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Temporal and modal logic
 HANDBOOK OF THEORETICAL COMPUTER SCIENCE
, 1995
"... We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic. ..."
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
OntheFly Symbolic Model Checking for RealTime Systems
 IN PROC. OF THE 18TH IEEE REALTIME SYSTEMS SYMPOSIUM
, 1997
"... This paper presents an onthefly and symbolic algorithm for checking whether a timed automaton satisfies a formula of a timed temporal logic which is more expressive than TCTL. The algorithm is onthefly in the sense that the statespace is generated dynamically and only the minimal amount of info ..."
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Cited by 37 (9 self)
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This paper presents an onthefly and symbolic algorithm for checking whether a timed automaton satisfies a formula of a timed temporal logic which is more expressive than TCTL. The algorithm is onthefly in the sense that the statespace is generated dynamically and only the minimal amount of information required by the verification procedure is stored in memory. The algorithm is symbolic in the sense that it manipulates sets of states, instead of states, which are represented as boolean combinations of linear inequalities of clocks. We show how a prototype implementation of our algorithm has improved the performances of the tool KRONOS for the verification of the FDDI protocol.
Counting on CTL*: On the Expressive Power of Monadic Path Logic
, 2003
"... Monadic secondorder logic (MSOL) provides a general framework for expressing properties of reactive systems as modelled by trees. Monadic path logic (MPL) is obtained by restricting secondorder quantification to paths reflecting computation sequences. In this paper we show that the expressive powe ..."
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Cited by 21 (1 self)
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Monadic secondorder logic (MSOL) provides a general framework for expressing properties of reactive systems as modelled by trees. Monadic path logic (MPL) is obtained by restricting secondorder quantification to paths reflecting computation sequences. In this paper we show that the expressive power of MPL over trees coincides with the usual branching time logic CTL # embellished with a simple form of counting. As a corollary, we derive an earlier result that CTL # coincides with the bisimulationinvariant properties of MPL. In order to prove the main result, we first prove a new Composition Theorem for trees.
Model Checking for Extended Timed Temporal Logics (extended abstract)
 In FTRTFT'96, LNCS 1135
, 1996
"... We introduce the realtime temporal logic BTATL p which is obtained by extending CTL with both past operators and timed automata constraints. These operators allow to express that, given a run of the system, the finite segment between the current state and some designated previous or future state o ..."
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Cited by 16 (7 self)
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We introduce the realtime temporal logic BTATL p which is obtained by extending CTL with both past operators and timed automata constraints. These operators allow to express that, given a run of the system, the finite segment between the current state and some designated previous or future state of the run is accepted by a given timed automaton. Considering together past operators and automata constraints allows expressing timing requirements in a simple and natural way. Modelchecking for full BTATL p is undecidable. Fortunately, there exist significant (both lineartime and branchingtime) fragments for which the verification problem is decidable. In particular, we identify a sublogic of BTATL p , which is more expressive than TCTL, and for which modelchecking can be effectively done. The practical interest of this logic is illustrated through the example of the Philips audio protocol. To appear in FTRTFT'96, Uppsala, Sweden, Sep 1113, 1996. y Verimag, MiniparcZirst, Rue Lavoisier, 38330 Montbonnot StMartin, France. z Institut fur Informatik und Praktische Mathematik ChristianAlbrechtsUniversitat zu Kiel, Preuerstr. 19, D24105 Kiel, Germany. x Ahmed.Bouajjani@imag.fr, yl@informatik.unikiel.d400.de, Sergio.Yovine@imag.fr 0 1
How Big Must Complete XML Query Languages Be?
"... Marx and de Rijke have shown that the navigational core of the w3c XML query language XPath is not firstorder complete – that is it cannot express every query definable in firstorder logic over the navigational predicates. How can one extend XPath to get a firstorder complete language? Marx has sh ..."
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Marx and de Rijke have shown that the navigational core of the w3c XML query language XPath is not firstorder complete – that is it cannot express every query definable in firstorder logic over the navigational predicates. How can one extend XPath to get a firstorder complete language? Marx has shown that Conditional XPath – an extension of XPath with an “Until ” operator – is first order complete. The completeness argument makes essential use of the presence of upward axes in Conditional XPath. We examine whether it is possible to get “forwardonly ” languages that are firstorder complete for XML Boolean queries. It is easy to see that a variant of the temporal logic CTL ∗ is firstorder complete; the variant has path quantifiers for downward, leftward and rightward paths, while along a path one can check arbitrary formulas of linear temporal logic (LTL). This language has two major disadvantages: it requires path quantification in both horizontal directions (in particular, it requires looking backward at the prior siblings of a node), and it requires the consideration of formulas of LTL of arbitrary complexity on vertical paths. This last is in contrast with Marx’s Conditional XPath, which requires only the checking of a single Until operator on a path. We investigate whether either of these restrictions can be eliminated. Our main results are negative ones. We show that if we restrict our CTL ∗ language by having an until operator in only one horizontal direction, then we lose completeness. We also show that no restriction to a “small ” subset of LTL along vertical paths is sufficient for first order completeness. Smallness here means of bounded “Until Depth”, a measure of complexity of LTL formulas defined by Etessami and Wilke. In particular, it follows from our work that Conditional XPath with only forward axes is not expressively complete; this extends results proved by Rabinovich and Maoz in the context of infinite unordered trees.