A taxonomy of problems with fast parallel algorithms
Information and Control
Finite monoids and the fine structure of NC1
Journal of the ACM (JACM)
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Extensions to Barrington's M-program model
Theoretical Computer Science - Special issue on structure in complexity theory
Polynomial closure of group languages and open sets of the Hall topology
ICALP '94 Selected papers from the 21st international colloquium on Automata, languages and programming
Languages recognized by finite aperiodic groupoids
Theoretical Computer Science
Circuits and expressions with nonassociative gates
Journal of Computer and System Sciences - Eleventh annual conference on computational learning theory&slash;Twelfth Annual IEEE conference on computational complexity
The Complexity of Computing
Varieties Of Formal Languages
Finite Loops Recognize Exactly the Regular Open Languages
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Circuit Definitions of Nondeterministic Complexity Classes
Proceedings of the Eighth Conference on Foundations of Software Technology and Theoretical Computer Science
The Complexity of Computing over Quasigroups
Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science
Finite groupoids and their applications to computational complexity
Finite groupoids and their applications to computational complexity
Parity, circuits, and the polynomial-time hierarchy
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
Log Depth Circuits For Division And Related Problems
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Faithful Loops for Aperiodic E-Ordered Monoids
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
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It is known that recognition of regular languages by finite monoids can be generalized to context-free languages and finite groupoids, which are finite sets closed under a binary operation. A loop is a groupoid with a neutral element and in which each element has a left and a right inverse. It has been shown that finite loops recognize exactly those regular languages that are open in the group topology. In this paper, we study the class of aperiodic loops, which are those loops that contain no nontrivial group. We show that this class is stable under various definitions, and we prove some closure properties. We also prove that aperiodic loops recognize only star-free open languages and give some examples. Finally, we show that the wreath product principle can be applied to groupoids, and we use it to prove a decomposition theorem for recognizers of regular open languages.