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Theoretical Computer Science
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Journal of the ACM (JACM)
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BOUNDED WIDTH BRANCHING PROGRAMS
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Star-Free Open Languages and Aperiodic Loops
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Learning Expressions over Monoids
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Algebraic Characterizations of Small Classes of Boolean Functions
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Complete Classifications for the Communication Complexity of Regular Languages
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A Generalized Quantifier Concept in Computational Complexity Theory
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Valuated and Valence Grammars: An Algebraic View
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A common algebraic description for probabilistic and quantum computations
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On the computational power of probabilistic and quantum branching program
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Learning expressions and programs over monoids
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An impossibility gap between width-4 and width-5 permutation branching programs
Information Processing Letters
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Counting, fanout and the complexity of quantum ACC
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Iterated group products and leakage resilience against NC1
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Nonuniform ACC Circuit Lower Bounds
Journal of the ACM (JACM)
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Recently a new connection was discovered between the parallel complexity class NC1 and the theory of finite automata in the work of Barrington on bounded width branching programs. There (nonuniform) NC1 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 NC1 and the class of automata are closely related.In particular, using Thérien's classification of finite monoids, we give new characterizations of the classes AC0, depth-k AC0, and ACC, the last being the AC0 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 NC1.