We show that several reconfiguration problems known to be PSPACE-complete remain so even when limited to graphs of bounded bandwidth. The essential step is noticing the similarity to very limited string rewriting systems, whose ability to directly simulate Turing Machines is classically known. This resolves a question posed open in [Bonsma P., 2012]. On the other hand, we show that a large clas...

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...

We review the concept of term graph narrowing as an approach for solving equations by transformations on term graphs. Term graph narrowing combines term graph rewriting with rst-order term uni cation. This mechanism is complete for all term rewriting systems over which term graph rewriting is normalizing and conuent. This includes, in particular, all convergent term rewriting systems. Completen...

Term rewriting can only be applied if practical implementations of term rewriting engines exist. New rewriting engines are designed and implemented either to experiment with new (theoretical) results or to be able to tackle new application areas. In this paper we present the Meta-Environment: an environment for rapidly implementing the syntax and semantics of term rewriting based formalisms. We...

We introduce term graph narrowing as an approach for solving equations by transformations on term graphs. Term graph narrowing combines term graph rewriting with rst-order term uniication. Our main result is that this mechanism is complete for all term rewriting systems over which term graph rewriting is normalizing and connuent. This includes, in particular, all convergent term rewriting syste...

We propose a new type of conditional term rewriting system: the membership-conditional term rewriting system, in which, each rewriting rule can have membership conditions which restrict the substitution values for the variables occurring in the rule. For example, the rule f(x, x, y) . g(x, y) if x ∈ T ′ yields the reduction f(M, M, N) → g(M, N) only when M is in the term set T ′. We study the c...

String rewriting can not only be applied on strings, but also on cycles and even on general graphs. In this paper we investigate termination of string rewriting applied on cycles, shortly denoted as cycle rewriting, which is a strictly stronger requirement than termination on strings. Most techniques for proving termination of string rewriting fail for proving termination of cycle rewriting, bu...

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1. I n t r o d u c t i o n Many term rewriting systems and their modifications are considered in logic, automated theorem proving, and programming language [2,3,4,6,8,9]. A fundamental property of term rewriting systems is the confluence property. A few sufficient criteria for the confluence are well known [2,3,4,5,8,9]. However, if a term rewriting system is nonterminating and nonlinear, we kn...