TY - GEN

T1 - State complexity of k-union and k-intersection for prefix-free regular languages

AU - Eom, Hae Sung

AU - Han, Yo Sub

AU - Salomaa, Kai

PY - 2013

Y1 - 2013

N2 - We investigate the state complexity of multiple unions and of multiple intersections for prefix-free regular languages. Prefix-free deterministic finite automata have their own unique structural properties that are crucial for obtaining state complexity upper bounds that are improved from those for general regular languages. We present a tight lower bound construction for k-union using an alphabet of size k + 1 and for k-intersection using a binary alphabet. We prove that the state complexity upper bound for k-union cannot be reached by languages over an alphabet with less than k symbols. We also give a lower bound construction for k-union using a binary alphabet that is within a constant factor of the upper bound.

AB - We investigate the state complexity of multiple unions and of multiple intersections for prefix-free regular languages. Prefix-free deterministic finite automata have their own unique structural properties that are crucial for obtaining state complexity upper bounds that are improved from those for general regular languages. We present a tight lower bound construction for k-union using an alphabet of size k + 1 and for k-intersection using a binary alphabet. We prove that the state complexity upper bound for k-union cannot be reached by languages over an alphabet with less than k symbols. We also give a lower bound construction for k-union using a binary alphabet that is within a constant factor of the upper bound.

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U2 - 10.1007/978-3-642-39310-5_9

DO - 10.1007/978-3-642-39310-5_9

M3 - Conference contribution

AN - SCOPUS:84884475434

SN - 9783642393099

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

SP - 78

EP - 89

BT - Descriptional Complexity of Formal Systems - 15th International Workshop, DCFS 2013, Proceedings

T2 - 15th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2013

Y2 - 22 July 2013 through 25 July 2013

ER -