Revisiting Interactive Markov Chains

Abstract The usage of process algebras for the performance modeling and evaluation of concurrent systems turned out to be convenient due to their feature of compositionality. A particularly simple and elegant solution in this field is the calculus of Interactive Markov Chains (IMCs), where the behavior of processes is just represented by Continuous Time Markov Chains extended with action transitions representing process interaction. The main advantage of IMCs with respect to other existing approaches is that a notion of bisimulation which abstracts from τ-transitions ("complete" interactions) can be defined which is a congruence. However in the original definition of the calculus of IMCs the high potentiality of compositionally minimizing the system state space given by the usage of a "weak" notion of equivalence and the elegance of the approach is somehow limited by the fact that the equivalence adopted over action transitions is a finer variant of Milner's observational congruence that distinguishes τ-divergent "Zeno" processes from non-divergent ones. In this paper we show that it is possible to reformulate the calculus of IMCs in such a way that we can just rely on simple standard observational congruence. Moreover we show that the new calculus is the first Markovian process algebra allowing for a new notion of Markovian bisimulation equivalence which is coarser than the standard one

Extensions of Standard Weak Bisimulation Machinery: Finite-state General Processes, Refinable Actions, Maximal-progress and Time

AbstractWe present our work on extending the standard machinery for weak bisimulation to deal with: finite-state processes of calculi with a full signature, including static operators like parallel; semantic action refinement and ST bisimulation; maximal-progress, i.e. priority of standard actions over unprioritized actions; representation of time: discrete real-time and Markovian stochastic time. For every such topic we show that it is possible to resort simply to weak bisimulation and that we can exploit this to obtain, via modifications to the standard machinery: finite-stateness of semantic models when static operators are not replicable by recursion, as for CCS with the standard semantics, thus yielding decidability of equivalence; structural operational semantics for terms; a complete axiomatization for finite-state processes via a modification of the standard theory of standard equation sets and of the normal-form derivation procedure

An Integrated Approach for the Specification and Analysis of Stochastic Real-Time Systems

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Non-determinism in Probabilistic Timed Systems with General Distributions

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Axiomatizing ST Bisimulation for a Process Algebra with Recursion and Action Refinement (Extended Abstract)

AbstractDue to the complex nature of bisimulation equivalences which express some form of history dependence, it turned out to be problematic to axiomatize them for non trivial classes of systems. Here we introduce the idea of "compositional level-wise renaming" which gives rise to the new possibility of axiomatizing the class of history dependent bisimulations with slight modifications to the machinery for standard bisimulation. We propose two techniques, which are based on this idea, in the special case of the ST semantics, defined for terms of a process algebra with recursion. The first technique, which is more intuitive, is based on dynamic names, allowing weak ST bisimulation to be decided and axiomatized for all processes that possess a finite state interleaving semantics. The second technique, which is based on pointers, preserves the possibility of deciding and axiomatizing weak ST bisimulation also when an action refinement operator P[a Q] is considered

Compositional Asymmetric Cooperations for Process Algebras with Probabilities, Priorities, and Time

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Adaptable processes

We propose the concept of adaptable processes as a way of overcoming the limitations that process calculi have for describing patterns of dynamic process evolution. Such patterns rely on direct ways of controlling the behavior and location of running processes, and so they are at the heart of the adaptation capabilities present in many modern concurrent systems. Adaptable processes have a location and are sensible to actions of dynamic update at runtime; this allows to express a wide range of evolvability patterns for concurrent processes. We introduce a core calculus of adaptable processes and propose two verification problems for them: bounded and eventual adaptation. While the former ensures that the number of consecutive erroneous states that can be traversed during a computation is bound by some given number k, the latter ensures that if the system enters into a state with errors then a state without errors will be eventually reached. We study the (un)decidability of these two problems in several variants of the calculus, which result from considering dynamic and static topologies of adaptable processes as well as different evolvability patterns. Rather than a specification language, our calculus intends to be a basis for investigating the fundamental properties of evolvable processes and for developing richer languages with evolvability capabilities

Reduction Semantics in Markovian Process Algebra

International audienceMarkovian process algebras allow for performance analysis by automatic generation of Continuous Time Markov Chains. The inclusion of exponential distribution rate information in process algebra terms, however, causes non trivial issues to arise in the definition of their semantics. As a consequence, technical settings previously considered do not make it possible to base Markovian semantics on directly computing reductions between communicating processes: this would require the ability to readjust processes, i.e. a commutative and associative parallel operator and a congruence relation on terms enacting such properties. Semantics in reduction style is, however, often used for complex languages, due to its simplicity and conciseness. In this paper we introduce a new technique based on stochastic binders that allows us to define Markovian semantics in the presence of such a structural congruence. As application examples, we define the reduction semantics of Markovian versions of the π-calculus, considering both the cases of Markovian durations: being additional standalone prefixes (as in Interactive Markov Chains) and being, instead, associated to standard synchro-nizable actions, giving them a duration (as in Stochastic π-calculus). Notably, in the latter case, we obtain a "natural" Markovian semantics for π-calculus (CCS) parallel that preserves, for the first time, its associativity. In both cases we show our technique for defining reduction semantics to be correct with respect to the standard Markovian one (in labeled style) by providing Markovian extensions of the classical π-calculus Harmony theorem