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Symbolic Model Checking: 10^20 States and Beyond
, 1992
"... Many different methods have been devised for automatically verifying finite state systems by examining stategraph models of system behavior. These methods all depend on decision procedures that explicitly represent the state space using a list or a table that grows in proportion to the number of st ..."
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Cited by 753 (40 self)
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Binary Decision Diagrams (Bryant, R. E., 1986, IEEE Trans. Comput. C35) to represent relations and formulas. We then show how our new MuCalculus model checking algorithm can be used to derive efficient decision procedures for CTL model checking, satistiability of lineartime temporal logic formulas
The Algebraic MuCalculus and MTBDDs
 In Proceedings of the 5th Workshop on Logic, Language, Information and Computation, (WoLLIC’98
, 1998
"... The paper presents a new calculus (called algebraic mucalculus) which generalizes Park's relational mucalculus by representing arithmetric expressions and realvalued functions rather than formulas and relations. Moreover, we give an algorithm for computing the MTBDDrepresentation of the s ..."
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Cited by 12 (0 self)
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The paper presents a new calculus (called algebraic mucalculus) which generalizes Park's relational mucalculus by representing arithmetric expressions and realvalued functions rather than formulas and relations. Moreover, we give an algorithm for computing the MTBDD
The propositional mucalculus is elementary
 of Lecture
"... ABSTRACT: The propositional mucalculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the Propositional Dynamic Logic of Fischer and Ladner, the infinite looping construct of Streett, and the Game Logic of Parikh. We give an elementary time decision p ..."
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Cited by 15 (0 self)
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ABSTRACT: The propositional mucalculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the Propositional Dynamic Logic of Fischer and Ladner, the infinite looping construct of Streett, and the Game Logic of Parikh. We give an elementary time decision
Observational muCalculus
, 1999
"... We propose an extended modal mucalculus to provide an `assembly language' for modal logics for real time, valuepassing calculi, and other extended models of computation. ..."
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Cited by 2 (1 self)
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We propose an extended modal mucalculus to provide an `assembly language' for modal logics for real time, valuepassing calculi, and other extended models of computation.
Games and Modal MuCalculus
 In Second International Workshop Tools and Algorithms for Construction and Analysis of Systems
, 1996
"... We define EhrenfeuchtFraiss'e games which exactly capture the expressive power of the extremal fixed point operators of modal mucalculus. The resulting games have significance, we believe, within and outside of concurrency theory. On the one hand they naturally extend the iterative bisimul ..."
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Cited by 13 (1 self)
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explores the technical contribution that games can make to understanding concurrency. We define EhrenfeuchtFraiss'e games which exactly capture the expressive power of the extremal fixed point operators of modal mucalculus. The resulting games have significance, we believe, within and outside
The Horn Mucalculus
, 1998
"... The Horn calculus is a logic programming language allowing arbitrary nesting of least and greatest fixed points. The Horn programs can naturally expresses safety and liveness properties for reactive systems. We extend the setbased analysis of classical logic programs by mapping arbitrary program ..."
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Cited by 13 (9 self)
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The Horn calculus is a logic programming language allowing arbitrary nesting of least and greatest fixed points. The Horn programs can naturally expresses safety and liveness properties for reactive systems. We extend the setbased analysis of classical logic programs by mapping arbitrary
Alternating Epistemic MuCalculus
"... Alternatingtime temporal logic (ATL) is a wellknown logic for reasoning about strategic abilities of agents. An important feature that distinguishes variants of ATL for imperfect information scenarios is that the standard fixed point characterizations of temporal modalities do not hold anymore. In ..."
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Cited by 4 (0 self)
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. In this paper, we show that adding explicit fixed point operators to the “nexttime ” fragment of ATL already allows to capture abilities that could not be expressed in ATL. We also illustrate that the new language allows to specify important kinds of abilities, namely ones where the agents can always recompute
TableauBased Model Checking in the Propositional MuCalculus
 Acta Informatica
, 1990
"... This paper describes a procedure, based around the construction of tableau proofs, for determining whether finitestate systems enjoy properties formulated in the propositional mucalculus. It presents a tableaubased proof system for the logic and proves it sound and complete, and it discusses tech ..."
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Cited by 102 (7 self)
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This paper describes a procedure, based around the construction of tableau proofs, for determining whether finitestate systems enjoy properties formulated in the propositional mucalculus. It presents a tableaubased proof system for the logic and proves it sound and complete, and it discusses
On the proof theory of modal mucalculus
 Studia Logica
, 2008
"... We study the prooftheoretic relationship between two deductive systems for the modal mucalculus. First we recall an infinitary system which contains an omega rule allowing to derive the truth of a greatest fixed point from the truth of each of its (infinitely many) approximations. Then we recall a ..."
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Cited by 9 (2 self)
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We study the prooftheoretic relationship between two deductive systems for the modal mucalculus. First we recall an infinitary system which contains an omega rule allowing to derive the truth of a greatest fixed point from the truth of each of its (infinitely many) approximations. Then we recall
Vacuity Checking in the Modal MuCalculus
 In Proceedings of AMAST’02, volume 2422 of LNCS
, 2002
"... Abstract. Vacuity arises when a logical formula is trivially true in a given model due, for example, to antecedent failure. Beer et al. have recently introduced a logicindependent notion of vacuity and shown that certain logics, i.e., those with polarity, admit an efficient decision procedure for v ..."
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Cited by 5 (1 self)
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for vacuity detection. We show that the modal mucalculus, a very expressive temporal logic, is a logic with polarity and hence the results of Beer et al. are applicable. We also extend the definition of vacuity to achieve a new notion of redundancy in logical formulas. Redundancy captures several forms
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