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Compositional Model Checking
, 1999
"... We describe a method for reducing the complexity of temporal logic model checking in systems composed of many parallel processes. The goal is to check properties of the components of a system and then deduce global properties from these local properties. The main difficulty with this type of approac ..."
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Cited by 2424 (62 self)
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We describe a method for reducing the complexity of temporal logic model checking in systems composed of many parallel processes. The goal is to check properties of the components of a system and then deduce global properties from these local properties. The main difficulty with this type of approach is that local properties are often not preserved at the global level. We present a general framework for using additional interface processes to model the environment for a component. These interface processes are typically much simpler than the full environment of the component. By composing a component with its interface processes and then checking properties of this composition, we can guarantee that these properties will be preserved at the global level. We give two example compositional systems based on the logic CTL*.
An AutomataTheoretic Approach to BranchingTime Model Checking
 JOURNAL OF THE ACM
, 1998
"... Translating linear temporal logic formulas to automata has proven to be an effective approach for implementing lineartime modelchecking, and for obtaining many extensions and improvements to this verification method. On the other hand, for branching temporal logic, automatatheoretic techniques ..."
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Cited by 299 (65 self)
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Translating linear temporal logic formulas to automata has proven to be an effective approach for implementing lineartime modelchecking, and for obtaining many extensions and improvements to this verification method. On the other hand, for branching temporal logic, automatatheoretic techniques have long been thought to introduce an exponential penalty, making them essentially useless for modelchecking. Recently, Bernholtz and Grumberg have shown that this exponential penalty can be avoided, though they did not match the linear complexity of nonautomatatheoretic algorithms. In this paper we show that alternating tree automata are the key to a comprehensive automatatheoretic framework for branching temporal logics. Not only, as was shown by Muller et al., can they be used to obtain optimal decision procedures, but, as we show here, they also make it possible to derive optimal modelchecking algorithms. Moreover, the simple combinatorial structure that emerges from the a...
Pushdown Processes: Games and Model Checking
, 1996
"... Games given by transition graphs of pushdown processes are considered. It is shown that ..."
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Cited by 135 (4 self)
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Games given by transition graphs of pushdown processes are considered. It is shown that
Reasoning about The Past with TwoWay Automata
 In 25th International Colloqium on Automata, Languages and Programming, ICALP ’98
, 1998
"... Abstract. The pcalculus can be viewed as essentially the "ultimate" program logic, as it expressively subsumes all propositional program logics, including dynamic logics, process logics, and temporal logics. It is known that the satisfiability problem for the pcalculus is EXPTIMEcomplete ..."
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Cited by 129 (12 self)
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Abstract. The pcalculus can be viewed as essentially the "ultimate" program logic, as it expressively subsumes all propositional program logics, including dynamic logics, process logics, and temporal logics. It is known that the satisfiability problem for the pcalculus is EXPTIMEcomplete. This upper bound, however, is known for a version of the logic that has only forward modalities, which express weakest preconditions, but not backward modalities, which express strongest postconditions. Our main result in this paper is an exponential time upper bound for the satisfiability problem of the pcalculus with both forward and backward modalities. To get this result we develop a theory of twoway alternating automata on infinite trees. 1
Weak alternating automata are not that weak
 ACM Trans. on Computational Logic
"... Automata on infinite words are used for specification and verification of nonterminating programs. Different types of automata induce different levels of expressive power, of succinctness, and of complexity. Alternating automata have both existential and universal branching modes and are particularl ..."
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Cited by 76 (25 self)
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Automata on infinite words are used for specification and verification of nonterminating programs. Different types of automata induce different levels of expressive power, of succinctness, and of complexity. Alternating automata have both existential and universal branching modes and are particularly suitable for specification of programs. In a weak alternating automaton, the state space is partitioned into partially ordered sets, and the automaton can proceed from a certain set only to smaller sets. Reasoning about weak alternating automata is easier than reasoning about alternating automata with no restricted structure. Known translations of alternating automata to weak alternating automata involve determinization, and therefore involve a doubleexponential blowup. In this paper we describe a quadratic translation, which circumvents the need for determinization, of Büchi and coBüchi alternating automata to weak alternating automata. Beyond the independent interest of such a translation, it gives rise to a simple complementation algorithm for nondeterministic Büchi automata. 1
Quantitative Stochastic Parity Games
"... We study perfectinformation stochastic parity games. These are twoplayer nonterminating games which are played on a graph with turnbased probabilistic transitions. A play results in an infinite path and the conflicting goals of the two players are!regular path properties, formalized as parity w ..."
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Cited by 52 (23 self)
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We study perfectinformation stochastic parity games. These are twoplayer nonterminating games which are played on a graph with turnbased probabilistic transitions. A play results in an infinite path and the conflicting goals of the two players are!regular path properties, formalized as parity winning conditions. The qualitative solution of such a game amounts to computing the set of vertices from which a player has a strategy to win with probability 1 (or with positive probability). The quantitative solution amounts to computing the value of the game in every vertex, i.e., the highest probability with which a player can guarantee satisfaction of his own objective in a play that starts from the vertex. For the important special case of oneplayer stochastic parity games (parity Markov decision processes) we give polynomialtime algorithms both for the qualitative and the quantitative solution. The running time of the qualitative solution is O(d \Delta m 3=2) for graphs with m edges and d priorities. The quantitative solution is based on a linearprogramming formulation.
On ModelChecking for Fragments of µCalculus
 In CAV'93, volume 697 of LNCS
, 1995
"... this paper we consider the problem of modelchecking for different fragments of propositional ¯calculus. This logic was studied by many authors [6, 9] for specifying the properties of concurrent programs. It has been shown to be as expressive of automata on infinite trees. Most of the known temporal ..."
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Cited by 52 (1 self)
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this paper we consider the problem of modelchecking for different fragments of propositional ¯calculus. This logic was studied by many authors [6, 9] for specifying the properties of concurrent programs. It has been shown to be as expressive of automata on infinite trees. Most of the known temporal and dynamic logics can be translated into this logic. The modelchecking problem for this logic was first considered in [7]. In this paper, the authors presented an algorithm that is O((mn)
Discounting the future in systems theory
 In Automata, Languages, and Programming, LNCS 2719
, 2003
"... ..."
Modal Logics and muCalculi: An Introduction
, 2001
"... We briefly survey the background and history of modal and temporal logics. We then concentrate on the modal mucalculus, a modal logic which subsumes most other commonly used logics. We provide an informal introduction, followed by a summary of the main theoretical issues. We then look at modelchec ..."
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Cited by 44 (3 self)
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We briefly survey the background and history of modal and temporal logics. We then concentrate on the modal mucalculus, a modal logic which subsumes most other commonly used logics. We provide an informal introduction, followed by a summary of the main theoretical issues. We then look at modelchecking, and finally at the relationship of modal logics to other formalisms.