The state complexities of some basic operations on regular languages
Theoretical Computer Science
Handbook of formal languages, vol. 1
Introduction to the Theory of Computation
Introduction to the Theory of Computation
On the state complexity of reversals of regular languages
Theoretical Computer Science
Complementing unary nondeterministic automata
Theoretical Computer Science - Descriptional complexity of formal systems
Finite automata and their decision problems
IBM Journal of Research and Development
Complexity in union-free regular languages
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Quotient complexity of ideal languages
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Quotient complexity of closed languages
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Descriptional complexity of biautomata
DCFS'12 Proceedings of the 14th 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
On the state and computational complexity of the reverse of acyclic minimal DFAs
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
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We present binary deterministic finite automata of n states that meet the upper bound 2n on the state complexity of reversal. The automata have a single final state and are one-cycle-free-path, thus the witness languages are deterministic union-free. This result allows us to describe a binary language such that the nondeterministic state complexity of the language and of its complement is n and n + 1, respectively, while the state complexity of the language is 2n. We also show that there is no regular language with state complexity 2n such that both the language and its complement have nondeterministic state complexity n.