Related papers: Number representations and term rewriting

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating…

We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite…

In this note we give a simple unifying proof of the undecidability of several diagrammatic properties of term rewriting systems that include: local confluence, strong confluence, diamond property, subcommutative property, and the existence…

Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However,…

In this extended abstract, we present a simple approach to convergence on term graphs that allows us to unify term graph rewriting and infinitary term rewriting. This approach is based on a partial order and a metric on term graphs. These…

Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical…

Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving…

On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…

Term rewriting plays a crucial role in software verification and compiler optimization. With dozens of highly parameterizable techniques developed to prove various system properties, automatic term rewriting tools work in an extensive…

Conditional term rewriting is an intuitive yet complex extension of term rewriting. In order to benefit from the simpler framework of unconditional rewriting, transformations have been defined to eliminate the conditions of conditional term…

Undecidability of various properties of first order term rewriting systems is well-known. An undecidable property can be classified by the complexity of the formula defining it. This gives rise to a hierarchy of distinct levels of…

Properties of Term Rewriting Systems are called modular iff they are preserved under (and reflected by) disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term…

We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…

We explore the Collatz conjecture and its variants through the lens of termination of string rewriting. We construct a rewriting system that simulates the iterated application of the Collatz function on strings corresponding to mixed…

Rewriting is a formalism widely used in computer science and mathematical logic. The classical formalism has been extended, in the context of functional languages, with an order over the rules and, in the context of rewrite based languages,…

So far, a very large amount of work in Natural Language Processing (NLP) rely on trees as the core mathematical structure to represent linguistic informations (e.g. in Chomsky's work). However, some linguistic phenomena do not cope properly…

We propose a functional description of rewriting systems on topological vector spaces. We introduce the topological confluence property as an approximation of the confluence property. Using a representation of linear topological rewriting…

Motivated by questions from program transformations, eight notions of isomorphisms between term rewriting systems are defined, analysed, and classified. The notions include global isomorphisms, where the renaming of variables and function…

Several types of term rewriting systems can be distinguished by the way their rules overlap. In particular, we define the classes of prefix, suffix, bottom-up and top-down systems, which generalize similar classes on words. Our aim is to…

Like termination, confluence is a central property of rewrite systems. Unlike for termination, however, there exists no known complexity hierarchy for confluence. In this paper we investigate whether the decreasing diagrams technique can be…