The state complexities of some basic operations on regular languages
Theoretical Computer Science
Handbook of formal languages, vol. 1
State complexity of regular languages
Journal of Automata, Languages and Combinatorics
Introduction to Automata Theory, Languages and Computability
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State complexity of combined operations
Theoretical Computer Science
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State complexity of basic language operations combined with reversal
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Theoretical Computer Science
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The state complexity of L2 and Lk
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State complexity of basic operations on nondeterministic finite automata
CIAA'02 Proceedings of the 7th international conference on Implementation and application of automata
Undecidability of the state complexity of composed regular operations
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
State complexity of four combined operations composed of union, intersection, star and reversal
DCFS'11 Proceedings of the 13th international conference on Descriptional complexity of formal systems
In search of most complex regular languages
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
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In this paper, we continue our study on the state complexity of combined operations on regular languages. We study the state complexities of @?"i"="1^kL"i^2, @?"i"="1^kL"i^2, @?"i"="1^kL"i^R, and @?"i"="1^kL"i^R, for regular languages L"i, 1@?i@?k, k=2. We obtain the exact bounds for these combined operations and show that the state complexities of @?"i"="1^kL"i^2 and @?"i"="1^kL"i^2 are the same as the mathematical compositions of the state complexities of their component individual operations, while, on the other hand, the state complexities of @?"i"="1^kL"i^R and @?"i"="1^kL"i^R are lower than the corresponding mathematical compositions.