Results 1  10
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15
A Logical Study of Distributed Transition Systems
, 1995
"... We extend labelled transition systems to distributed transition systems by labelling the transition relation with a finite set of actions, representing the fact that the actions occur as a concurrent step. We design an actionbased temporal logic in which one can explicitly talk about steps. The log ..."
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Cited by 29 (5 self)
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We extend labelled transition systems to distributed transition systems by labelling the transition relation with a finite set of actions, representing the fact that the actions occur as a concurrent step. We design an actionbased temporal logic in which one can explicitly talk about steps. The logic is studied to establish a variety of positive and negative results in terms of axiomatizability and decidability. Our positive results show that the step notion is amenable to logical treatment via standard techniques. They also help us to obtain a logical characterization of two well known models for distributed systems: labelled elementary net systems and labelled prime event structures. Our negative results show that demanding deterministic structures when dealing with a "noninterleaved " notion of transitions is, from a logical standpoint, very expressive. They also show that another well known model of distributed systems called asynchronous transition systems exhibits a surprising a...
Algebraiccoalgebraic specification in CoCasl
 J. LOGIC ALGEBRAIC PROGRAMMING
, 2006
"... We introduce CoCasl as a simple coalgebraic extension of the algebraic specification language Casl. CoCasl allows the nested combination of algebraic datatypes and coalgebraic process types. We show that the wellknown coalgebraic modal logic can be expressed in CoCasl. We present sufficient criter ..."
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Cited by 19 (8 self)
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We introduce CoCasl as a simple coalgebraic extension of the algebraic specification language Casl. CoCasl allows the nested combination of algebraic datatypes and coalgebraic process types. We show that the wellknown coalgebraic modal logic can be expressed in CoCasl. We present sufficient criteria for the existence of cofree models, also for several variants of nested cofree and free specifications. Moreover, we describe an extension of the existing proof support for Casl (in the shape of an encoding into higherorder logic) to CoCasl.
Fixpoint Alternation: Arithmetic, Transition Systems, and the Binary Tree
, 1998
"... We provide an elementary proof of the xpoint alternation hierarchy in arithmetic, which in turn allows us to simplify the proof of the modal mucalculus alternation hierarchy. ..."
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Cited by 13 (1 self)
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We provide an elementary proof of the xpoint alternation hierarchy in arithmetic, which in turn allows us to simplify the proof of the modal mucalculus alternation hierarchy.
Sequent Calculi for Process Verification: HennessyMilner Logic for an Arbitrary GSOS
, 2003
"... We argue that, by supporting a mixture of “compositional” and “structural” styles of proof, sequentbased proof systems provide a useful framework for the formal verification of processes. As a worked example, we present a sequent calculus for establishing that processes from a process algebra satis ..."
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Cited by 11 (1 self)
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We argue that, by supporting a mixture of “compositional” and “structural” styles of proof, sequentbased proof systems provide a useful framework for the formal verification of processes. As a worked example, we present a sequent calculus for establishing that processes from a process algebra satisfy assertions in HennessyMilner logic. The main novelty lies in the use of the operational semantics to derive introduction rules, on the left and right of sequents, for the operators of the process calculus. This gives a generic proof system applicable to any process algebra with an operational semantics specified in the GSOS format. Using a general algebraic notion of GSOS model, we prove a completeness theorem for the cutfree fragment of the proof system, thereby establishing the admissibility of the cut rule. Under mild (and necessary) conditions on the process algebra, an ωcompleteness result, relative to the “intended” model of closed process terms, follows.
Enhanced propositional dynamic logic for reasoning about concurrent actions (extended abstract
 In Working notes of the AAAI 1995 Spring Symposium on Extending Theories of Action: Formal and Practical Applications
, 1995
"... This paper presents a work in progress on enhanced Propositional Dynamic Logics for reasoning about actions. Propositional Dynamic Logics (PDL's) are modal logics for describing and reasoning about system ..."
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Cited by 10 (6 self)
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This paper presents a work in progress on enhanced Propositional Dynamic Logics for reasoning about actions. Propositional Dynamic Logics (PDL's) are modal logics for describing and reasoning about system
Enriched µ–calculus pushdown module checking
 In LPAR’07, volume 4790 of LNAI
, 2007
"... Abstract. The model checking problem for open systems (called module checking) has been intensively studied in the literature, both for finite–state and infinite–state systems. In this paper, we focus on pushdown module checking with respect to decidable fragments of the fully enriched µ–calculus. W ..."
