Split-2 Bisimilarity has a Finite Axiomatization over CCS with<br> Hennessy&#39;s Merge

This note shows that split-2 bisimulation equivalence (also known as timed equivalence) affords a finite equational axiomatization over the process algebra obtained by adding an auxiliary operation proposed by Hennessy in 1981 to the recursion, relabelling and restriction free fragment of Milner's Calculus of Communicating Systems. Thus the addition of a single binary operation, viz. Hennessy's merge, is sufficient for the finite equational axiomatization of parallel composition modulo this non-interleaving equivalence. This result is in sharp contrast to a theorem previously obtained by the same authors to the effect that the same language is not finitely based modulo bisimulation equivalence

The agent programming language meta-APL

Abstract. We describe a novel agent programming language, Meta-APL, and give its operational semantics. Meta-APL allows both agent programs and their associated deliberation strategy to be encoded in the same programming language. We define a notion of equivalence between programs written in different agent programming languages based on the notion of weak bisimulation equivalence. We show how to simulate (up to this notion of equivalence) programs written in other agent programming languages by programs of Meta-APL. This involves translating both the agent program and the deliberation strategy under which it is executed into Meta-APL.

When Are Two Workflows the Same?

In the area of workflow management, one is confronted with a large number of competing languages and the relations between them (e.g. relative expressiveness) are usually not clear. Moreover, even within the same language it is generally possible to express the same workflow in different ways, a feature known as variability. This paper aims at providing some of the formal groundwork for studying relative expressiveness and variability by defining notions of equivalence capturing different views on how workflow systems operate. Firstly, a notion of observational equivalence in the absence of silent steps is defined and related to classical bisimulation. Secondly, a number of equivalence notions in the presence of silent steps are defined. A distinction is made between the case where silent steps are visible (but not controllable) by the environment and the case where silent steps are not visible, i.e., there is an alternation between system events and environment interactions. It is shown that these notions of equivalence are different and do not coincide with classical notions of bisimulation with silent steps (e.g. weak and branching)

Behavioural equivalences for timed systems

Timed transition systems are behavioural models that include an explicit treatment of time flow and are used to formalise the semantics of several foundational process calculi and automata. Despite their relevance, a general mathematical characterisation of timed transition systems and their behavioural theory is still missing. We introduce the first uniform framework for timed behavioural models that encompasses known behavioural equivalences such as timed bisimulations, timed language equivalences as well as their weak and time-abstract counterparts. All these notions of equivalences are naturally organised by their discriminating power in a spectrum. We prove that this result does not depend on the type of the systems under scrutiny: it holds for any generalisation of timed transition system. We instantiate our framework to timed transition systems and their quantitative extensions such as timed probabilistic systems

Bisimulation of Labelled State-to-Function Transition Systems Coalgebraically

Labeled state-to-function transition systems, FuTS for short, are characterized by transitions which relate states to functions of states over general semirings, equipped with a rich set of higher-order operators. As such, FuTS constitute a convenient modeling instrument to deal with process languages and their quantitative extensions in particular. In this paper, the notion of bisimulation induced by a FuTS is addressed from a coalgebraic point of view. A correspondence result is established stating that FuTS-bisimilarity coincides with behavioural equivalence of the associated functor. As generic examples, the equivalences underlying substantial fragments of major examples of quantitative process algebras are related to the bisimilarity of specific FuTS. The examples range from a stochastic process language, PEPA, to a language for Interactive Markov Chains, IML, a (discrete) timed process language, TPC, and a language for Markov Automata, MAL. The equivalences underlying these languages are related to the bisimilarity of their specific FuTS. By the correspondence result coalgebraic justification of the equivalences of these calculi is obtained. The specific selection of languages, besides covering a large variety of process interaction models and modelling choices involving quantities, allows us to show different classes of FuTS, namely so-called simple FuTS, combined FuTS, nested FuTS, and general FuTS

Some Remarks on the Model Theory of Epistemic Plausibility Models

Classical logics of knowledge and belief are usually interpreted on Kripke models, for which a mathematically well-developed model theory is available. However, such models are inadequate to capture dynamic phenomena. Therefore, epistemic plausibility models have been introduced. Because these are much richer structures than Kripke models, they do not straightforwardly inherit the model-theoretical results of modal logic. Therefore, while epistemic plausibility structures are well-suited for modeling purposes, an extensive investigation of their model theory has been lacking so far. The aim of the present paper is to fill exactly this gap, by initiating a systematic exploration of the model theory of epistemic plausibility models. Like in 'ordinary' modal logic, the focus will be on the notion of bisimulation. We define various notions of bisimulations (parametrized by a language L) and show that L-bisimilarity implies L-equivalence. We prove a Hennesy-Milner type result, and also two undefinability results. However, our main point is a negative one, viz. that bisimulations cannot straightforwardly be generalized to epistemic plausibility models if conditional belief is taken into account. We present two ways of coping with this issue: (i) adding a modality to the language, and (ii) putting extra constraints on the models. Finally, we make some remarks about the interaction between bisimulation and dynamic model changes.Comment: 19 pages, 3 figure