@inproceedings{3719, abstract = {The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a math- ematical model is an important challenge in systems biology. Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the com- binatorial complexity by quotienting the reachable set of molecular species, into species aggregates while preserving the deterministic semantics of the thermodynamic limit. Recently we proposed a quotienting that also preserves the stochastic semantics and that is complete in the sense that the semantics of individual species can be recovered from the aggregate semantics. In this paper we prove that this quotienting yields a sufficient condition for weak lumpability and that it gives rise to a backward Markov bisimulation between the original and aggregated transition system. We illustrate the framework on a case study of the EGF/insulin receptor crosstalk.}, author = {Feret, Jérôme and Henzinger, Thomas A and Koeppl, Heinz and Petrov, Tatjana}, location = {Jena, Germany}, pages = {142--161}, publisher = {Open Publishing Association}, title = {{Lumpability abstractions of rule-based systems}}, volume = {40}, year = {2010}, } @article{3834, abstract = {Background The chemical master equation (CME) is a system of ordinary differential equations that describes the evolution of a network of chemical reactions as a stochastic process. Its solution yields the probability density vector of the system at each point in time. Solving the CME numerically is in many cases computationally expensive or even infeasible as the number of reachable states can be very large or infinite. We introduce the sliding window method, which computes an approximate solution of the CME by performing a sequence of local analysis steps. In each step, only a manageable subset of states is considered, representing a "window" into the state space. In subsequent steps, the window follows the direction in which the probability mass moves, until the time period of interest has elapsed. We construct the window based on a deterministic approximation of the future behavior of the system by estimating upper and lower bounds on the populations of the chemical species. Results In order to show the effectiveness of our approach, we apply it to several examples previously described in the literature. The experimental results show that the proposed method speeds up the analysis considerably, compared to a global analysis, while still providing high accuracy. Conclusions The sliding window method is a novel approach to address the performance problems of numerical algorithms for the solution of the chemical master equation. The method efficiently approximates the probability distributions at the time points of interest for a variety of chemically reacting systems, including systems for which no upper bound on the population sizes of the chemical species is known a priori.}, author = {Wolf, Verena and Goel, Rushil and Mateescu, Maria and Henzinger, Thomas A}, journal = {BMC Systems Biology}, number = {42}, pages = {1 -- 19}, publisher = {BioMed Central}, title = {{Solving the chemical master equation using sliding windows}}, doi = {10.1186/1752-0509-4-42}, volume = {4}, year = {2010}, } @inproceedings{3838, abstract = {We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe net- works of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is based on the construction of a stochastic hybrid model in which certain discrete random variables of the original Markov chain are approximated by continuous deterministic variables. We compute the solution of the stochastic hybrid model using a numerical algorithm that discretizes time and in each step performs a mutual update of the transient prob- ability distribution of the discrete stochastic variables and the values of the continuous deterministic variables. We im- plemented the algorithm and we demonstrate its usefulness and efficiency on several case studies from systems biology.}, author = {Henzinger, Thomas A and Mateescu, Maria and Mikeev, Linar and Wolf, Verena}, location = {Trento, Italy}, pages = {55 -- 65}, publisher = {Springer}, title = {{Hybrid numerical solution of the chemical master equation}}, doi = {10.1145/1839764.1839772}, year = {2010}, } @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{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{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}, } @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}, } @article{3863, abstract = {We consider two-player parity games with imperfect information in which strategies rely on observations that provide imperfect information about the history of a play. To solve such games, i.e., to determine the winning regions of players and corresponding winning strategies, one can use the subset construction to build an equivalent perfect-information game. Recently, an algorithm that avoids the inefficient subset construction has been proposed. The algorithm performs a fixed-point computation in a lattice of antichains, thus maintaining a succinct representation of state sets. However, this representation does not allow to recover winning strategies. In this paper, we build on the antichain approach to develop an algorithm for constructing the winning strategies in parity games of imperfect information. One major obstacle in adapting the classical procedure is that the complementation of attractor sets would break the invariant of downward-closedness on which the antichain representation relies. We overcome this difficulty by decomposing problem instances recursively into games with a combination of reachability, safety, and simpler parity conditions. We also report on an experimental implementation of our algorithm: to our knowledge, this is the first implementation of a procedure for solving imperfect-information parity games on graphs.