Related papers: Bottom-up rewriting for words and terms
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
Constructor rewriting systems are said to be cons-free if any constructor term occurring in the rhs of a rule must be a subterm of the lhs of the rule. Roughly, such systems cannot build new data structures during their evaluation. In…
A central computational task in database theory, finite model theory, and computer science at large is the evaluation of a first-order sentence on a finite structure. In the context of this task, the \emph{width} of a sentence, defined as…
Rewriting Induction (RI) is a method to prove inductive theorems, originating from equational reasoning. By using Logically Constrained Simply-typed Term Rewriting Systems (LCSTRSs) as an intermediate language, rewriting induction becomes a…
We consider the problem of exact identification for read-once functions over arbitrary Boolean bases. We introduce a new type of queries (subcube identity ones), discuss its connection to previously known ones, and study the complexity of…
We develop a rewriting theory suitable for diagrammatic algebras and lay down the foundations of a systematic study of their higher structures. In this paper, we focus on the question of finding bases. As an application, we give the first…
Bottom-up knowledge compilation is a paradigm for generating representations of functions by iteratively conjoining constraints using a so-called apply function. When the input is not efficiently compilable into a language - generally a…
Logically constrained term rewriting is a relatively new rewriting formalism that naturally supports built-in data structures, such as integers and bit vectors. In the analysis of logically constrained term rewrite systems (LCTRSs),…
Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms to normal forms, as well as comparing the different reduction paths that lead to those normal forms. This higher structure can be captured by…
Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained…
This paper investigates the problem of testing clause sets for membership in classes known from literature. In particular, we are interested in classes defined via renaming: Is it possible to rename the predicates in a way such that…
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…
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…
Reversible Boolean Circuits are an interesting computational model under many aspects and in different fields, ranging from Reversible Computing to Quantum Computing. Our contribution is to describe a specific class of Reversible Boolean…
First-order applicative term rewriting systems provide a natural framework for modeling higher-order aspects. In earlier work we introduced an uncurrying transformation which is termination preserving and reflecting. In this paper we…
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…
Machine unlearning addresses the problem of updating a machine learning model/system trained on a dataset $S$ so that the influence of a set of deletion requests $U \subseteq S$ on the unlearned model is minimized. The gold standard…
The downward closure of a language $L$ of words is the set of all (not necessarily contiguous) subwords of members of $L$. It is well known that the downward closure of any language is regular. Although the downward closure seems to be a…
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…
Time complexity in rewriting is naturally understood as the number of steps needed to reduce terms to normal forms. Establishing complexity bounds to this measure is a well-known problem in the rewriting community. A vast majority of…