Prefix iteration is a variation on the original binary version of the Kleene star operation P ∗Q, obtained by restricting the first argument to be an atomic action. Aceto and Ingólfsdóttir provided an axiom system for observation congruence over basic CCS with prefix iteration. However hitherto the only direct completeness proof given for such a system is very long and technical. In this paper,...

In 1990, we published the following result: Let m be a regular cardinal > א0. Every m-algebraic lattice L can be represented as the lattice of m-complete congruence relations of an m-complete modular lattice K. In this note, we present a short proof of this theorem. In fact, we present a significant improvement: The lattice K we construct is 2-distributive.

Stochastic Process Algebras (SPA) are process algebras in which the duration of each activity is given by a random variable. If the stochastic aspect is restricted to Markovian, i.e. exponentially distributed durations, nice algebraic foundations are available. They include a formal semantics and an equational theory for Markovian bisimulation , a congruence that can be seen as a stochastic cou...

We show that the problems of checking π-Calculus structural congruence (πSC) and graph isomorphism (GI) are Karp reducible to each other. The reduction from GI to πSC is given explicitly, and the reduction in the opposite direction proceeds by transforming πSC into an instance of the term equality problem (i.e., the problem of deciding equivalence of two terms in the presence of associative and...

This paper introduces the counterpart of strong bisimilarity for labelled transition systems extended with time-out transitions. It supports this concept through a modal characterisation, congruence results standard process algebra recursion, and complete axiomatisation.

Complete lattices and closure operators in ordered sets are considered from the point of view of fuzzy logic. A typical example of a fuzzy order is the graded subsethood of fuzzy sets. Graded subsethood makes the set of all fuzzy sets in a given universe into a completely lattice fuzzy ordered set (i.e. a complete lattice in fuzzy setting). Another example of a completely lattice fuzzy ordered ...

This paper studies the complexity of determining if a finite algebra generates a variety that satisfies various Maltsev conditions, such as congruence distributivity or modularity. For idempotent algebras we show that there are polynomial time algorithms to test for these conditions but that in general these problems are EXPTIME complete. In addition, we provide sharp bounds in terms of the siz...

It is well known that bisimulation on μ-expressions cannot be finitely axiomatised in equational logic. Complete axiomatisations such as those of Milner and Bloom/Ésik necessarily involve implicational rules. However, both systems rely on features which go beyond pure equational Horn logic: either the rules are impure by involving non-equational side-conditions, or they are schematically infini...

It is well known that bisimulation on μ-expressions cannot be finitely axiomatised in equational logic. Complete axiomatisations such as those of Milner and Bloom/Ésik necessarily involve implicational rules. However, both systems rely on features beyond pure equational Horn logic: either rules that are impure by involving non-equational side-conditions, or rules that are schematically infinita...

We have previously introduced Generalized Semi-Markovian Process Algebra (GSMPA), a process algebra based on ST semantics which is capable of expressing durational actions, where durations are expressed by general probability distributions. In this paper we introduce the calculus of Interactive Generalized Semi-Markov Processes (IGSMP), a variant of GSMPA where synchronizable actions are restri...