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On the Expressive Completeness of the Propositional MuCalculus With Respect to Monadic Second Order Logic
, 1996
"... . Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional calculus. This expressive completeness result implies that every logic over tran ..."
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Cited by 65 (3 self)
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. Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional calculus. This expressive completeness result implies that every logic over transition systems invariant under bisimulation and translatable into MSOL can be also translated into the calculus. This gives a precise meaning to the statement that most propositional logics of programs can be translated into the calculus. 1 Introduction Transition systems are structures consisting of a nonempty set of states, a set of unary relations describing properties of states and a set of binary relations describing transitions between states. It was advocated by many authors [26, 3] that this kind of structures provide a good framework for describing behaviour of programs (or program schemes), or even more generally, engineering systems, provided their evolution in time is disc...
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.
ModelChecking of Causality Properties
, 1995
"... A temporal logic for causality (Tlc) is introduced. The logic is interpreted over causal structures corresponding to partial order executions of programs. For causal structures describing the behavior of a finite fixed set of processes, a Tlcformula can, equivalently, be interpreted over their line ..."
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Cited by 43 (10 self)
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A temporal logic for causality (Tlc) is introduced. The logic is interpreted over causal structures corresponding to partial order executions of programs. For causal structures describing the behavior of a finite fixed set of processes, a Tlcformula can, equivalently, be interpreted over their linearizations. The main result of the paper is a tableau construction that gives a singlyexponential translation from a Tlc formula ' to a Streett automaton that accepts the set of linearizations satisfying '. This allows both checking the validity of Tlc formulas and modelchecking of program properties. As the logic Tlc does not distinguish among different linearizations of the same partial order execution, partial order reduction techniques can be applied to alleviate the statespace explosion problem of modelchecking. 1 Introduction One of the most successful techniques for automatic verification of finitestate systems has been modelchecking . A modelchecking algorithm decides wheth...
An Expressively Complete Linear Time Temporal Logic for Mazurkiewicz Traces
, 1997
"... A basic result concerning LTL, the propositional temporal logic of linear time, is that it is expressively complete; it is equal in expressive power to the first order theory of sequences. We present here a smooth extension of this result to the class of partial orders known as Mazurkiewicz traces. ..."
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Cited by 42 (5 self)
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A basic result concerning LTL, the propositional temporal logic of linear time, is that it is expressively complete; it is equal in expressive power to the first order theory of sequences. We present here a smooth extension of this result to the class of partial orders known as Mazurkiewicz traces. These partial orders arise in a variety of contexts in concurrency theory and they provide the conceptual basis for many of the partial order reduction methods that have been developed in connection with LTLspecifications. We show that LTrL, our linear time temporal logic, is equal in expressive power to the first order theory of traces when interpreted over (finite and) infinite traces. This result fills a prominent gap in the existing logical theory of infinite traces. LTrL also constitutes a characterisation of the so called trace consistent (robust) LTLspecifications. These are specifications expressed as LTL formulas that do not distinguish between different linearisations of the same trace and hence are amenable to partial order reduction methods.
Logics for Specifying Concurrent Information Systems
 LOGICS FOR DATABASES AND INFORMATION SYSTEMS
, 1998
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Object Specification
 IFIP WG14.3 BOOK ON ALGEBRAIC FOUNDATIONS OF SYSTEMS SPECIFICATION
, 1997
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LTL is expressively complete for Mazurkiewicz Traces
, 2000
"... A long standing open problem in the theory of (Mazurkiewicz) traces has been the question whether LTL (Linear Time Logic) is expressively complete with respect to the rst order theory. We solve this problem positively for nite and in nite traces and for the simplest temporal logic, which is b ..."
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Cited by 19 (8 self)
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A long standing open problem in the theory of (Mazurkiewicz) traces has been the question whether LTL (Linear Time Logic) is expressively complete with respect to the rst order theory. We solve this problem positively for nite and in nite traces and for the simplest temporal logic, which is based only on next and until modalities. Similar results were established previously, but they were all weaker, since they used additional past or future modalities. Another feature of our work is that our proof is direct and does not use any reduction to the word case.
Pure future local temporal logics are expressively complete for Mazurkiewicz traces
 Conference version in LATIN 2004, LNCS 2976
"... Mazurkiewicz traces ⋆ ..."
ModelChecking for a Subclass of Event Structures
 Proc. of TACAS'97, LNCS 1217
, 1997
"... . A finite representation of the prime event structure corresponding to the behaviour of a program is suggested. The algorithm of linear complexity using this representation for model checking of the formulas of Discrete Event Structure Logic without past modalities is given. A method of building fi ..."
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Cited by 15 (8 self)
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. A finite representation of the prime event structure corresponding to the behaviour of a program is suggested. The algorithm of linear complexity using this representation for model checking of the formulas of Discrete Event Structure Logic without past modalities is given. A method of building finite representations of event structures in an efficient way by applying partial order reductions is provided. 1 Introduction Model checking is one of the most successful methods of automatic verification of program properties. A modelchecking algorithm decides whether a finitestate concurrent system satisfies its specification, given as a formula of a temporal logic [3, 10]. Behaviour of a concurrent system can be modeled in two ways. In the interleaving semantics, the meaning of a program is an execution tree, temporallogic assertions are interpreted over paths of this tree. In partialorder semantics (or event structure semantics), behaviour is an event structure, where the ordering r...
Strategic Directions in Concurrency Research
 ACM COMPUTING SURVEYS
, 1996
"... Concurrency is concerned with the fundamental aspects of systems of multiple, simultaneously active computing agents that interact with one another. This notion is ..."
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Cited by 14 (0 self)
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Concurrency is concerned with the fundamental aspects of systems of multiple, simultaneously active computing agents that interact with one another. This notion is