The chemical concrete machine is a graph rewriting system which uses only local moves (rewrites), seen as chemical reactions involving molecules which are graphs made up by 4 trivalent nodes. It is Turing complete, therefore it might be used as a model of computation in algorithmic chemistry.

The aim of this paper is to implement the-reduction in the-calculus with a hypergraph rewriting mechanism called collapsed-tree rewriting. It turns out that collapsed-tree rewriting is sound with respect to-reduction and complete with respect to the Gross-Knuth strategy. As a consequence, there exists a normal form for a collapsed-tree if and only if there exists a normal form for the represent...

Rewriting systems are used in various areas of computer science, and especially in lambda-calculus, higherorder logics and functional programming. We show that the unsupervised learning networks can implement parallel rewriting. We show how this general correspondence can be refined in order to perform parallel term rewriting in neural networks, for any given first-order term. We simulate these...

We define infinitary combinatory reduction systems (iCRSs). This provides the first extension of infinitary rewriting to higher-order rewriting. We lift two well-known results from infinitary term rewriting systems and infinitary λ-calculus to iCRSs: 1. every reduction sequence in a fully-extended left-linear iCRS is compressible to a reduction sequence of length at most ω, and 2. every complet...

We give a complete proof of the fact that the following problem is undecidable: Given: A term rewriting system, where the termination of its rewrite relation is provable by a total reduction order on ground terms, Wanted: Does there exist a strictly monotonic interpretation in the positive integers that proves termination?

Rewriting with associativity, commutativity and identity has been an open problem for a long time. In 1989, Baird, Peterson and Wilkerson introduced the notion of constrained rewriting, to avoid the problem of non-termination inherent to the use of identities. We build up on this idea in two ways: by giving a complete set of rules for completion modulo these axioms; by showing how to build appr...

Query rewriting using views is a technique that allows a query to be answered efficiently by using pre-computed materialized views. It has many applications, such as data caching, query optimization, schema integration, etc. This issue has been studied extensively for relational databases and, as a result, the technology is maturing. For XML proposed for query rewriting using views for XPath qu...

The completeness property of SK combinators is well known. We consider an analogous property in the context of Lafont's Interaction Nets, a graph rewriting system based on classical linear logic. The result is a set of combinators which is complete in the sense of being able to encode all possible patterns of interaction.

A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. e term calculus is proved complete for a semantics in linearly distributive categories with additives. It is also shown that proof equivalence is decidable by showing that the cut elimination rewrites supply a conžuent rewriting system modul...