S. Graf and J. Sifakis. A modal characterization of observational congruence on nite terms of CCS. Information and Control, 68:125-145, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... of the Danish National Research Foundation 1 two state transition graphs is usually expressed in terms of a behavioural relation in the linear time branching time spectrum [12] One of the bridges between these two approaches to verification is provided by the notion of characteristic formula [13, 15, 26]. A characteristic formula is a formula in a temporal logic that completely characterizes the behaviour of a (state in a) state transition graph modulo a chosen notion of behavioural relation. Using it, checking whether two state transition graphs A and B are related with respect to a behavioural ....

....we propose constitute a first step towards the application of the model checking approach to implementation verification in the timed setting. A prototype tool based on the theory we present in this study is described in [25] Further Related Work Characteristic formulae were introduced in [13] to relate equational reasoning about processes to reasoning in a modal logic, and therefore to allow proofs about processes to be carried out in a logical framework. The initial research within characteristic formulae concerned terminating processes and bisimulation equivalences, but extensions ....

S. Graf and J. Sifakis, A modal characterization of observational congruence on finite terms of CCS, Information and Control, 68 (1986), pp. 125--145.

....of modelcheckers. In [MO98] we show how modal mu calculus formulas characterising finitestate processes up to bisimulation can be derived directly from the greatest fixpoint characterisations of the bisimulation relations. Our derivation simplifies earlier proofs for the strong bisimulation case [GS86,SI94] and, by virtue of derivation, immediately generalises to various other bisimulation like relations, in particular weak bisimulation and many behavioural preorders. Characteristic formulas allow to apply model checkers for automatically checking equivalence or refinement between finite state ....

Susanne Graf and Joseph Sifakis. A modal characterization of observational congruence on finite terms of CCS. Information and Control, 68:125--145, 1986.

....In another sense, however, the expressiveness of HML is too poor: there is in general no single formula, i.e. no characteristic formula, satisfied by just the processes bisimilar to a given process P . Bisimulation classes are thus only characterized by sets of formulae. Graf and Sifakis [2] show that characteristic formulae can be constructed for finite, i.e. non cyclic, CCS processes in the modal mu calculus, an extension of HML with fixpoint formulae. This result has been extended to finite state processes by Ste#en and Ingolfsdottir [10,11] While Graf and Sifakis considered ....

S. Graf and J. Sifakis. A modal characterization of observational congruence on finite terms of CCS. Information and Control, 68:125--145, 1986.

....literature are given by Glabbeek [vG90] We say that two systems are bisimular, if they have the same behavior, that is, they have the same branching structure. Automata based veri cation techniques and the model checking problem are related to each other by the notion of characteristic formulas [GS86, SI94]. A characteristic formula is a characterization of the behavior of a transition system modulo a given behavioral relation. The problem of verifying whether two systems are bisimular can be reduced to a model checking problem, that is, whether one system satis es the characteristic formula of the ....

S. Graf and J. Sifakis. A modal characterization of observational congruence on nite terms of CCS. Information and Control, 68(1{ 3):125-145, January/February/March 1986.

....theory of CCS and bisimulation has been extensively studied in [Bou85, GS85, HM80, Mil80, Mil81, Mil83, Mil84, Tho89] Mil88] is perhaps the most recent and detailed survey of the theory of CCS. The connections between logic and bisimulation, in particular Hennessy Milner logic, are discussed in [HM85, Mil88, GS86] Other research in the comparison of various kinds of semantics for CCS and related languages can be found in [Abr, AV, GV89] Other researchers have investigated the possibility of understanding bisimulation as a congruence with respect to some extension of CCS. Samson Abramsky [Abr87] gave a ....

Susanne Graf and Joseph Sifakis. A modal characterization of observational congruence on finite terms of CCS. Information and Computation, 68(1--3):125--145, 1986.

....of modelcheckers. In [MO98] we show how modal mu calculus formulas characterising finitestate processes up to bisimulation can be derived directly from the greatest fixpoint characterisations of the bisimulation relations. Our derivation simplifies earlier proofs for the strong bisimulation case [GS86,SI94] and, by virtue of derivation, immediately generalises to various other bisimulation like relations, in particular weak bisimulation and many behavioural preorders. Characteristic formulas allow to apply model checkers for automatically checking equivalence or refinement between finite state ....

