Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Journal of Computer and System Sciences
Extensions to Barrington's M-program model
Theoretical Computer Science - Special issue on structure in complexity theory
Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
Context-free languages and pushdown automata
Handbook of formal languages, vol. 1
Aspects of classical language theory
Handbook of formal languages, vol. 1
Characterizations of Pushdown Machines in Terms of Time-Bounded Computers
Journal of the ACM (JACM)
On the Tape Complexity of Deterministic Context-Free Languages
Journal of the ACM (JACM)
Counter-Free Automata (M.I.T. research monograph no. 65)
Counter-Free Automata (M.I.T. research monograph no. 65)
Theoretical Computer Science
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
The Many Faces of a Translation
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
A Generalization of the Büchi-Elgot-Trakhtenbrot Theorem
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
First-order expressibility of languages with neutral letters or: The Crane Beach conjecture
Journal of Computer and System Sciences
Circuits and context-free languages
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
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Building upon the known generalized-quantifier-based firstorder characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantifiers. Our work extends the elaborate theory relating monoidal quantifiers to NC1 and its subclasses. In the absence of the BIT predicate, we resolve the main issues: we show in particular that no single outermost unary groupoidal quantifier with FO can capture all the context-free languages, and we obtain the surprising result that a variant of Greibach's "hardest contextfree language" is LOGCFL-complete under quantifier-free BIT-free interpretations. We then prove that FO with unary groupoidal quantifiers is strictly more expressive with the BIT predicate than without. Considering a particular groupoidal quantifier, we prove that first-order logic with majority of pairs is strictly more expressive than first-order with majority of individuals. As a technical tool of independent interest, we define the notion of an aperiodic nondeterministic finite automaton and prove that FO translations are precisely the mappings computed by single-valued aperiodic nondeterministic finite transducers.