Results on Transforming NFA into DFCA

  • Authors:

  • Cezar Câmpeanu;Lila Kari;Andrei Păun

  • Affiliations:

  • Department of Computer Science and Information Technology, University of Prince Edward Island, Charlottetown, P.E.I., Canada, C1A 4P3. cezar@sun11.math.upei.ca;Department of Computer Science, University of Western Ontario, London, Ontario, Canada, N6A 5B7. lila@csd.uwo.ca;(Correspd.) Department of Computer Science, College of Engineering and Science, Louisiana Tech University, Ruston, Louisiana, P.O. Box 10348, LA-71272, USA. apaun@latech.edu

  • Venue:
  • Fundamenta Informaticae - Contagious Creativity - In Honor of the 80th Birthday of Professor Solomon Marcus
  • Year:
  • 2005

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Abstract

In this paper we consider the transformation from (minimal) non-deterministic finite automata (NFAs) to deterministic finite cover automata (DFCAs). We want to compare the two equivalent accepting devices with respect to their number of states; this becomes in fact a comparison between the expression power of the nondeterministic device and the expression power of the deterministic with loops device. We prove a lower bound for the maximum state complexity of deterministic finite cover automata obtained from non-deterministic finite automata of a given state complexity n, considering the case of a binary alphabet. We show, for such binary alphabets, that the difference between maximum blow-up state complexity of DFA and DFCA can be as small as 2⌈n/2;⌉−2 compared to the number of states of the minimal DFA. Moreover, we show the structure of automata for worst case exponential blow-up complexity from NFA to DFCA. We conjecture that the lower bound given in the paper is also the upper bound. Several results clarifying some of the structure of the automata in the worst case are given (we strongly believe they will be pivotal in the upper bound proof).