This paper propagates the use of term graph rewriting systems as a formal computational model. The deenition of both term graphs and the reduction relation on term graphs are more complex than their corresponding notions in term rewriting systems. Consequently, it is often believed that reasoning about term graph rewriting systems is inherently more diicult than reasoning about term rewriting s...

The direct sum of two term rewriting systems is the union of systems having disjoint sets of function symbols. It is shown that the direct sum of two term rewriting systems is not terminating, even if these systems are both terminating. Keyword: Term rewriting system, termination Introduction A term rewriting system R is a set of rewriting rules M → N , where M and N are terms [1, 3, 5]. The di...

This article describes a generalization of term rewriting system technique used as a basis for decision algorithm for equational theories. The or-deral term rewriting system technique is presented. The main innovation of the proposed technique is that reductions according to some rules of such a system are performed only if special restrictions are satissed. The restrictions are based on term o...

In this paper we will consider some extensions of the usual term rewrite format, namely: term rewriting with conditions, infmi~y term rewriting and term rewriting with bound variables. Rather than aiming at a complete survey, we discuss some aspects of these three extensions.

We present extended term rewriting systems as a means to describe a simpliication relation for an equational speciication with a built-in domain of external objects. Even if the extended term rewriting system is canonical, the combined relation including built-in computations of`ground terms' needs neither be terminating nor connuent. We investigate restrictions on the extended term rewriting s...

Learning from entailment is a learning model suitable for learning rst-order formulas, in which examples are formulas in the rst-order language which are implied or not implied. In this paper, we study the learnability of term rewriting systems in this framework. A term rewriting system is a simple model of tree transduction used for semi-structured data and Web, which can be considered as a fr...

We provide some new results concerning the use of trans-nite rewriting for giving semantics to rewrite systems. We especially (but not only) consider the computation of possibly innnite constructor terms by transsnite rewriting due to their interest in many programming languages. We reconsider the problem of compressing transsnite rewrite sequences into shorter (possibly nite) ones. We also inv...

We address the problem of an efficient rewriting strategy for general term rewriting systems. Several strategies have been proposed over the last two decades for rewriting, the most efficient of all being the natural rewriting strategy [9]. All the strategies so far, including natural rewriting, assume that the given term rewriting system is a left-linear constructor system. Although these rest...