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Cited by 7 (4 self)
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Abstract. The model checking problem for open systems (called module checking) has been intensively studied in the literature, both for finite–state and infinite–state systems. In this paper, we focus on pushdown module checking with respect to decidable fragments of the fully enriched µ–calculus. We recall that finite–state module checking with respect to fully enriched µ–calculus is undecidable and hence the extension of this problem to pushdown systems remains undecidable as well. On the contrary, for the fragments of the fully enriched µ–calculus we consider here, we show that pushdown module checking is decidable and solvable in double–exponential time in the size of the formula and in exponential time in the size of the system. This result is obtained by exploiting a classical automata–theoretic approach via pushdown nondeterministic parity tree automata. In particular, we reduce in exponential time our problem to the emptiness problem for these automata, which is known to be decidable in Exptime. As a key step of our algorithm, we show an exponential improvement of the construction of a nondeterministic parity tree automaton accepting all models of a formula of the considered logic. This result, does not only allow our algorithm to match the known lower bound, but also to investigate decision problems related to the fragments of the enriched µcalculus in a greatly simplified manner. 1
Model checking FTA
 FME 2003: Formal Methods, LNCS 2805
, 2003
"... Abstract. Safety is increasingly important for software based, critical systems. Fault tree analysis (FTA) is a safety technique from engineering, developed for analyzing and assessing system safety by uncovering safety flaws and weaknesses of the system. The main drawback of this analysis technique ..."
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Cited by 5 (3 self)
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Abstract. Safety is increasingly important for software based, critical systems. Fault tree analysis (FTA) is a safety technique from engineering, developed for analyzing and assessing system safety by uncovering safety flaws and weaknesses of the system. The main drawback of this analysis technique is, that it is based on informal grounds, so safety flaws may be overlooked. This is an issue, where formal proofs can help. They are a safety techniques from software engineering, which are based on precise system descriptions and allow to prove consistency and other (safety) properties. We present an approach which automatically proves the consistency of fault trees based on a formal model by model checking. Therefore, we define consistency conditions in Computational Tree Logic, a widely used input language for model checkers. In the second part, we exemplify our approach with a case study from the Fault Tree Handbook.
The DAGWidth of Directed Graphs
, 2009
"... Treewidth is a wellknown metric on undirected graphs that measures how treelike a graph is and gives a notion of graph decomposition that proves useful in algorithm development. Treewidth can be characterised by a graph searching game where a number of cops attempt to capture a robber. We consid ..."
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Cited by 5 (0 self)
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Treewidth is a wellknown metric on undirected graphs that measures how treelike a graph is and gives a notion of graph decomposition that proves useful in algorithm development. Treewidth can be characterised by a graph searching game where a number of cops attempt to capture a robber. We consider the natural adaptation of this game to directed graphs and show that monotone strategies in the game yield a measure that can be seen to describe how close a directed graph is to a directed acyclic graph (DAG). We also provide an associated decomposition and show how it is useful for developing algorithms on directed graphs. In particular, we show that the problem of determining the winner of a parity game is solvable in polynomial time on graphs of bounded DAGwidth. We also consider the relationship between DAGwidth and other measures of connectivity such as entanglement and directed treewidth. One consequence we obtain is that certain NPcomplete problems such as Hamiltonicity and disjoint paths are polynomialtime computable on graphs of bounded DAGwidth.
ENRICHED µ–CALCULI MODULE CHECKING
"... Abstract. The model checking problem for open systems has been widely studied in the literature, for both finite–state (module checking) and infinite–state (pushdown module checking) systems, with respect to CTL and CTL ∗. In this paper, we further investigate this problem with respect to the µcalc ..."
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Cited by 4 (3 self)
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Abstract. The model checking problem for open systems has been widely studied in the literature, for both finite–state (module checking) and infinite–state (pushdown module checking) systems, with respect to CTL and CTL ∗. In this paper, we further investigate this problem with respect to the µcalculus enriched with nominals and graded modalities (hybrid graded µcalculus), in both the finite–state and infinitestate settings. Using an automatatheoretic approach, we show that hybrid graded µcalculus module checking is solvable in exponential time, while hybrid graded µcalculus pushdown module checking is solvable in doubleexponential time. These results are also tight since they match the known lower bounds for CTL. We also investigate the module checking problem with respect to the hybrid graded µcalculus enriched with inverse programs (Fully enriched µcalculus): by showing a reduction from the tiling problem, we show its undecidability. We conclude with a short overview of the model checking problem for the Fully enriched µcalculus and the fragments obtained by dropping at least one of the additional constructs. 1.