ion Rule (KFAR) (Baeten, Bergstra & Klop [3]), expresses a global fairness assumption. It says that when possible a system will escape from any cycle of internal actions. Some form of KFAR is crucial for many protocal verifications with unreliable channels, and for that reason preorders and equivalences that satisfy KFAR are of special interest. Must preorders and divergence sensitive ones cannot satisfy KFAR. In Bergstra, Klop & Olderog [7] it is shown that the combination of KFAR with failure semantics is inconsistent, but they formulate a weaker version of KFAR that is satisfied in failure may-semantics. Still the combination of KFAR \Gamma and the liveness requirement appears to require global testing, and is only satisfied in the semantics between contrasimulation (C) and stability respecting branching bisimulation (BB s ). These requirements would reduce the number of suitable preorders to 18. It is in general a good strategy to do your verifications using the finest preorde...

This paper presents various semantics in the branching-time spectrum of discrete-time and continuous-time Markov chains (DTMCs and CTMCs). Strong and weak bisimulation equivalence and simulation pre-orders are covered and are logically characterised in terms of the temporal logics PCTL (Probabilistic Computation Tree Logic) and CSL (Continuous Stochastic Logic). Apart from presenting various existing branching-time relations in a uniform manner, this paper presents the following new results: (i) strong simulation for CTMCs, (ii) weak simulation for CTMCs and DTMCs, (iii) logical characterizations thereof (including weak bisimulation for DTMCs), (iv) a relation between weak bisimulation and weak simulation equivalence, and (v) various connections between equivalences and pre-orders in the continuous- and discrete-time setting. The results are summarized in a branching-time spectrum for DTMCs and CTMCs elucidating their semantics as well as their relationship. Key Words: comparative semantics, Markov chain, (weak) simulation, (weak) bisimulation, temporal logic

This paper is concerned with bisimulation relations which do not only require related agents to simulate each others behavior in the direction of the arrows, but also to simulate each other when going back in history. First it is demonstrated that the back and forth variant of strong bisimulation leads to the same equivalence as the ordinary notion of strong bisimulation. Then it is shown that the back and forth variant of Milner's observation equivalence is different from (and finer than) observation equivalence. In fact we prove that it coincides with the branching bisimulation equivalence of Van Glabbeek & Weijland. Also the back and forth variants of branching, ~ and delay bisimulation lead to branching bisimulation equivalence. The notion of back and forth bisimulation moreover leads to characterizations of branching bisimulation in terms of abstraction homomorphisms and in terms of Hencessy-Milner logic with backward modalities. In our view these results support the claim that branching bisimulation is a natural and important notion. The notion of bisimulation relation has been introduced by PARK [18]. It leads to an equivalence on labelled transition systems which, in case image finiteness is assumed, coincides with the strong equivalence of ~IILNER [12]. The great importance and usefulness of bisimulalions

The language CRL allows to specify processes with data and to reason with them in an algebraic vein. This allows to express and reason about global correctness of systems. Sometimes, one only needs to analyse particular properties of CRL-processes. Modal logics are very convenient toexpressandverify such properties. Therefore, we de ne a modal logic for CRL. It is a branching time modal logic based on actions. It has future and past operators and it allows for reasoning about data, for instance using rst order quanti cation over data variables. It is shown that these modal formulae cannot distinguish between divergence sensitive branching bisimilar processes. The rst author is partly supported by the Netherlands Computer Science Research Foundation (SION) with nancial support of the Netherlands Organisation for Scienti c Research (NWO).

We present two modal logics, interpreted over prime event structures without silent moves, that characterize history-preserving bisimulation. That is, two event structures satisfy the same formulae iff they are history-preserving bisimilar. These logics use past-tense modalities and pomsets observations. Though quite different in form and spirit, the two logics turn out to have the same expressive power, in the sense that there exists a two-way translation between them. Keywords: Semantics of concurrency, modal logics for true concurrency, expressivity of modal logics. Introduction During the past decade, partial order semantics have been studied in depth as a promising approach to the semantic aspects of reactive systems [Gra81, GR83, Pra86]. In particular, causality-based models enable one to formalize interesting features of systems' behaviors for which concurrency is no longer identified with sequential non-determinism as it is in interleaving models. As it has been pointed out [...

The language µCRL allows to specify processes with data and to reason with them in an algebraic vein. This allows to express and reason about global correctness of systems. Sometimes, one only needs to analyse particular properties of µCRL-processes. Modal logics are very convenient to express and verify such properties. Therefore, we define a modal logic for µCRL. It is a branching time modal logic based on actions. It has future and past operators and it allows for reasoning about data, for instance using first order quantification over data variables. It is shown that these modal formulae cannot distinguish between divergence sensitive branching bisimilar processes.

dan garanderen dat er precies 'e'en token wordt gecreeerd. Bij het ontwerp van het algoritme zijn de volgende aannames gemaakt: 1 ffl Er zijn n processen, A 0 ; : : : ; A n\Gamma1 . Deze processen zijn allemaal identiek, alleen heeft ieder process A i bij aanvang van het algoritme een unieke waarde id i , afkomstig uit een oneindige, totaal geordende verzameling D. ffl De individuele processen weten niet hoeveel andere processen er zich in de ring bevinden. ffl Processen kunnen communiceren met hun buren in de ring door het versturen van boodschappen. Communicatie tussen processen is asynchroon, d.w.z. verloopt via een FIFO kanaal, en vindt uitsluitend plaats in 'e'en richting (zeg met de klok mee). In het algoritme is ieder proces hetzij actief, hetzij in doorgeeftoestand

This paper describes a technique for generating diagnostic information for the timed bisimulation equivalence and the timed simulation preorder. More precisely,