Susanne Graf and Joseph Sifakis. A modal characterization of observational congruence on finite terms of CCS. Information and Control, 68:125--145, 1986.

.... automata and the corresponding real time logics: Given a finite automaton, both CTL and the modal calculus are sufficiently expressive that corresponding characteristic formulas may be expressed with respect to a number of behavioural preorders and equivalences (e.g. bisimilarity) [BCG88, GS86, IS94]: i.e. an automaton is related to another in the preorder if and only if the first automaton satisfies the characteristic formula of the second. As characteristic formulas can be automatically constructed in time linear in the size of the argument automaton, this yields a preorder checking method ....

....the truth value of any given L formula with respect to the finite transition system hN Theta R C k ; A[fg; oe 0 ; i corresponding to the extended symbolic semantics of A. 5 Characteristic Properties First let us recall the characteristic formula construction for finite automata 8 [IS94, GS86, BCG88] (see Figure 3) The construction defines the characteristic formula Phi(A) of a node A in terms of similar characteristic formulas of the derivates A 1 : A n of A: whenever A has an a i transition to A i this is reflected in Phi(A) by addition of a conjunct ha i i Phi(A i ) To ....

S. Graf and J. Sifakis. A Modal Characterization of Observational Congruence on Finite Terms of CCS. Information and Control, 68:125--145, 1986. 18

....] n i j=1 A ij ) where A ij is the formula associated with p ij . 2 The following lemma shows that the formula A p associated with a process p characterizes the equivalence class of p with respect to the strong equivalence. The similar result is obtained independently by Graf and Sifakis in [6]. Lemma 3.3 We have the followings for any processes p; p 0 : 1) p j= A p (2) p p 0 = p 0 j= A p (3) p 0 j= A p = p p 0 Proof. 1) By induction on the depth of p, where the depth of a process p is the depth of the tree representation of p. The base case, i.e. p = 0, is clear from ....

Graf S., Sifakis J., A Modal Characterization of Observational Congruence on Finite Terms of CCS, Inf. and Contr., vol.68, pp.125--145, 1986.

....such that s a T t. We write T for the transitive closure of T . A finite behaviour is a state s in a labelled transition system T such that: the set S = fsg[ft j s T tg is finite; and the restriction of T to S is irreflexive. An important property of finite behaviours (cf. [5]) is that, for any such s in T , there exists a formula A (the characteristic formula of s) such that, for any state t in any transition system T 0 , we have that t is bisimilar to s if and only if t fl T 0 A (the existence of A relies on the set of all actions being finite) The GSOS system R ....

S. Graf and J. Sifakis. A modal characterization of observational congruence on finite terms of CCS. Information and Control, 68:125--145, 1986.

....automata. In particular a timed logic L is put forward, which is sufficiently expressive that we for any timed automaton may (effectively) construct a single characteristic L formula uniquely characterizing the automaton up to timed bisimilarity. The construction is a timed extension of those in [5, 12, 16], and reduces timed bisimilarity between automata to a model checking problem, which when combined with the model checking algorithm for L yields an alternative algorithm for timed bisimulation compared with [6] In addition, characteristic formula constructions may be given for other ....

....since, given 2 L , it suffices to check the truth value of any given L formula with respect to a finite transition system corresponding to the extended symbolic semantics of A. 5 Characteristic Properties First let us recall the characteristic formula construction for finite automata [16, 12, 5] (see Figure 3) The construction defines the characteristic formula Phi(A) of a node A in terms of similar characteristic formulas of the derivates A 1 : An of A: whenever A has an a i transition to A i this is reflected in Phi(A) by addition of a conjunct ha i i Phi(A i ) To ....

S. Graf and J. Sifakis. A Modal Characterization of Observational Congruence on Finite Terms of CCS. Information and Control, 68:125--145, 1986.

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S. Graf and J. Sifakis. A modal characterization of observational congruence on nite terms of CCS. Information and Control, 68:125-145, 1986.

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S. Graf and J. Sifakis. A modal characterization of observational congruence on nite terms of CCS. Information and Control, 68:125{ 145, 1986. 40

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S. Graf and J. Sifakis. A modal characterization of observational congruence on nite terms of CCS. Information and Control, 68:125-145, 1986.

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