相关论文: Logged Rewriting for Monoids

We present an algorithmic approach to the conjugacy problems in monoids and semigroups, using rewriting systems. There is a class of monoids and semigroups that satisfy the condition that the transposi- tion problem and the left and right…

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…

The concept of a system has proliferated through natural and social sciences. While myriad theories of systems exist, there is no mathematical general theory of systems. In this thesis, we take a first step towards formulating such a…

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…

Rewriting logic is naturally concurrent: several subterms of the state term can be rewritten simultaneously. But state terms are global, which makes compositionality difficult to achieve. Compositionality here means being able to decompose…

Kan extensions provide a natural general framework for a variety of combinatorial problems. We have developed rewriting procedures for Kan extensions (over the category of sets) and this enables one program to address a wide range of…

Higher-order rewriting is a framework in which one can write higher-order programs and study their properties. One such property is termination: the situation that for all inputs, the program eventually halts its execution and produces an…

The construction of bases for quotients is an important problem. In this paper, applying the method of rewriting systems, we give a unified approach to construct sections---an alternative name for bases in semigroup theory---for quotients…

Higher-dimensional rewriting is founded on a duality of rewrite systems and cell complexes, connecting computational mathematics to higher categories and homotopy theory: the two sides of a rewrite rule are two halves of the boundary of an…

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…

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…

Multiset rewriting systems provide a formalism particularly suitable for the description of biological systems. We present an extension of this formalism with additional controls on the derivations as a tool for reducing possible…

Monoidal algebraic structures consist of operations that can have multiple outputs as well as multiple inputs, which have applications in many areas including categorical algebra, programming language semantics, representation theory,…

We introduce homotopical methods based on rewriting on higher-dimensional categories to prove coherence results in categories with an algebraic structure. We express the coherence problem for (symmetric) monoidal categories as an…

Over the recent years, the theory of rewriting has been used and extended in order to provide systematic techniques to show coherence results for strict higher categories. Here, we investigate a further generalization to Gray categories,…

This paper is an extended abstract of an analysis of term rewriting where the terms in the rewrite rules as well as the term to be rewritten are compressed by a singleton tree grammar (STG). This form of compression is more general than…

In synchronous rewriting, the productions of two rewriting systems are paired and applied synchronously in the derivation of a pair of strings. We present a new synchronous rewriting system and argue that it can handle certain phenomena…

Coherence theorems for covariant structures carried by a category have traditionally relied on the underlying term rewriting system of the structure being terminating and confluent. While this holds in a variety of cases, it is not a…

A symmetric monoidal category is a category equipped with an associative and commutative (binary) product and an object which is the unit for the product. In fact, those properties only hold up to natural isomorphisms which satisfy some…

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…