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An automatatheoretic approach to reasoning about infinitestate systems
 LNCS
, 2000
"... Abstract. We develop an automatatheoretic framework for reasoning about infinitestate sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions betw ..."
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Cited by 41 (4 self)
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Abstract. We develop an automatatheoretic framework for reasoning about infinitestate sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finitestate automata. Checking that the system satisfies a temporal property can then be done by an alternating twoway tree automaton that navigates through the tree. As has been the case with finitestate systems, the automatatheoretic framework is quite versatile. We demonstrate it by solving several versions of the modelchecking problem for §calculus specifications and prefixrecognizable systems, and by solving the realizability and synthesis problems for §calculus specifications with respect to prefixrecognizable environments. 1
Alternating Automata and Program Verification
 In Computer Science Today. LNCS 1000
, 1995
"... . We describe an automatatheoretic approach to the automatic verification of finitestate programs. The basic idea underlying this approach is that for any temporal formula we can construct an alternating automaton that accepts precisely the computations that satisfy the formula. For linear tempora ..."
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Cited by 37 (3 self)
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. We describe an automatatheoretic approach to the automatic verification of finitestate programs. The basic idea underlying this approach is that for any temporal formula we can construct an alternating automaton that accepts precisely the computations that satisfy the formula. For linear temporal logics the automaton runs on infinite words while for branching temporal logics the automaton runs on infinite trees. The simple combinatorial structures that emerge from the automatatheoretic approach decouple the logical and algorithmic components of finitestateprogram verification and yield clear and general verification algorithms. 1 Introduction Temporal logics, which are modal logics geared towards the description of the temporal ordering of events, have been adopted as a powerful tool for specifying and verifying concurrent programs [Pnu77, MP92]. One of the most significant developments in this area is the discovery of algorithmic methods for verifying temporal logic properties...
Synthesis with incomplete informatio
 In Advances in Temporal Logic
, 2000
"... Abstract. In program synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. When the system is open, then at each moment it reads input signals and writes output signals, which depend on the input signals and the history of the computation so far. The ..."
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Cited by 31 (7 self)
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Abstract. In program synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. When the system is open, then at each moment it reads input signals and writes output signals, which depend on the input signals and the history of the computation so far. The specification considers all possible input sequences. Thus, if the specification is linear, it should hold in every computation generated by the interaction, and if the specification is branching, it should hold in the tree that embodies all possible input sequences. Often, the system cannot read all the input signals generated by its environment. For example, in a distributed setting, it might be that each process can read input signals of only part of the underlying processes. Then, we should transform a specification into a system whose output depends only on the readable parts of the input signals and the history of the computation. This is called synthesis with incomplete information. In this work we solve the problem of synthesis with incomplete information in its full generality. We consider linear and branching settings with complete and incomplete information. We claim that alternation is a suitable and helpful mechanism for coping with incomplete information. Using alternating tree automata, we show that incomplete information does not make the synthesis problem more complex, in both the linear and the branching paradigm. In particular, we prove that independently of the presence of incomplete information, the synthesis problems for CTL and CTL ⋆ are complete for EXPTIME and 2EXPTIME, respectively. 1.
The Complexity of the Graded µCalculus
"... In classical logic, existential and universal quantifiers express that there exists at least one individual satisfying a formula, or that all individuals satisfy a formula. In many logics, these quantifiers have been generalized to express that, for a nonnegative integer n, at least n individual ..."
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Cited by 30 (2 self)
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In classical logic, existential and universal quantifiers express that there exists at least one individual satisfying a formula, or that all individuals satisfy a formula. In many logics, these quantifiers have been generalized to express that, for a nonnegative integer n, at least n individuals or all but n individuals satisfy a formula. In modal logics, graded modalities generalize standard existential and universal modalities in that they express, e.g., that there exist at least n accessible worlds satisfying a certain formula. Graded modalities are useful expressive means in knowledge representation; they are present in a variety of other knowledge representation formalisms closely related to modal logic.
THE COMPLEXITY OF ENRICHED µCALCULI
, 2008
"... The fully enriched µcalculus is the extension of the propositional µcalculus with inverse programs, graded modalities, and nominals. While satisfiability in several expressive fragments of the fully enriched µcalculus is known to be decidable and EXPTIMEcomplete, it has recently been proved tha ..."
