Bi-rewrite Systems

Bi-Rewrite Systems

In this article we propose an extension of term rewriting techniques to automate the deduction in monotone pre-order theories. To prove an inclusion a b from a given set I of them, we generate from I, using a completion procedure, a bi-rewrite system hR ; R i, that is, a pair of rewrite relations ??! R and ??! R , and seek a common term c such that a ??! R c and b ??! R c. Each component of the...

Rewrite Systems

Process Rewrite Systems

Many formal models for in nite-state concurrent systems are equivalent to special classes of rewrite systems. We classify these models by their expressiveness and de ne a hierarchy of classes of rewrite systems. We show that this hierarchy is strict with respect to bisimulation equivalence. The most general and most expressive class of systems in this hierarchy is called Process Rewrite Systems...

Pattern Graph Rewrite Systems

String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the po...

Modal Process Rewrite Systems

We consider modal transition systems with infinite state space generated by finite sets of rules. In particular, we extend process rewrite systems to the modal setting and investigate decidability of the modal refinement relation between systems from various subclasses. Since already simulation is undecidable for most of the cases, we focus on the case where either the refined or the refining p...