Non-Orthodox Combinatorial Models Based on Discordant Structures

Details Non-Orthodox Combinatorial Models Based on Discordant Structures Non-Orthodox Combinatorial Models Based on Discordant Structures

2010-11-17

arxiv.org/abs/1011.3944v2

Computer Science

Data Structures and Algorithms

19 pages; typeset in LaTeX, some typos fixed

Scientific paper

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.

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