Related papers: Knuth-Bendix algorithm and the conjugacy problems …
This work presents a formalization of the theorem of existence of most general unifiers in first-order signatures in the higher-order proof assistant PVS. The distinguishing feature of this formalization is that it remains close to the…
In this paper, we propose an improved numerical algorithm for solving minimax problems based on nonsmooth optimization, quadratic programming and iterative process. We also provide a rigorous proof of convergence for our algorithm under…
The main novelty of this paper is to consider an extension of the Calculus of Constructions where predicates can be defined with a general form of rewrite rules. We prove the strong normalization of the reduction relation generated by the…
The paper studies the rewriting problem, that is, the decision problem whether, for a given conjunctive query $Q$ and a set $\mathcal{V}$ of views, there is a conjunctive query $Q'$ over $\mathcal{V}$ that is equivalent to $Q$, for cases…
For the lambda-calculus with surjective pairing and terminal type, Curien and Di Cosmo were inspired by Knuth-Bendix completion, and introduced a confluent rewriting system that (1) extends the naive rewriting system, and (2) is stable…
In this paper, we construct an implementable algorithm which solves the conjugacy problem in twisted right-angled Artin groups (T-RAAGs). In certain cases, the complexity is known to be linear, by reducing the problem to the twisted…
During recent years, quantum computers have received increasing attention, primarily due to their ability to significantly increase computational performance for specific problems. Computational performance could be improved for…
The confluence of untyped lambda-calculus with unconditional rewriting has already been studied in various directions. In this paper, we investigate the confluence of lambda-calculus with conditional rewriting and provide general results in…
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…
Optimization problems is one of the most challenging applications of quantum computers, as well as one of the most relevants. As a consequence, it has attracted huge efforts to obtain a speedup over classical algorithms using quantum…
In complex systems such as spin systems and protein systems, conventional simulations in the canonical ensemble will get trapped in states of energy local minima. We employ the generalized-ensemble algorithms in order to overcome this…
We construct a class of finitely generated groups which have arbitrarily large conjugacy separability function, but in which the conjugacy problem can be solved in polynomial time, demonstrating that the McKinsey algorithm for the conjugacy…
We establish a one-to-one correspondence between conjugacy classes of any Hecke group and irreducible systems of poles of rational period functions for automorphic integrals on the same group. We use this correspondence to construct…
Modern neural network architectures still struggle to learn algorithmic procedures that require to systematically apply compositional rules to solve out-of-distribution problem instances. In this work, we focus on formula simplification…
Mixed-integer linear programming problems are extensively used in industry for a wide range of optimization tasks. However, as they get larger, they present computational challenges for classical solvers within practical time limits.…
We show how decreasing diagrams introduced in the theory of rewriting systems can be used to prove coherence type theorems in category theory. We apply this method to describe a coherent presentation of the $0$-Hecke monoid…
String diagrams are a powerful and intuitive graphical syntax for terms of symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming increasingly relevant in other fields such as physics and…
The recent advent of commercially available quantum annealing hardware (QAH) has expanded opportunities for research into quantum annealing-based algorithms. In the domain of power systems, this advancement has driven increased interest in…
A simple scheme was proposed by Knuth to generate binary balanced codewords from any information word. However, this method is limited in the sense that its redundancy is twice that of the full sets of balanced codes. The gap between…
We give a complete complexity classification for the problem of finding a solution to a given system of equations over a fixed finite monoid, given that a solution over a more restricted monoid exists. As a corollary, we obtain a complexity…