Handbook of formal languages, vol. 1
Translating regular expressions into small εe-free nondeterministic finite automata
Journal of Computer and System Sciences
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Constructing NFA s by Optimal Use of Positions in Regular Expressions
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
Theoretical Computer Science - Descriptional complexity of formal systems
State Elimination Heuristics for Short Regular Expressions
Fundamenta Informaticae
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The aim of this study is the random generation of non-deterministic automata. We focus our attention on the random generation processed with bitstreams for which we present a probabilistic analysis. Let m be the size of the alphabet. We show that the DFAs obtained by subset construction from n-state NFAs based on equiprobable bitstreams have a probability of being of size m + 2 that tends to 1 when n tends to infinity. This property gives an asymptotical explanation to van Zijl's experimental results concerning the succinctness of NFAs. We also determine the probability that a state is reachable from an equiprobably chosen DFA state. We show that the distribution of the subsets that appear during the subset construction is an equiprobable one in the case of bitstreams generated with the probability 2 - 2n-1/n. This result is related to the conjecture of Leslie, Raymond and Wood, which says that the number of states of the DFA is maximum when the density of the NFA is approximately equal to 2/n. Finally we extend this probabilistic study to the case of *-NFAs defined by van Zijl.