Tight bounds on the number of states of DFAs that are equivalent to n-state NFAs
K Iwama, Y Kambayashi, K Takaki - Theoretical Computer Science, 2000 - Elsevier
K Iwama, Y Kambayashi, K Takaki
Theoretical Computer Science, 2000•Elsevier… When we discuss the number of states of a DFA M, M must be a minimal DFA, ie, it must
be guaranteed that there is no other DFA M that is equivalent to M and has fewer states than
M. It is a fundamental fact [8] that a DFA M is minimal if (i) all states can be reachable from
the initial state and (ii) there are no two equivalent states. Here, two … Note that our basic
approach in this paper is to divide the whole F-states into two groups and to prohibit the
whole group-A states from appearing in the equivalent DFA. Thus …
be guaranteed that there is no other DFA M that is equivalent to M and has fewer states than
M. It is a fundamental fact [8] that a DFA M is minimal if (i) all states can be reachable from
the initial state and (ii) there are no two equivalent states. Here, two … Note that our basic
approach in this paper is to divide the whole F-states into two groups and to prohibit the
whole group-A states from appearing in the equivalent DFA. Thus …
It is shown that if α is an integer which can be expressed as 2 k or 2 k+1 for some integer 0⩽k⩽n/2−2 , then there exist nondeterministic finite automata with n states whose equivalent deterministic finite automata need exactly 2 n−α states.
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