Related papers: Bottom-up rewriting for words and terms
We present decidability results for termination of classes of term rewriting systems modulo permutative theories. Termination and innermost termination modulo permutative theories are shown to be decidable for term rewrite systems (TRS)…
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,…
Uniqueness of normal forms ($UN^=$) is an important property of term rewrite systems. $UN^=$ is decidable for ground (i.e., variable-free) systems and undecidable in general. Recently it was shown to be decidable for linear, shallow…
Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of omega-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is…
Finite automata whose computations can be reversed, at any point, by knowing the last k symbols read from the input, for a fixed k, are considered. These devices and their accepted languages are called k-reversible automata and k-reversible…
We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast…
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…
Algebraic Branching Programs(ABPs) are standard models for computing polynomials. Syntactic multilinear ABPs (smABPs) are restrictions of ABPs where every variable is allowed to occur at most once in every path from the start to the…
In this paper, we introduce a rewriting theory of linear monoidal categories. Those categories are a particular case of what we will define as linear (n, p)-categories. We will also define linear (n, p)-polygraphs, a linear adapation of…
Narrowing is a procedure that was first studied in the context of equational E-unification and that has been used in a wide range of applications. The classic completeness result due to Hullot states that any term rewriting derivation…
It is proved that, given a (von Neumann) regular semigroup with finitely many left and right ideals, if every maximal subgroup is presentable by a finite complete rewriting system, then so is the semigroup. To achieve this, the following…
Deep machine unlearning is the problem of `removing' from a trained neural network a subset of its training set. This problem is very timely and has many applications, including the key tasks of removing biases (RB), resolving confusion…
Large Language Models (LLMs) have shown remarkable prowess in text generation, yet producing long-form, factual documents grounded in extensive external knowledge bases remains a significant challenge. Existing "top-down" methods, which…
The downward closure of a language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of every language is regular. Moreover, recent results show that downward closures are…
Viewing Dehn's algorithm as a rewriting system, we generalise to allow an alphabet containing letters which do not necessarily represent group elements. This extends the class of groups for which the algorithm solves the word problem to…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
We consider a minimal extension of the language of arithmetic, such that the bounded formulas provably total in a suitably-defined theory \`a la Buss (expressed in this new language) precisely capture polytime random functions. Then, we…
A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…
For linear recurrence systems, the problem of finding rational solutions is reduced to the problem of computing polynomial solutions by computing a content bound or a denominator bound. There are several bounds in the literature. The…
Recently it was shown that it is undecidable whether a term rewrite system can be proved terminating by a polynomial interpretation in the natural numbers. In this paper we show that this is also the case when restricting the…