Related papers: Logged Rewriting Procedures with Application to Id…
This thesis concentrates on the development and application of rewriting and Groebner basis methods to a range of combinatorial problems. Chapter Two contains the most important result, which is the application of Knuth-Bendix procedures to…
A rewriting system is a set of equations over a given set of terms called rules that characterize a system of computation and is a powerful general method for providing decision procedures of equational theories, based upon the principle of…
We present an algorithmic approach to the conjugacy problems in monoids, using rewriting systems. We extend the classical theory of rewriting developed by Knuth and Bendix to a rewriting that takes into account the cyclic conjugates.
We generalize the notion of identities among relations, well known for presentations of groups, to presentations of n-categories by polygraphs. To each polygraph, we associate a track n-category, generalizing the notion of crossed module…
We present an online deliberation system using mutual evaluation in order to collaboratively develop solutions. Participants submit their proposals and evaluate each other's proposals; some of them may then be invited by the system to…
It is shown how to use a small finite state automaton in two variables in order to carry out the Knuth-Bendix process for rewriting words in a group in shortlex order. The two-variable automaton can be used to store an infinite set of rules…
We describe several technical tools that prove to be efficient for investigating the rewrite systems associated with a family of algebraic laws, and might be useful for more general rewrite systems. These tools consist in introducing a…
Event logs recorded during the execution of business processes constitute a valuable source of information. Applying process mining techniques to them, event logs may reveal the actual process execution and enable reasoning on quantitative…
It is shown how to use a small finite state automaton in two variables in order to carry out part of the Knuth--Bendix process for rewriting words in a group. The main objective is to provide a substitute for the most space-demanding module…
Rewriting for semigroups is a special case of Groebner basis theory for noncommutative polynomial algebras. The fact is a kind of folklore but is not fully recognised. The aim of this paper is to elucidate this relationship, showing that…
Record linkage is the process of identifying records that refer to the same entities from several databases. This process is challenging because commonly no unique entity identifiers are available. Linkage therefore has to rely on partially…
In this article we investigate how a subterm pattern matching algorithm can be exploited to implement efficient term rewriting procedures. From the left-hand sides of the rewrite system we construct a set automaton, which can be used to…
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…
Language-integrated query is a powerful programming construct allowing database queries and ordinary program code to interoperate seamlessly and safely. Language-integrated query techniques rely on classical results about the nested…
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…
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…
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…
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,…
Conversational assistants often require a question rewriting algorithm that leverages a subset of past interactions to provide a more meaningful (accurate) answer to the user's question or request. However, the exact rewriting approach may…
We propose a generalized version of context-sensitivity in term rewriting based on the notion of "forbidden patterns". The basic idea is that a rewrite step should be forbidden if the redex to be contracted has a certain shape and appears…