Derivatives of Regular Expressions
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Transition graphs and the star height problem
SWAT '68 Proceedings of the 9th Annual Symposium on Switching and Automata Theory (swat 1968)
On the star height of regular events
FOCS '67 Proceedings of the 8th Annual Symposium on Switching and Automata Theory (SWAT 1967)
Information science: The loop complexity of regular events
Information Sciences: an International Journal
General properties of star height of regular events
Journal of Computer and System Sciences
Star Height of Reversible Languages and Universal Automata
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Complexity measures for regular expressions
Journal of Computer and System Sciences
General properties of star height of regular events
Journal of Computer and System Sciences
Chop operations and expressions: descriptional complexity considerations
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Some variants of the star height problem
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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This paper studies the relationship between the apparent star height of a given regular expression and the structure of its reduced deterministic state graph. Sufficient conditions for the star height of a regular event R to equal the cycle rank of its reduced state graph G"R are derived. The cycle rank of G"R is also shown to constitute a lower bound to the star height of certain subsets of R. These results are then applied to fully characterize the star height of events consisting of @? sets of paths in finite digraphs and two open problems posed by Eggan are answered.