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arXiv · 1405.2553

Graph Spectral Properties of Deterministic Finite Automata

Ryoma Sin'ya
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Abstract

We prove that a minimal automaton has a minimal adjacency matrix rank and a minimal adjacency matrix nullity using equitable partition (from graph spectra theory) and Nerode partition (from automata theory). This result naturally introduces the notion of matrix rank into a regular language L, the minimal adjacency matrix rank of a deterministic automaton that recognises L. We then define and focus on rank-one languages: the class of languages for which the rank of minimal automaton is one. We also define the expanded canonical automaton of a rank-one language.

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Ryoma Sin'ya. 2014-05-11. Graph Spectral Properties of Deterministic Finite Automata. https://arxiv.org/abs/1405.2553

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