This paper explores the algebraic matching approach for detection of vulnerabilities in binary codes. The algebraic programming system is used for implementing this method. It is anticipated that models of vulnerabilities and programs to be verified are presented as behavior algebra and action language specifications. The methods of algebraic matching are based on rewriting rules and techniques...

In this paper, we show that the SR transformation, a computationally equivalent transformation proposed by Şerbănuţă and Roşu, is a sound structure-preserving transformation for weakly-left-linear deterministic conditional term rewriting systems. More precisely, we show that every weakly-leftlinear deterministic conditional term rewriting system can be converted to an equivalent weakly-leftline...

Gene assembly is an intricate biological process that has been studied formally and modeled through string and graph rewriting systems. Recently, a restriction of the general (intramolecular) model, called simple gene assembly, has been introduced. This restriction has subsequently been defined as a string rewriting system. We show that by extending the notion of overlap graph it is possible to...

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...

A modular property of term rewriting systems is one that holds for the direct sum of two disjoint term rewriting systems iff it holds for every involved term rewriting system. A term rewriting system is r-consistent iff there is no term that can be rewritten to two different variables. We show that the subclass of left-linear and r-consistent term rewriting systems has the modular termination p...