Results on Transforming NFA into DFCA

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 2d n 2 e−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 ∗A preliminary version of the paper was presented at DCGARS 2004 conference. †Work supported by Natural Sciences and Engineering Research Council of Canada (NSERC) grant 600089 ‡Work supported by Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canada Research Chair Program to L.K. §Work supported by Louisiana Board of Regents grant 32-0967-40766 and a LATECH-CenIT grant. 2 C. CÂMPEANU, L. KARI, A. PĂUN / Results on Transforming NFA into DFCA structure of the automata in the worst case are given (we strongly believe they will be pivotal in the upper bound proof).