TY - CONF
AB - 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.
AU - Henzinger, Thomas A
AU - Hottelier, Thibaud
AU - Kovács, Laura
AU - Voronkov, Andrei
ID - 3839
TI - Invariant and type inference for matrices
VL - 5944
ER -
TY - CONF
AB - 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.
AU - Henzinger, Thomas A
ID - 3840
IS - 1
TI - From boolean to quantitative notions of correctness
VL - 45
ER -
TY - JOUR
AB - 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.
AU - Didier, Frédéric
AU - Henzinger, Thomas A
AU - Mateescu, Maria
AU - Wolf, Verena
ID - 3842
IS - 6
JF - IET Systems Biology
TI - Fast adaptive uniformization of the chemical master equation
VL - 4
ER -
TY - CONF
AB - 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.
AU - Henzinger, Thomas A
AU - Hottelier, Thibaud
AU - Kovács, Laura
AU - Rybalchenko, Andrey
ID - 3845
TI - Aligators for arrays
VL - 6397
ER -
TY - CONF
AB - 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.
AU - Didier, Frédéric
AU - Henzinger, Thomas A
AU - Mateescu, Maria
AU - Wolf, Verena
ID - 3847
TI - SABRE: A tool for the stochastic analysis of biochemical reaction networks
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Edelsbrunner, Herbert
AU - Henzinger, Thomas A
AU - Rannou, Philippe
ID - 3853
TI - Mean-payoff automaton expressions
VL - 6269
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 3855
TI - Qualitative analysis of partially-observable Markov Decision Processes
VL - 6281
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Gimbert, Hugo
AU - Henzinger, Thomas A
ID - 3856
TI - Randomness for free
VL - 6281
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
ID - 3857
TI - Probabilistic Automata on infinite words: decidability and undecidability results
VL - 6252
ER -
TY - GEN
AB - 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.
ED - Chatterjee, Krishnendu
ED - Henzinger, Thomas A
ID - 3859
TI - Formal modeling and analysis of timed systems
VL - 6246
ER -