Related papers: Number representations and term rewriting
Term graph rewriting provides a formalism for implementing term rewriting in an efficient manner by avoiding duplication. Infinitary term rewriting has been introduced to study infinite term reduction sequences. Such infinite reductions can…
Rewriting systems are often defined as binary relations over a given set of objects. This simple definition is used to describe various properties of rewriting such as termination, confluence, normal forms etc. In this paper, we introduce a…
In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not…
Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…
This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…
We present techniques to prove termination of cycle rewriting, that is, string rewriting on cycles, which are strings in which the start and end are connected. Our main technique is to transform cycle rewriting into string rewriting and…
Rewriting systems on words are very useful in the study of monoids. In good cases, they give finite presentations of the monoids, allowing their manipulation by a computer. Even better, when the presentation is confluent and terminating,…
We study the properties, in particular termination, of dependent types systems for lambda calculus and rewriting.
This paper studies 3-polygraphs as a framework for rewriting on two-dimensional words. A translation of term rewriting systems into 3-polygraphs with explicit resource management is given, and the respective computational properties of each…
We introduce techniques for proving uniform termination of graph transformation systems, based on matrix interpretations for string rewriting. We generalize this technique by adapting it to graph rewriting instead of string rewriting and by…
The goal of this note is to compare two notions, one coming from the theory of rewrite systems and the other from proof theory: confluence and cut elimination. We show that to each rewrite system on terms, we can associate a logical system:…
An integer sequence that is defined by initial values and a linear recurrence with constant integer coefficients, can be represented by the difference of two arithmetic terms containing exponentiation. All constants occuring in the term are…
String rewriting systems have proved very useful to study monoids. In good cases, they give finite presentations of monoids, allowing computations on those and their manipulation by a computer. Even better, when the presentation is…
We present an extension of the Angluin-style learning algorithm for tree automata that incorporates deductive inference. The learning algorithm is provided with a term rewriting system that specifies properties of the target tree language…
We describe a method for proving non-looping non-termination, that is, of term rewriting systems that do not admit looping reductions. As certificates of non-termination, we employ regular (tree) automata.
This paper introduces a new term rewriting system that is similar to the embedded read-back mechanism for interaction nets presented in our previous work, but is easier to follow than in the original setting and thus to analyze its…
Term rewriting is a Turing complete model of computation. When taught to students of computer science, key properties of computation as well as techniques to analyze programs on an abstract level are conveyed. This paper gives a swift…
This article describes the *Confluence Framework*, a novel framework for proving and disproving confluence using a divide-and-conquer modular strategy, and its implementation in CONFident. Using this approach, we are able to automatically…
We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees. We show a uniform inverse preservation of recognizability result for the resulting class of term…
The relationship between Term Graph Rewriting and Term Rewriting is well understood: a single term graph reduction may correspond to several term reductions, due to sharing. It is also known that if term graphs are allowed to contain…