Related papers: Notes on Lynch-Morawska Systems
The theory of finite and infinitary term rewriting is extensively developed for orthogonal rewrite systems, but to a lesser degree for weakly orthogonal rewrite systems. In this note we present some contributions to the latter case of weak…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…
Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…
Dedukti is a type-checker for the $\lambda$$\Pi$-calculus modulo rewriting, an extension of Edinburgh's logicalframework LF where functions and type symbols can be defined by rewrite rules. It thereforecontains an engine for rewriting LF…
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
Constant-rate multi-mode systems (MMS) are hybrid systems with finitely many modes and real-valued variables that evolve over continuous time according to mode-specific constant rates. We introduce a variant of linear temporal logic (LTL)…
In this paper, we study the global convergence of majorization minimization (MM) algorithms for solving nonconvex regularized optimization problems. MM algorithms have received great attention in machine learning. However, when applied to…
We give a Markov chain based algorithm for sampling almost uniform solutions of constraint satisfaction problems (CSPs). Assuming a canonical setting for the Lov\'asz local lemma, where each constraint is violated by a small number of…
Large language models (LLMs) can produce long, coherent passages of text, suggesting that LLMs, although trained on next-word prediction, must represent the latent structure that characterizes a document. Prior work has found that internal…
Ensuring large language model (LLM) reliability requires distinguishing objective unsolvability (inherent contradictions) from subjective capability limitations (tasks exceeding model competence). Current LLMs often conflate these…
We investigate the computational power of periodically iterated morphisms, also known as D0L systems with periodic control, PD0L systems for short. These systems give rise to a class of one-sided infinite sequences, called PD0L words. We…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
This paper presents a solver-friendly logic-based mixed-integer nonlinear programming model (LB-MINLP) to solve economic dispatch (ED) problems considering disjoint operating zones and valve-point effects. A simultaneous consideration of…
Complex Word Identification (CWI) is an essential step in the lexical simplification task and has recently become a task on its own. Some variations of this binary classification task have emerged, such as lexical complexity prediction…
Metric Temporal Logic (MTL) is a prominent specification formalism for real-time systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also…
Lattice reduction is a NP-hard problem well known in computer science and cryptography. The Lenstra-Lenstra-Lovasz (LLL) algorithm based on the calculation of orthogonal Gram-Schmidt (GS) bases is efficient and gives a good solution in…
We show confluence of a conditional term rewriting system CL-pc${}^1$, which is an extension of Combinatory Logic by Boolean constants. This solves problem 15 from the RTA list of open problems. The proof has been fully formalised in the…
A relation modification problem gets a logical structure and a natural number k as input and asks whether k modifications of the structure suffice to make it satisfy a predefined property. We provide a complete classification of the…
Determining whether a program terminates is a central problem in computer science. Turing's Halting Problem established termination as undecidable, showing that no algorithm can universally determine termination for all programs and inputs.…
The Lambek calculus is a well-known logical formalism for modelling natural language syntax. The original calculus covered a substantial number of intricate natural language phenomena, but only those restricted to the context-free setting.…