Алгоритмы Решения Систем Линейных Диофантовых Уравнений в Дискретных Областях

Abstract.The algorithms for computation of minimal supported set of solutions for systems of linear Diophantine homogeneous equations over set of natural numbers and basis of systems of linear Diophantine homogeneous and inhomogeneous equations in ring and field of remainders on modulo of a number.Аннотация. Предложены алгоритмы построения минимального порождающего множества решений систем линейных однородных уравнений в множестве натуральных чисел и базиса множества решений системы линейных однородных и неоднородных диофантовых уравнений в кольцах и полях вычетов по модулю некоторого числа

Ontology View on Automata Theory

The summary of automata theory ontology is presented in the paper. It is based on the following dependences: a type of an automaton – the language accepted by the automaton – applications. The given ontology does not claim to be exhaustive as automata theory is very extensive and it is a complicated problem to survey all its aspects within one article. Only the main properties of automata and their applications are considered

Concolic Testing in CLP

[EN] Concolic testing is a popular software verification technique based on a combination of concrete and symbolic execution. Its main focus is finding bugs and generating test cases with the aim of maximizing code coverage. A previous approach to concolic testing in logic programming was not sound because it only dealt with positive constraints (by means of substitutions) but could not represent negative constraints. In this paper, we present a novel framework for concolic testing of CLP programs that generalizes the previous technique. In the CLP setting, one can represent both positive and negative constraints in a natural way, thus giving rise to a sound and (potentially) more efficient technique. Defining verification and testing techniques for CLP programs is increasingly relevant since this framework is becoming popular as an intermediate representation to analyze programs written in other programming paradigms.This author has been partially supported by EU (FEDER) and Spanish MCI/AEI under grants TIN2016-76843-C4-1-R and PID2019-104735RB-C41, and by the Generalitat Valenciana under grant Prometeo/2019/098 (DeepTrust).Mesnard, F.; Payet, E.; Vidal, G. (2020). Concolic Testing in CLP. Theory and Practice of Logic Programming. 20(5):671-686. https://doi.org/10.1017/S1471068420000216S67168620

Anti-Pattern Matching Modulo

International audienceNegation is intrinsic to human thinking and most of the time when searching for something, we base our patterns on both positive and negative conditions. In a previous work, we have extended the notion of term to the one of anti-term that may contain complement symbols. Matching such anti-terms against terms has the nice property of being unitary. Here we generalize the syntactic anti-pattern matching to anti-pattern matching modulo an arbitrary equational theory E, and we study the specific and practically very useful case of associativity, possibly with a unity (AU). To this end, based on the syntacticness of associativity, we present a rule-based associative matching algorithm, and we extend it to AU. This algorithm is then used to solve AU anti-pattern matching problems. This allows us to be generic enough so that for instance, the AllDiff standard predicate of constraint programming becomes simply expressible in this framework. AU anti-patterns are implemented in the Tom language and we show some examples of their usage

JavaSplitter. A Java Implementation of Variable Splitting Proof Search

This thesis describes the design and implementation of JavaSplitter, a prototype incremental proof search engine based on a variable splitting sequent calculus. The prover also includes modes for variable pure derivations, and for variable sharing derivations without splitting. The splitting calculus uses an index system to achieve variable sharing derivations, and to keep track of how variables are split into different branches of a derivation. A graph representation of the indices occurring in a skeleton and operations on this graph are used to determine when splitting of such variables is sound. The design and implementation of the data structures and operations necessary for the proof search procedures are described. Further, the three modes of proof search are compared with regard to number of steps used to reach a proof for a set of valid input sequents

2 Constraint Solving on Terms

In this chapter, we focus on constraint solving on terms, also called Herbrand constraints in the introductory chapter, and we follow the main concepts introduced in that chapter. The most popular constraint system on terms is probably unification problem

Increasing model building capabilities by constraint solving on terms with integer components

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : 17660, issue : a.1996 n.966-I / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Increasing Model Building Capabilities by Constraint Solving on Terms with Integer Exponents

this paper the decidability of first order theory of the language of I-terms