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Logicians study and apply a multiplicity of various logical systems. Consequently, there is necessity to build foundations and common grounds for all these systems. This is done in metalogic. Like metamathematics studies formalized…
Programmers often use an iterative process of hypothesis generation ("perhaps this function is called twice?") and hypothesis testing ("let's count how many times this breakpoint fires") to understand the behavior of unfamiliar or…
The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for…
Integrating logic rules with other language features is increasingly sought after for advanced applications that require knowledge-base capabilities. To address this demand, increasingly more languages and extensions for such integration…
I describe a method for computer algebra that helps with laborious calculations typically encountered in theoretical microhydrodynamics. The program mimics how humans calculate by matching patterns and making replacements according to the…
We investigate the expressiveness of backward jumps in a framework of formalized sequential programming called program algebra. We show that - if expressiveness is measured in terms of the computability of partial Boolean functions - then…
Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been…
We redesigned an advanced physics laboratory course to include a project component. The intention was to address learning outcomes such as modeling, design of experiments, teamwork, and developing technical skills in using apparatus and…
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows to overcome these…
In this paper we propose a calculus for expressing algorithms for programming languages transformations. We present the type system and operational semantics of the calculus, and we prove that it is type sound. We have implemented our…
Recent progress in large language models (LLM) found chain-of-thought prompting strategies to improve the reasoning ability of LLMs by encouraging problem solving through multiple steps. Therefore, subsequent research aimed to integrate the…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
We aim to reason about the correctness of behaviour-preserving transformations of Erlang programs. Behaviour preservation is characterised by semantic equivalence. Based upon our existing formal semantics for Core Erlang, we investigate…
A thoughtful approach to designing and improving labs, particularly at the advanced level, is critical for the effective preparation of physics majors for professional work in industry or graduate school. With that in mind, physics…
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.
We propose a variant of the CCS process algebra with new features aiming at allowing multiscale modelling of biological systems. In the usual semantics of process algebras for modelling biological systems actions are instantaneous. When…
Reactive programs are ubiquitous in modern applications, and so verification is highly desirable. We present a verification strategy for reactive programs with a large or infinite state space utilising algebraic laws for reactive relations.…
If the result of an expensive computation is invalidated by a small change to the input, the old result should be updated incrementally instead of reexecuting the whole computation. We incrementalize programs through their derivative. A…
New model of software safety is offered. Distribution of mistakes in program on stages of life cycle is researched. Study of ways of increase of reliability of software at help simulation program is leaded.