Lower Bound Methods for the Size of Nondeterministic Finite Automata Revisited

Conference paper

DOI: 10.1007/978-3-319-53733-7_19

Part of the Lecture Notes in Computer Science book series (LNCS, volume 10168)
Cite this paper as:
Tamm H., van der Merwe B. (2017) Lower Bound Methods for the Size of Nondeterministic Finite Automata Revisited. In: Drewes F., Martín-Vide C., Truthe B. (eds) Language and Automata Theory and Applications. LATA 2017. Lecture Notes in Computer Science, vol 10168. Springer, Cham

Abstract

We revisit the following lower bound methods for the size of a nondeterministic finite automaton: the fooling set technique, the extended fooling set technique, and the biclique edge cover technique, presenting these methods in terms of quotients and atoms of regular languages. Although the lower bounds obtained by these methods are not necessarily tight, some classes of languages for which tight bounds can be achieved, are known. We show that languages with maximal reversal complexity belong to the class of languages for which the fooling set technique provides a tight bound. We also show that the extended fooling set technique is tight for a subclass of unary cyclic languages.

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of CyberneticsTallinn University of TechnologyTallinnEstonia
  2. 2.Department of Computer ScienceStellenbosch UniversityMatielandSouth Africa

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