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Cited by 29 (9 self)
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The fully enriched µcalculus is the extension of the propositional µcalculus with inverse programs, graded modalities, and nominals. While satisfiability in several expressive fragments of the fully enriched µcalculus is known to be decidable and EXPTIMEcomplete, it has recently been proved that the full calculus is undecidable. In this paper, we study the fragments of the fully enriched µcalculus that are obtained by dropping at least one of the additional constructs. We show that, in all fragments obtained in this way, satisfiability is decidable and EXPTIMEcomplete. Thus, we identify a family of decidable logics that are maximal (and incomparable) in expressive power. Our results are obtained by introducing two new automata models, showing that their emptiness problems are EXPTIMEcomplete, and then reducing satisfiability in the relevant logics to these problems. The automata models we introduce are twoway graded alternating parity automata over infinite trees (2GAPTs) and fully enriched automata (FEAs) over infinite forests. The former are a common generalization of two incomparable automata models from the literature. The latter extend alternating automata in a similar way as the fully enriched µcalculus extends the standard µcalculus.
Distributive laws for the coinductive solution of recursive equations
 Information and Computation
"... This paper illustrates the relevance of distributive laws for the solution of recursive equations, and shows that one approach for obtaining coinductive solutions of equations via infinite terms is in fact a special case of a more general approach using an extended form of coinduction via distributi ..."
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Cited by 23 (1 self)
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This paper illustrates the relevance of distributive laws for the solution of recursive equations, and shows that one approach for obtaining coinductive solutions of equations via infinite terms is in fact a special case of a more general approach using an extended form of coinduction via distributive laws. 1
Pushdown Module Checking with Imperfect Information
, 2012
"... The model checking problem for finitestate open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinitestate systems ( ..."
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Cited by 23 (14 self)
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The model checking problem for finitestate open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinitestate systems (pushdown module checking). In this paper, we extend pushdown module checking to the imperfect information setting; i.e., to the case where the environment has only a partial view of the system’s control states and pushdown store content. We study the complexity of this problem with respect to the branchingtime temporal logics CTL, CTL ∗ and the propositional µcalculus. We show that pushdown module checking, which is by itself harder than pushdown model checking, becomes undecidable when the environment has imperfect information.
An AutomataTheoretic Approach to Modular Model Checking
, 1998
"... this paper we consider assumeguarantee specifications in which the guarantee is specified by branching temporal formulas. We distinguish between two approaches. In the first approach, the assumption is specified by branching temporal formulas too. In the second approach, the assumption is specified ..."
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Cited by 22 (0 self)
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this paper we consider assumeguarantee specifications in which the guarantee is specified by branching temporal formulas. We distinguish between two approaches. In the first approach, the assumption is specified by branching temporal formulas too. In the second approach, the assumption is specified by linear temporal logic. We consider guarantees in 8CTL and 8CTL
Rational Synthesis
"... Abstract. Synthesis is the automated construction of a system from its specification. The system has to satisfy its specification in all possible environments. Modern systems often interact with other systems, or agents. Many times these agents have objectives of their own, other than to fail the sy ..."
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Cited by 22 (5 self)
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Abstract. Synthesis is the automated construction of a system from its specification. The system has to satisfy its specification in all possible environments. Modern systems often interact with other systems, or agents. Many times these agents have objectives of their own, other than to fail the system. Thus, it makes sense to model system environments not as hostile, but as composed of rational agents; i.e., agents that act to achieve their own objectives. We introduce the problem of synthesis in the context of rational agents (rational synthesis, for short). The input consists of a temporallogic formula specifying the system, temporallogic formulas specifying the objectives of the agents, and a solution concept definition. The output is an implementation T of the system and a profile of strategies, suggesting a behavior for each of the agents. The output should satisfy two conditions. First, the composition of T with the strategy profile should satisfy the specification. Second, the strategy profile should be an equilibrium in the sense that, in view of their objectives, agents have no incentive to deviate from the strategies assigned to them, where “no incentive to deviate” is interpreted as dictated by the given solution concept. We provide a method for solving the rationalsynthesis problem, and show that for the classical definitions of equilibria studied in game theory, rational synthesis is not harder than traditional synthesis. We also consider the multivalued case in which the objectives of the system and the agents are still temporal logic formulas, but involve payoffs from a finite lattice. 1