Graph Spectral Properties of Deterministic Finite Automata

(Short Paper)
  • Ryoma Sin’ya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8633)


We prove that a minimal automaton has the minimal adjacency matrix rank and the minimal adjacency matrix nullity among all equivalent deterministic automata. Our proof uses equitable partition (from graph spectra theory) and Nerode partition (from automata theory). This result leads to the notion of rank of a regular language L, which is the minimal adjacency matrix rank of a deterministic automaton that recognises L. We then define and focus on rank-one languages. We also define the expanded canonical automaton of a rank-one language.


Adjacency Matrix Ranking Function Regular Language Counting Function Automaton Theory 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ryoma Sin’ya
    • 1
  1. 1.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyJapan

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