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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 758 (41 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
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 13 (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
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
On closure ordinals for the modal mucalculus
"... The closure ordinal of a formula of modal µcalculus µXφ is the least ordinal κ, if it exists, such that the denotation of the formula and the κth iteration of the monotone operator induced by φ coincide across all transition systems (finite and infinite). It is known that for every α < ω2 there ..."
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Cited by 1 (0 self)
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The closure ordinal of a formula of modal µcalculus µXφ is the least ordinal κ, if it exists, such that the denotation of the formula and the κth iteration of the monotone operator induced by φ coincide across all transition systems (finite and infinite). It is known that for every α < ω2
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
Infinitary Systems for the Modal muCalculus
"... Our work is concerned with the proof theoretic relationship between two infinitary deductive systems for the propositional modal µcalculus. The µcalculus is defined by the addition of least and greatest fixed point operators to (multi)modal logic. This results in a great increase in the expressive ..."
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global condition is then added which (roughly) says that in every such an infinite branch, there must be an outermost greatest fixed point unfolded infinitely many often. Such a system is proposed for example in [1]. We show that given a Tω µ+ proof of a formula A of the µcalculus, one can explicitly
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"... Abstract. The paper proposes a bottomup approach to the verification of systems with modular structure: when modules are composed in specific ways, the complete software system verifies a composition of the properties each component does. The focus of the work is on the process of upgrading system ..."
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systems with new functionalities, where the validity of old requirements needs to be ensured, but also an understanding of the new properties the upgraded system would enjoy is useful. Each component is supposed to be specified by a CCS process, and the properties expressed by selective mucalculus
Sahlqvist correspondence for modal mucalculus, Studia Logica
"... Abstract. We define analogues of modal Sahlqvist formulas for the modal mucalculus, and prove a correspondence theorem for them. ..."
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Cited by 3 (3 self)
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Abstract. We define analogues of modal Sahlqvist formulas for the modal mucalculus, and prove a correspondence theorem for them.
Alternationfree modal mucalculus for data trees
 In LICS’07
, 2007
"... An alternationfree modal µcalculus over data trees is introduced and studied. A data tree is an unranked ordered tree whose every node is labelled by a letter from a finite alphabet and an element (“datum”) from an infinite set. For expressing datasensitive properties, the calculus is equipped wi ..."
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Cited by 27 (3 self)
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An alternationfree modal µcalculus over data trees is introduced and studied. A data tree is an unranked ordered tree whose every node is labelled by a letter from a finite alphabet and an element (“datum”) from an infinite set. For expressing datasensitive properties, the calculus is equipped
Results 1  10
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