}, author = {Berwanger, Dietmar and Chatterjee, Krishnendu and De Wulf, Martin and Doyen, Laurent and Henzinger, Thomas A}, journal = {Information and Computation}, number = {10}, pages = {1206 -- 1220}, publisher = {Elsevier}, title = {{Strategy construction for parity games with imperfect information}}, doi = {10.1016/j.ic.2009.09.006}, volume = {208}, year = {2010}, } @inproceedings{3864, abstract = {Often one has a preference order among the different systems that satisfy a given specification. Under a probabilistic assumption about the possible inputs, such a preference order is naturally expressed by a weighted automaton, which assigns to each word a value, such that a system is preferred if it generates a higher expected value. We solve the following optimal-synthesis problem: given an omega-regular specification, a Markov chain that describes the distribution of inputs, and a weighted automaton that measures how well a system satisfies the given specification tinder the given input assumption, synthesize a system that optimizes the measured value. For safety specifications and measures that are defined by mean-payoff automata, the optimal-synthesis problem amounts to finding a strategy in a Markov decision process (MDP) that is optimal for a long-run average reward objective, which can be done in polynomial time. For general omega-regular specifications, the solution rests on a new, polynomial-time algorithm for computing optimal strategies in MDPs with mean-payoff parity objectives. We present some experimental results showing optimal systems that were automatically generated in this way.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Jobstmann, Barbara and Singh, Rohit}, location = {Edinburgh, United Kingdom}, pages = {380 -- 395}, publisher = {Springer}, title = {{Measuring and synthesizing systems in probabilistic environments}}, doi = {10.1007/978-3-642-14295-6_34}, volume = {6174}, year = {2010}, } @inproceedings{3866, abstract = {Systems ought to behave reasonably even in circumstances that are not anticipated in their specifications. We propose a definition of robustness for liveness specifications which prescribes, for any number of environment assumptions that are violated, a minimal number of system guarantees that must still be fulfilled. This notion of robustness can be formulated and realized using a Generalized Reactivity formula. We present an algorithm for synthesizing robust systems from such formulas. For the important special case of Generalized Reactivity formulas of rank 1, our algorithm improves the complexity of [PPS06] for large specifications with a small number of assumptions and guarantees.}, author = {Bloem, Roderick and Chatterjee, Krishnendu and Greimel, Karin and Henzinger, Thomas A and Jobstmann, Barbara}, editor = {Touili, Tayssir and Cook, Byron and Jackson, Paul}, location = {Edinburgh, UK}, pages = {410 -- 424}, publisher = {Springer}, title = {{Robustness in the presence of liveness}}, doi = {10.1007/978-3-642-14295-6_36}, volume = {6174}, year = {2010}, } @article{3867, abstract = {Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages L that assign to each word w a real number L(w). In the case of infinite words, the value of a run is naturally computed as the maximum, limsup, liminf, limit-average, or discounted-sum of the transition weights. The value of a word w is the supremum of the values of the runs over w. We study expressiveness and closure questions about these quantitative languages. We first show that the set of words with value greater than a threshold can be omega-regular for deterministic limit-average and discounted-sum automata, while this set is always omega-regular when the threshold is isolated (i.e., some neighborhood around the threshold contains no word). In the latter case, we prove that the omega-regular language is robust against small perturbations of the transition weights. We next consider automata with transition weights 0 or 1 and show that they are as expressive as general weighted automata in the limit-average case, but not in the discounted-sum case. Third, for quantitative languages L-1 and L-2, we consider the operations max(L-1, L-2), min(L-1, L-2), and 1 - L-1, which generalize the boolean operations on languages, as well as the sum L-1 + L-2. We establish the closure properties of all classes of quantitative languages with respect to these four operations.}, author = {Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A}, journal = {Logical Methods in Computer Science}, number = {3}, pages = {1 -- 23}, publisher = {International Federation for Computational Logic}, title = {{Expressiveness and closure properties for quantitative languages}}, doi = {10.2168/LMCS-6(3:10)2010}, volume = {6}, year = {2010}, } @misc{5393, abstract = {Gist is a tool that (a) solves the qualitative analysis problem of turn-based probabilistic games with ω-regular objectives; and (b) synthesizes reasonable environment assumptions for synthesis of unrealizable specifications. Our tool provides efficient implementations of several reduction based techniques to solve turn-based probabilistic games, and uses the analysis of turn-based probabilistic games for synthesizing environment assumptions for unrealizable specifications.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Jobstmann, Barbara and Radhakrishna, Arjun}, issn = {2664-1690}, pages = {12}, publisher = {IST Austria}, title = {{Gist: A solver for probabilistic games}}, doi = {10.15479/AT:IST-2009-0003}, year = {2009}, }