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
Star height of certain families of regular events
Journal of Computer and System Sciences
On the Construction of Reversible Automata for Reversible Languages
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Star Height of Reversible Languages and Universal Automata
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Language operations with regular expressions of polynomial size
Theoretical Computer Science
The decidability of a mapping problem for generalized sequential machines with final states
Journal of Computer and System Sciences
Star height of certain families of regular events
Journal of Computer and System Sciences
| Hi-index | 0.00 |
Properties of star height of regular events are investigated. It is shown that star height is preserved under such operations as taking quotients, addition or subtraction of a finite event, removal of all words beginning with a given letter, and removal of certain subsets of smaller star height. Next it is shown that there exist events of arbitrarily large star height whose union, concatenation, and star is of star height one. Also, arbitrarily large increases in star height can be obtained by using the intersection or complement operations. In the second part of the paper a technique for establishing the star height of regular events is developed. It is shown that for every regular event R of star height n there exists a nondeterministic state graph G whose states correspond to subsets of the set of states Q of the reduced automaton accepting R and whose cycle rank is precisely n. Unfortunately a given subset Q' of Q may have to be repeated k times in G and no bound on k is known. Thus it is still not known whether an algorithm for determining star height exists. However, it is felt that the techniques presented here provide new insight into the problem.