Algebraic and Topological Theory of Languages

Journal of Mathematics and Computer Science, 2015

Journal of the ACM, 1988

Recently a new connection was discovered between the parallel complexity class NC 1 and the theory of finite automata in the work of Barrington on bounded width branching programs. There (nonuniform) NC 1 was characterized as those languages recognized by a certain nonuniform version of a DFA. Here we extend this characterization to show that the internal structures of NC 1 and the class of automata are closely related. In particular, using Thérien's classification of finite monoids, we give new characterizations of the classes AC 0 , depth- k AC 0 , and ACC , the last being the AC 0 closure of the mod q functions for all constant q . We settle some of the open questions in [3], give a new proof that the dot-depth hierarchy of algebraic automata theory is infinite [8], and offer a new framework for understanding the internal structure of NC 1 .

Journal of Algebra, 1987

Journal of Computer and System Sciences, 1967

Semigroup Forum, 1998

Electronic Proceedings in Theoretical Computer Science, 2017

Arxiv preprint arXiv: …, 2010

Arithmetical invariants---such as sets of lengths, catenary and tame degrees---describe the non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids.

Mathematical Proceedings of the Cambridge Philosophical Society, 2005

Theoretical Computer Science, 2002

Acta Mathematica Hungarica, 1990