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@inproceedings{961394, author = {Kunc, Michal and Okhotin, Alexander}, address = {Berlin}, booktitle = {Descriptional Complexity of Formal Systems: 13th International Workshop, DCFS 2011, Gießen/Limburg, Germany, July 25-27, 2011. Proceedings}, doi = {http://dx.doi.org/10.1007/978-3-642-22600-7_18}, editor = {Markus Holzer, Martin Kutrib, Giovanni Pighizzini}, keywords = {finite automata; two-way automata; state complexity}, language = {eng}, location = {Berlin}, isbn = {978-3-642-22599-4}, pages = {222-234}, publisher = {Springer}, title = {State complexity of operations on two-way deterministic finite automata over a unary alphabet}, year = {2011} }
TY - JOUR ID - 961394 AU - Kunc, Michal - Okhotin, Alexander PY - 2011 TI - State complexity of operations on two-way deterministic finite automata over a unary alphabet PB - Springer CY - Berlin SN - 9783642225994 KW - finite automata KW - two-way automata KW - state complexity N2 - 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 g(n) = e^(sqrt(n.ln(n))(1 + o(1))) is the maximum value of lcm(p1,...,pk) for p1 +...+ pk <= n, 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, e^((1 + o(1)).sqrt((m + n).ln(m + n))) states. ER -
KUNC, Michal a Alexander OKHOTIN. State complexity of operations on two-way deterministic finite automata over a unary alphabet. In Markus Holzer, Martin Kutrib, Giovanni Pighizzini. \textit{Descriptional Complexity of Formal Systems: 13th International Workshop, DCFS 2011, Gießen/Limburg, Germany, July 25-27, 2011. Proceedings}. Berlin: Springer, 2011, s.~222-234. ISBN~978-3-642-22599-4. Dostupné z: https://dx.doi.org/10.1007/978-3-642-22600-7\_{}18.
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