Comparisons between Measures of Nondeterminism on Finite Automata
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We study the interrelationships between various measures of nondeterminism for finite automata. The tree width of an NFA (nondeterministic finite automaton) A is a function that associates a positive integer n to the maximum number of leaves in any computation tree of A on an input of length n. The trace of an NFA is defined in terms of the maximum product of the degrees of nondeterministic choices in computation on inputs of given length. We establish upper and lower bounds for the trace function of an NFA in terms of its tree width. Additionally, the unbounded trace of an NFA has exponential growth.
Keywordsfinite automata limited nondeterminism state complexity
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