Theory Of Atomata

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Date

2014-06-19

Authors

Brzozowski, Janusz
Tamm, Hellis

Advisor

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Publisher

Elsevier

Abstract

We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call "atomaton", 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 atomaton, and prove that it is isomorphic to the reverse automaton of the minimal deterministic finite automaton (DFA) of the reverse language. We study "atomic" NFAs 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. We prove that Sengoku's claim that his method always finds a minimal NFA is false.

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The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.tcs.2014.04.016 © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

Atom, Atomic NFA, Atomaton, Left quotient, Minimization by double reversal, NFA, Regular language

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