The paper determines the number of states in a two-way deterministic finite automaton (2DFA) over a one-letter alphabet sufficient and in the worst case necessary to represent the results of the following operations: (i) intersection of an m-state 2DFA and an n-state 2DFA requires between m∈+∈n and m∈+∈n∈+∈1 states; (ii) union of an m-state 2DFA and an n-state 2DFA, between m∈+∈n and 2m∈+∈n∈+∈4 states; (iii) Kleene star of an n-state 2DFA, (g(n)∈+∈O(n))2 states, where is the maximum value of lcm(p 1, ..., p k ) for , known as Landau's function; (iv) k-th power of an n-state 2DFA, between (k∈-∈1)g(n)∈-∈k and k(g(n)∈+∈n) states; (v) concatenation of an m-state and an n-state 2DFAs, states. © 2011 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Kunc, M., & Okhotin, A. (2011). State complexity of operations on two-way deterministic finite automata over a unary alphabet. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6808 LNCS, pp. 222–234). https://doi.org/10.1007/978-3-642-22600-7_18
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