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29
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...
Safety for Branching Time Semantics
, 1991
"... We study in a first part of this paper safety and liveness properties for any given program semantics. We give a topological definition of these properties using a safety preorder. Then, we consider the case of branching time semantics where a program is modeled by a set of infinite computation tree ..."
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Cited by 36 (3 self)
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We study in a first part of this paper safety and liveness properties for any given program semantics. We give a topological definition of these properties using a safety preorder. Then, we consider the case of branching time semantics where a program is modeled by a set of infinite computation trees modulo bisimulation. We propose and study a safety preorder for this semantics based on simulation and dealing with silent actions. We focus on regular safety properties and characterize them by both treeautomata and formulas of a branching time logic. We show that verifying safety properties on trees reduces to simulation testing.
Logics for unranked trees: an overview
 Logical Methods in Computer Science 2, Issue 3, Paper 2
, 2006
"... Vol. 2 (3:2) 2006, pp. 1–31 www.lmcsonline.org ..."
Monadic SecondOrder Logic, Graph Coverings and Unfoldings of Transition Systems
"... We prove that every monadic secondorder property of the unfolding of a transition system is a monadic secondorder property of the system itself. An unfolding is an instance of the general notion of graph covering. We consider two more instances of this notion. A similar result is possible for ..."
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Cited by 27 (6 self)
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We prove that every monadic secondorder property of the unfolding of a transition system is a monadic secondorder property of the system itself. An unfolding is an instance of the general notion of graph covering. We consider two more instances of this notion. A similar result is possible for one of them but not for the other.
Logical Specifications of Infinite Computations
 A Decade of Concurrency: Reflections and Perspectives, volume 803 of LNCS
, 1993
"... . Starting from an identification of infinite computations with ! words, we present a framework in which different classification schemes for specifications are naturally compared. Thereby we connect logical formalisms with hierarchies of descriptive set theory (e.g., the Borel hierarchy), of recu ..."
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Cited by 20 (2 self)
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. Starting from an identification of infinite computations with ! words, we present a framework in which different classification schemes for specifications are naturally compared. Thereby we connect logical formalisms with hierarchies of descriptive set theory (e.g., the Borel hierarchy), of recursion theory, and with the hierarchy of acceptance conditions of !automata. In particular, it is shown in which sense these hierarchies can be viewed as classifications of logical formulas by the complexity measure of quantifier alternation. In this context, the automaton theoretic approach to logical specifications over !words turns out to be a technique to reduce quantifier complexity of formulas. Finally, we indicate some perspectives of this approach, discuss variants of the logical framework (firstorder logic, temporal logic), and outline the effects which arise when branching computations are considered (i.e., when infinite trees instead of !words are taken as model of computation)...
Relating Hierarchies of Word and Tree Automata
 In Symposium on Theoretical Aspects in Computer Science, LNCS 1373
, 1998
"... For an !word language L, the derived tree language Path(L) is the language of trees having all their paths in L. We consider the hierarchies of deterministic automata on words and nondeterministic automata on trees with Rabin conditions in chain form. We show that L is on some level of the hier ..."
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Cited by 14 (3 self)
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For an !word language L, the derived tree language Path(L) is the language of trees having all their paths in L. We consider the hierarchies of deterministic automata on words and nondeterministic automata on trees with Rabin conditions in chain form. We show that L is on some level of the hierarchy of deterministic word automata iff Path(L) is on the same level of the hierarchy of nondeterministic tree automata. 1
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 programs into "uniform" programs. Our two main results are that uniform programs express regular sets of trees and that emptiness for uniform programs is EXPTIMEcomplete. Hence we have a nontrivial decidable relaxation for the Horn calculus. In a different reading, the results express a kind of robustness of the notion of regularity: alternating Rabin tree automata preserve the same expressiveness and algorithmic complexity if we extend them with pushdown transition rules (in the same way B uchi extended word automata to canonical systems).
A Complete Deductive System for the µCalculus
, 1995
"... The propositional µcalculus as introduced by Kozen in [12] is considered. In that paper ..."
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Cited by 13 (0 self)
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The propositional µcalculus as introduced by Kozen in [12] is considered. In that paper
Automata for the µcalculus and Related Results
, 1995
"... The propositional µcalculus as introduced by Kozen in [4] is considered. The notion of disjunctive formula is defined and it is shown that every formula is semantically equivalent to a disjunctive formula. For these ..."
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Cited by 11 (2 self)
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The propositional µcalculus as introduced by Kozen in [4] is considered. The notion of disjunctive formula is defined and it is shown that every formula is semantically equivalent to a disjunctive formula. For these
Combining temporal logics for querying XML documents
 In International Conference on Database Theory
, 2006
"... Abstract. Close relationships between XML navigation and temporal logics have been discovered recently, in particular between logics LTL and CTL ⋆ and XPath navigation, and between the µcalculus and navigation based on regular expressions. This opened up the possibility of bringing modelchecking t ..."
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Cited by 8 (2 self)
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Abstract. Close relationships between XML navigation and temporal logics have been discovered recently, in particular between logics LTL and CTL ⋆ and XPath navigation, and between the µcalculus and navigation based on regular expressions. This opened up the possibility of bringing modelchecking techniques into the field of XML, as documents are naturally represented as labeled transition systems. Most known results of this kind, however, are limited to Boolean or unary queries, which are not always sufficient for complex querying tasks. Here we present a technique for combining temporal logics to capture nary XML queries expressible in two yardstick languages: FO and MSO. We show that by adding simple terms to the language, and combining a temporal logic for words together with a temporal logic for unary tree queries, one obtains logics that select arbitrary tuples of elements, and can thus be used as building blocks in complex query languages. We present general results on the expressiveness of such temporal logics, study their modelchecking properties, and relate them to some common XML querying tasks. 1