Theory of Átomata

  • Janusz Brzozowski
  • Hellis Tamm
Conference paper

DOI: 10.1007/978-3-642-22321-1_10

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)
Cite this paper as:
Brzozowski J., Tamm H. (2011) Theory of Átomata. In: Mauri G., Leporati A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg

Abstract

We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call “átomaton”, whose states are the “atoms” of the language, that is, non-empty intersections of complemented or uncomplemented left quotients of the language. We describe methods of constructing the átomaton, and prove that it is isomorphic to the normal automaton of Sengoku, and to an automaton of Matz and Potthoff. We study “atomic” NFA’s in which the right language of every state is a union of atoms. We generalize Brzozowski’s double-reversal method for minimizing a deterministic finite automaton (DFA), showing that the result of applying the subset construction to an NFA is a minimal DFA if and only if the reverse of the NFA is atomic.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Janusz Brzozowski
    • 1
  • Hellis Tamm
    • 2
  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Institute of CyberneticsTallinn University of TechnologyTallinnEstonia

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