NFA minimization

In automata theory (a branch of theoretical computer science), NFA minimization is the task of transforming a given nondeterministic finite automaton (NFA) into an equivalent NFA that has a minimum number of states, transitions, or both. While efficient algorithms exist for DFA minimization, NFA minimization is PSPACE-complete.¹ No efficient (polynomial time) algorithms are known, and under the standard assumption that P ≠ PSPACE, none exist. The most efficient known algorithm is the Kameda–Weiner algorithm.²

Non-uniqueness of minimal NFA

Unlike deterministic finite automata, minimal NFAs may not be unique. There may be multiple NFAs with the same number of states that accept the same regular language, but for which there is no equivalent NFA or DFA with fewer states.

References

Jiang, Tao; Ravikumar, B. (1993), "Minimal NFA Problems are Hard", SIAM Journal on Computing, 22 (6): 1117–1141, doi:10.1137/0222067
Kameda, Tsunehiko; Weiner, Peter (August 1970). "On the State Minimization of Nondeterministic Finite Automata". IEEE Transactions on Computers. C-19 (7). IEEE: 617–627. doi:10.1109/T-C.1970.222994. S2CID 31188224. Retrieved 2020-05-03.

External links

A modified C# implementation of Kameda–Weiner (1970) [1]

[TaoRavikumar93-1] Jiang, Tao; Ravikumar, B. (1993), "Minimal NFA Problems are Hard", SIAM Journal on Computing, 22 (6): 1117–1141, doi:10.1137/0222067

[Kameda-Weiner_1970-2] Kameda, Tsunehiko; Weiner, Peter (August 1970). "On the State Minimization of Nondeterministic Finite Automata". IEEE Transactions on Computers. C-19 (7). IEEE: 617–627. doi:10.1109/T-C.1970.222994. S2CID 31188224. Retrieved 2020-05-03.

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