Data Structures and Algorithms


Fractality and Coherent Structures in Satisfiability Problems

Authors: Theophanes Raptis

We utilize a previously reported methodological framework [5], to find a general set of mappings for any satisfiability (SAT) problem to a set of arithmetized codes allowing a classification hierarchy enumerable via integer partition functions. This reveals a unique unsatisfiability criterion via the introduction of certain universal indicator functions associating the validity of any such problem with a mapping between Mersenne integers and their complements in an inclusive hierarchy of exponential intervals. Lastly, we present means to reduce the complexity of the original problem to that of a special set of binary sequences and their bit block analysis via a reduction of any expression to a type of a Sequential Dynamical System (SDS) using the technique of clause equalization. We specifically notice the apparent analogy of certain dynamical properties behind such problems with resonances and coherencies of multi-periodic systems leading to the possibility of certain fast analog or natural implementations of dedicated SAT-machines. A Matlab toolbox is also offered as additional aid in exploring certain simple examples.

Comments: 47 Pages. Typo correction in eq. (29a-b) and (35a-b)

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Submission history

[v1] 2017-07-05 07:51:08
[v2] 2017-07-11 13:15:48

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