Non-Orthodox Combinatorial Models Based on Discordant Structures

TL;DR

This paper presents a new compact representation method called CTS for sets of binary sequences, applying it to solve the 3-Satisfiability problem efficiently and expanding tools for tackling intractable problems.

Contribution

Introduces a novel compact triplets structures (CTS) method for representing and analyzing binary sequences, with a polynomial algorithm for the 3-Satisfiability problem.

Findings

CTS method effectively represents large binary sets.

Algorithm demonstrates efficiency on high-dimension problems.

Expands resources for solving intractable problems.

Abstract

This paper introduces a novel method for compact representation of sets of n-dimensional binary sequences in a form of compact triplets structures (CTS), supposing both logic and arithmetic interpretations of data. Suitable illustration of CTS application is the unique graph-combinatorial model for the classic intractable 3-Satisfiability problem and a polynomial algorithm for the model synthesis. The method used for Boolean formulas analysis and classification by means of the model is defined as a bijective mapping principle for sets of components of discordant structures to a basic set. The statistic computer-aided experiment showed efficiency of the algorithm in a large scale of problem dimension parameters, including those that make enumeration procedures of no use. The formulated principle expands resources of constructive approach to investigation of intractable problems.