. "14310" . . . . "13"^^ . "Berlin" . "State complexity of operations on two-way deterministic finite automata over a unary alphabet" . "finite automata; two-way automata; state complexity"@en . "State complexity of operations on two-way deterministic finite automata over a unary alphabet"@en . . . "[344BBA628676]" . . . . . "978-3-642-22599-4" . . "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\u2019s 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." . "State complexity of operations on two-way deterministic finite automata over a unary alphabet" . "2"^^ . "Gie\u00DFen/Limburg, Germany" . "1"^^ . "232149" . "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\u2019s 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."@en . "State complexity of operations on two-way deterministic finite automata over a unary alphabet"@en . "2011-01-01+01:00"^^ . "Descriptional Complexity of Formal Systems: 13th International Workshop, DCFS 2011, Gie\u00DFen/Limburg, Germany, July 25-27, 2011. Proceedings" . . "Okhotin, Alexander" . . . "0302-9743" . . . "Springer-Verlag" . . . "RIV/00216224:14310/11:00050222!RIV12-GA0-14310___" . "Kunc, Michal" . . "P(GA201/09/1313), Z(MSM0021622409)" . "RIV/00216224:14310/11:00050222" . "10.1007/978-3-642-22600-7_18" .