Journal of the ACM (JACM)
The Mathematical Theory of Context-Free Languages
The Mathematical Theory of Context-Free Languages
Finite automata and their decision problems
IBM Journal of Research and Development
The origins of combinatorics on words
European Journal of Combinatorics
On Brzozowski's Conjecture for the free burnside semigroup satisfying x2= x3
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Membership and finiteness problems for rational sets of regular languages
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
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An event E is a subset of the free monoid A^* generated by the finite alphabet A. E is noncounting if and only if there exists an integer k=0, called the order of E, such that for any x, y, z @? A^*, xy^kz @? E if and only if xy^k^+^1z @? E. From semigroup theory it follows that the number of noncounting events of order @?1 is finite. Each such event is regular and the finite automata accepting such events over a fixed alphabet are homomorphic images of a universal automaton. Star-free regular expressions for such events are easily obtainable. It is next shown that the number of distinct noncounting events of order =2 over any alphabet with two or more letters is infinite. Furthermore, there exist noncounting events which are of any ''arbitrary degree of complexity,'' e.g. not recursively enumerable.