International Conference on Formal Modeling and Analysis of Timed Systems, FORMATS 2010, held in Klosterneuburg, Austria in September 2010. The 14 papers presented were carefully reviewed and selected from 31 submissions. In addition, the volume contains 3 invited talks and 2 invited tutorials.The aim of FORMATS is to promote the study of fundamental and practical aspects of timed systems, and to bring together researchers from different disciplines that share an interest in the modeling and analysis of timed systems. Typical topics include foundations and semantics, methods and tools, and applications.}, editor = {Chatterjee, Krishnendu and Henzinger, Thomas A}, location = {Klosterneuburg, Austria}, publisher = {Springer}, title = {{Formal modeling and analysis of timed systems}}, doi = {10.1007/978-3-642-15297-9}, volume = {6246}, year = {2010}, } @inproceedings{3860, abstract = {In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Generalized mean-payoff and energy games replace individual weights by tuples, and the limit average (resp. running sum) of each coordinate must be (resp. remain) nonnegative. These games have applications in the synthesis of resource-bounded processes with multiple resources. We prove the finite-memory determinacy of generalized energy games and show the inter- reducibility of generalized mean-payoff and energy games for finite-memory strategies. We also improve the computational complexity for solving both classes of games with finite-memory strategies: while the previously best known upper bound was EXPSPACE, and no lower bound was known, we give an optimal coNP-complete bound. For memoryless strategies, we show that the problem of deciding the existence of a winning strategy for the protagonist is NP-complete.}, author = {Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A and Raskin, Jean}, location = {Chennai, India}, pages = {505 -- 516}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Generalized mean-payoff and energy games}}, doi = {10.4230/LIPIcs.FSTTCS.2010.505}, volume = {8}, year = {2010}, } @article{3861, abstract = {We introduce strategy logic, a logic that treats strategies in two-player games as explicit first-order objects. The explicit treatment of strategies allows us to specify properties of nonzero-sum games in a simple and natural way. We show that the one-alternation fragment of strategy logic is strong enough to express the existence of Nash equilibria and secure equilibria, and subsumes other logics that were introduced to reason about games, such as ATL, ATL*, and game logic. We show that strategy logic is decidable, by constructing tree automata that recognize sets of strategies. While for the general logic, our decision procedure is nonelementary, for the simple fragment that is used above we show that the complexity is polynomial in the size of the game graph and optimal in the size of the formula (ranging from polynomial to 2EXPTIME depending on the form of the formula).}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Piterman, Nir}, journal = {Information and Computation}, number = {6}, pages = {677 -- 693}, publisher = {Elsevier}, title = {{Strategy logic}}, doi = {10.1016/j.ic.2009.07.004}, volume = {208}, year = {2010}, }