Decidable call-by-need computations in term rewriting

Decidable Call by Need Computations in term Rewriting (Extended Abstract)

In this paper we study decidable approximations to call by need computations to normal and root-stable forms in term rewriting. We obtain uniform decidability proofs by making use of elementary tree automata techniques. Surprisingly, by avoiding complicated concepts like index and sequentiality we are able to cover much larger classes of term rewriting systems.

Call-by-need reduction for membership conditional term rewriting Systems

This paper proves that, for a normal membership conditional term rewriting system (MCTRS), (1) a reducible term has a needed redex if the MCTRS is nonoverlapping, and (2) whether a redex is nv-needed is decidable.

Call by need computations in orthogonal term rewriting systems

On the Complexity of Deciding Call-by-Need

In a recent paper we introduced a new framework for the study of call by need computations to normal form and root-stable form in term rewriting. Using elementary tree automata techniques and ground tree transducers we obtained simple decidability proofs for classes of rewrite systems that are much larger than earlier classes defined using the complicated sequentiality concept. In this paper we...

Optimal Normalization in Orthogonal Term Rewriting Systems

We design a normalizing strategy for orthogonal term rewriting systems (OTRSs), which is a generalization of the call-by-need strategy of Huet-L evy 4]. The redexes contracted in our strategy are essential in the sense that they have \descendants" under any reduction of a given term. There is an essential redex in any term not in normal form. We further show that contraction of the innermost es...