Finite automata and unary languages
Theoretical Computer Science
Nondeterministic computations in sublogarithmic space and space constructibility
SIAM Journal on Computing
A lower bound for the nondeterministic space complexity of context-free recognition
Information Processing Letters
An optimal lower bound for nonregular languages
Information Processing Letters
Tight bounds on the number of states of DFAs that are equivalent to n-state NFAs
Theoretical Computer Science
Number Theory for Computing
Optimal Simulations between Unary Automata
SIAM Journal on Computing
Space hierarchy theorem revised
Theoretical Computer Science - Mathematical foundations of computer science
Converting two-way nondeterministic unary automata into simpler automata
Theoretical Computer Science - Mathematical foundations of computer science
Nondeterminism and the size of two way finite automata
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
A family of NFAs which need 2n - α deterministic states
Theoretical Computer Science
On the state complexity of reversals of regular languages
Theoretical Computer Science
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Finite automata and their decision problems
IBM Journal of Research and Development
Nondeterministic Finite Automata--Recent Results on the Descriptional and Computational Complexity
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
Concatenation of Regular Languages and Descriptional Complexity
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Chrobak normal form revisited, with applications
CIAA'11 Proceedings of the 16th international conference on Implementation and application of automata
DCFS'11 Proceedings of the 13th international conference on Descriptional complexity of formal systems
State complexity of projected languages
DCFS'11 Proceedings of the 13th international conference on Descriptional complexity of formal systems
Pairs of complementary unary languages with “balanced” nondeterministic automata
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
On a structural property in the state complexity of projected regular languages
Theoretical Computer Science
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
Fundamenta Informaticae - MFCS & CSL 2010 Satellite Workshops: Selected Papers
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A number d is magic for n, if there is no regular language for which an optimal nondeterministic finite state automaton (nfa) uses exactly n states and, at the same time, the optimal deterministic finite state automaton (dfa) uses exactly d states. We show that, in the case of unary regular languages, the state hierarchy of dfa's, for the family of languages accepted by n-state nfa's, is not contiguous. There are some ''holes'' in the hierarchy, i.e., magic numbers in between values that are not magic. This solves, for automata with a single letter input alphabet, an open problem of existence of magic numbers. Actually, most of the numbers is magic in the unary case. As an additional bonus, we also get a new universal lower bound for the conversion of unary d-state dfa's into equivalent nfa's: nondeterminism does not reduce the number of states below log^2d, not even in the best case.