Definability with bounded number of bound variables
Information and Computation
Characterization of associative operations with prefix circuits of constant depth and linear size
SIAM Journal on Computing
Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
Regular languages defined with generalized quantifiers
Information and Computation
Handbook of formal languages, vol. 1
Over words, two variables are as powerful as one quantifier alternation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Weakly Iterated Block Products of Finite Monoids
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
On Logical Descriptions of Regular Languages
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Computational complexity questions related to finite monoids and semigroups
Computational complexity questions related to finite monoids and semigroups
Bounded-depth circuits: separating wires from gates
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Counter-Free Automata (M.I.T. research monograph no. 65)
Counter-Free Automata (M.I.T. research monograph no. 65)
Circuit Complexity of Regular Languages
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Languages with bounded multiparty communication complexity
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
An algebraic point of view on the crane beach property
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Linear circuits, two-variable logic and weakly blocked monoids
Theoretical Computer Science
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We obtain a logical characterization of an important class of regular languages, denoted ${\mathcal DO}$, and of its most important subclasses in terms of two-variable sentences with ordinary and modular quantifiers but in which all modular quantifiers lie outside the scope of ordinary quantifiers. The result stems from a new decomposition of the variety of monoids DO in terms of iterated block products. This decomposition and the ensuing logical characterization allows us to shed new light on recent results on regular languages which are recognized by bounded-depth circuits with a linear number of wires and regular languages with small communication complexity.