TY - GEN

T1 - State complexity of operations on two-way deterministic finite automata over a unary alphabet

AU - Kunc, Michal

AU - Okhotin, Alexander

PY - 2011/8/11

Y1 - 2011/8/11

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 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79961190841&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-22600-7_18

DO - 10.1007/978-3-642-22600-7_18

M3 - Conference contribution

AN - SCOPUS:79961190841

SN - 9783642225994

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 222

EP - 234

BT - Descriptional Complexity of Formal Systems - 13th International Workshop, DCFS 2011, Proceedings

T2 - 13th International Workshop of Descriptional Complexity of Formal Systems, DCFS 2011

Y2 - 25 July 2011 through 27 July 2011

ER -