State complexity of operations on two-way deterministic finite automata over a unary alphabet
| Authors | |
|---|---|
| Year of publication | 2011 |
| Type | Article in Proceedings |
| Conference | Descriptional Complexity of Formal Systems: 13th International Workshop, DCFS 2011, Gießen/Limburg, Germany, July 25-27, 2011. Proceedings |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1007/978-3-642-22600-7_18 |
| Field | General mathematics |
| Keywords | finite automata; two-way automata; state complexity |
| Description | 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. |
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