In this paper, a connection between rewriting systems and embedding of monoids in groups is found. We show that if a group with a positive presentation has a complete rewriting system R that satisfies the condition that each rule in R with positive left-hand side has a positive right-hand side, then the monoid presented by the subset of positive rules from R embeds in the group. As an example, ...

We characterize sets of strings using two central properties from rewriting: normalization and termination. We recall the well-known result that any recursively enumerable set of strings can occur as the set of normalizing strings over a “small” alphabet if the rewriting system is allowed access to a “larger” alphabet (and extend the result to termination). We then show that these results do no...

We study the complexity of the confluence problem for restricted kinds of semi–Thue systems, vector replacement systems and general trace rewriting systems. We prove that confluence for length– reducing semi–Thue systems is P–complete and that this complexity reduces to NC in the monadic case. For length–reducing vector replacement systems we prove that the confluence problem is PSPACE– complet...

In this paper we address the problem of query answering and rewriting in global-as-view data integration systems, when key and inclusion dependencies are expressed on the global integration schema. In the case of sound views, we provide sound and complete rewriting techniques for a maximal class of constraints for which decidability holds. Then, we introduce a semantics which is able to cope wi...

Based on a simple metric and a simple partial order on term graphs, we develop two infinitary calculi of term graph rewriting. We show that, similarly to infinitary term rewriting, the partial order formalisation yields a conservative extension of the metric formalisation of the calculus. By showing that the resulting calculi simulate the corresponding well-established infinitary calculi of ter...

ROSA is an e-learning system, which enables the creation, storage, reuse and management of Learning Objects (LOs). LO is a collection of reusable material used to support learning, education, or training. However, since ROSA is still a centralized system, it does not provide yet a complete integration of LOs created in local ROSAs of other institutions. This paper presents the evolution of ROSA...

Synchronous model is a type of formal models for modelling and specifying reactive systems. It has great advantage over other real-time that its paradigm supports deterministic concurrent behaviour Various approaches have been utilized verification synchronous based on different techniques, such as checking, SAT/SMT sovling, term rewriting, inference so on. In this paper, we propose approach co...

Abstract Ontology-mediated querying (OMQ) provides a paradigm for query answering according to which users not only records at the database but also implicit information inferred from ontology. A key challenge in OMQ is that may be infinite, cannot stored and queried by off -the -shelf engine. The commonly adopted technique deal with infinite entailments rewriting, which, however, comes cost of...