This paper shows that a finitely presented monoid with linear Dehn function need not have a regular cross-section, strengthening the previously-known result that such a monoid need not be presented by a finite complete string rewriting system, and contrasting the fact that finitely presented groups with linear Dehn function always have regular cross-sections.

Let S be a monoid and let T be a submonoid of nite index in S. The main results in this paper state that S can be presented by a nite complete rewriting system if T can, and S has nite derivation type if T has.

We show that the structures of binding algebras and Σmonoids by Fiore, Plotkin and Turi are sound and complete models of Klop’s Combinatory Reduction Systems (CRSs). These algebraic structures play the same role of universal algebra for term rewriting systems. Restricting the algebraic structures to the ones equipped with wellfounded relations, we obtain a complete characterisation of terminati...

ROSA is an e-learning system, which enables the management of Learning Objects (LOs). However, since ROSA is a centralized system, it does not provide a complete integration of LOs created in local ROSAs of other institutions. This paper presents the evolution of ROSA into a peer-to-peer (P2P) system the ROSA P2P, and describes the integration process of LOs in this environment. It provides the...

D This paper explains new results relating modal propositional logic and rewrite rule systems. More precisely, we give complete term rewriting systems for the modal propositional systems known as K, Q, T, and S5. These systems are presented as extensions of Hsiang’s system for classical propositional calculus. We have checked local confluence with the rewrite rule system K.B. (cf. the Knuth-Ben...

It is shown that it is undecidable in general whether a terminating graph rewriting system is confluent or not—in contrast to the situation for term and string rewriting systems. Critical pairs are introduced to hypergraph rewriting, a generalisation of graph rewriting, where it turns out that the mere existence of common reducts for all critical pairs of a graph rewriting system does not imply...

Synchronising Graphs is a system of parallel graph transformation designed for modeling process interaction in a network environment. Although notions of observational equivalence are abundant in the literature for process calculi, not so for graph rewriting, where system behaviour is typically context dependent. We propose a theory of context-free synchronising graphs and a novel notion of bis...