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12,003
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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of states. We describe a general method that represents the state space symbolical/y instead of explicitly. The generality of our method comes from using a dialect of the MuCalculus as the primary specification language. We describe a model checking algorithm for MuCalculus formulas that uses Bryant’s
Quotientbased Control Synthesis for NonDeterministic Plants with MuCalculus Specifications
 In 45th IEEE Conference on Decision and Control
, 2006
"... Abstract — We study the control of a nondeterministic discrete event system (DES) subject to a control specification expressed in the propositional mucalculus, under complete observation of events. Given a plant automaton model and a mucalculus specification we provide a set of rules that computes ..."
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Cited by 4 (1 self)
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that computes the “quotient” of the specification against the plant, which is another mucalculus formula such that a supervisor exists if and only if the quotiented formula is satisfiable. Thus the control problem is reduced to one of mucalculus satisfiability. We also present a tableaubased satisfiability
Model checking and the Mucalculus
 DIMACS Series in Discrete Mathematics
, 1997
"... There is a growing recognition of the need to apply formal mathematical methods in the design of "high confidence" computing systems. Such systems operate in safety critical contexts (e.g., air traffic control systems) or where errors could have major adverse economic consequences (e.g., ..."
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Cited by 47 (0 self)
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attention on a particularly important type of temporal logic known as the Mucalculus.
Derivation of Characteristic Formulae
, 2001
"... This paper shows how modal mucalculus formulae characterizing finitestate processes up to strong or weak bisimulation can be derived directly from the wellknown greatest fixpoint characterizations of the bisimulation relations. Our derivation simplifies earlier proofs for the strong bisimulation ..."
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Cited by 23 (1 self)
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This paper shows how modal mucalculus formulae characterizing finitestate processes up to strong or weak bisimulation can be derived directly from the wellknown greatest fixpoint characterizations of the bisimulation relations. Our derivation simplifies earlier proofs for the strong bisimulation
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
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 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.
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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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 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 their strategy while executing it. Thus, the agents are not assumed to remember their strategy by definition, like in the existing variants of ATL. Last but not least, we show that verification of such abilities can be cheaper than for all the variants of “ATL with imperfect information ” considered so far. 1
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