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arXiv · 1805.06685

The Synchronizing Probability Function for Primitive Sets of Matrices

Costanza Catalano·Raphaël M. Jungers
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Abstract

Motivated by recent results relating synchronizing DFAs and primitive sets, we tackle the synchronization process and the related longstanding \v{C}ern\'{y} conjecture by studying the primitivity phenomenon for sets of nonnegative matrices having neither zero-rows nor zero-columns. We formulate the primitivity process in the setting of a two-player probabilistic game and we make use of convex optimization techniques to describe its behavior. We develop a tool for approximating and upper bounding the exponent of any primitive set and supported by numerical results we state a conjecture that, if true, would imply a quadratic upper bound on the reset threshold of a new class of automata.

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Costanza Catalano, Raphaël M. Jungers. 2018-05-17. The Synchronizing Probability Function for Primitive Sets of Matrices. https://arxiv.org/abs/1805.06685

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