NFA-to-DFA Trade-Off for Regular Operations
Abstract
We examine the operational state complexity assuming that the operands of a regular operation are represented by nondeterministic finite automata, while the language resulting from the operation is required to be represented by a deterministic finite automaton. We get tight upper bounds 2n
for complementation, reversal, and star, 2m
for left and right quotient, 2m+n
for union and symmetric difference, 2m+n−2m−2n+2
for intersection, 2m+n−2n+1
for difference, 342m+n
for concatenation, and 2mn
for shuffle. We use a binary alphabet to describe witnesses for complementation, reversal, star, and left and right quotient, and a quaternary alphabet otherwise. Whenever we use a binary alphabet, it is always optimal.
Domains
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