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Bisimulation is not Finitely (First Order) Equationally Axiomatisable
 in Proceedings 9 th Annual Symposium on Logic in Computer Science
, 1994
"... This paper considers the existence of finite equational axiomatisations of bisimulation over a calculus of finite state processes. To express even simple properties such as ¯XE = ¯XE[E=X] equationally it is necessary to use some notation for substitutions. Accordingly the calculus is embedded in a s ..."
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This paper considers the existence of finite equational axiomatisations of bisimulation over a calculus of finite state processes. To express even simple properties such as ¯XE = ¯XE[E=X] equationally it is necessary to use some notation for substitutions. Accordingly the calculus is embedded in a simply typed lambda calculus, allowing axioms such as the above to be written as equations of higher type rather than as equation schemes. Notions of higher order transition system and bisimulation are then defined and using them the nonexistence of finite axiomatisations containing at most first order variables is shown. The same technique is then applied to calculi of star expressions containing a zero process  in contrast to the positive result given in [FZ93] for BPA ? , which differs only in that it does not contain a zero. 1 Introduction In this paper we consider the existence of finite equational axiomatisations for bisimulation over finite state processes. Such questions of axio...
Decidability Issues for InfiniteState Processes  a Survey
, 1996
"... ... In this paper we survey recent developments and current trends within a new field of study within process algebra, namely that of decidability issues for processes with infinite transition graphs. ..."
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... In this paper we survey recent developments and current trends within a new field of study within process algebra, namely that of decidability issues for processes with infinite transition graphs.
Initial Algebras of Terms, with binding and algebraic structure
, 2013
"... Abstract. One of the many results which makes Joachim Lambek famous is: an initial algebra of an endofunctor is an isomorphism. This fixed point result is often referred to as “Lambek’s Lemma”. In this paper, we illustrate the power of initiality by exploiting it in categories of algebravalued pres ..."
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Abstract. One of the many results which makes Joachim Lambek famous is: an initial algebra of an endofunctor is an isomorphism. This fixed point result is often referred to as “Lambek’s Lemma”. In this paper, we illustrate the power of initiality by exploiting it in categories of algebravalued presheaves EM(T)N, for a monad T on Sets. The use of presheaves to obtain certain calculi of expressions (with variable binding) was introduced by Fiore, Plotkin, and Turi. They used setvalued presheaves, whereas here the presheaves take values in a category EM(T) of EilenbergMoore algebras. This generalisation allows us to develop a theory where more structured calculi can be obtained. The use of algebras means also that we work in a linear context and need a separate operation! for replication, for instance to describe strength for an endofunctor on EM(T). We apply the resulting theory to give systematic descriptions of nontrivial calculi: we introduce nondeterministic and weighted lambda terms and expressions for automata as initial algebras, and we formalise relevant equations diagrammatically. 1
A specification language for Reo connectors
"... Abstract. Recent approaches to componentbased software engineering employ coordinating connectors to compose components into software systems. Reo is a model of component coordination, wherein complex connectors are constructed by composing various types of primitive channels. Reo automata are ..."
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Abstract. Recent approaches to componentbased software engineering employ coordinating connectors to compose components into software systems. Reo is a model of component coordination, wherein complex connectors are constructed by composing various types of primitive channels. Reo automata are a simple and intuitive formal model of context dependent connectors, which provided a compositional semantics for Reo. In this paper, we study Reo automata from a coalgebraic perspective. This enables us to apply the recently developed coalgebraic theory of generalized regular expressions in order to derive a specification language, tailormade for Reo automata, and sound and complete axiomatizations with respect to three distinct notions of equivalence: (coalgebraic) bisimilarity, the bisimulation notion studied in the original papers on Reo automata and trace equivalence. The obtained language is simple, but nonetheless expressive enough to specify all possible finite Reo automata. Moreover, it comes equipped with a Kleenelike theorem: we provide algorithms to translate expressions to Reo automata and, conversely, to compute an expression equivalent to a state in a Reo automaton. 1