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
Languages that capture complexity classes
SIAM Journal on Computing
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
Non-uniform automata over groups
Information and Computation
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Formulas, regular languages and Boolean circuits
Theoretical Computer Science - Special issue on logic and applications to computer science
Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
Regular languages defined with generalized quantifiers
Information and Computation
Superlinear lower bounds for bounded-width branching programs
Journal of Computer and System Sciences
Communication complexity
Handbook of formal languages, vol. 1
Languages, automata, and logic
Handbook of formal languages, vol. 3
Languages defined with modular counting quantifiers
Information and Computation
An Algebraic Approach to Communication Complexity
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Algebraic Characterizations of Small Classes of Boolean Functions
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
The computing power of programs over finite monoids
Journal of Automata, Languages and Combinatorics - Selected papers of the workshop on logic and algebra for concurrency
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Computational complexity questions related to finite monoids and semigroups
Computational complexity questions related to finite monoids and semigroups
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
First-order expressibility of languages with neutral letters or: The Crane Beach conjecture
Journal of Computer and System Sciences
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Definability of languages by generalized first-order formulas over (N,+)
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Restricted two-variable FO + MOD sentences, circuits and communication complexity
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Non-definability of Languages by Generalized First-order Formulas over (N,+)
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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A letter e ∈Σ is said to be neutral for a language L if it can be inserted and deleted at will in a word without affecting membership in L. The Crane Beach Conjecture, which was recently disproved, stated that any language containing a neutral letter and definable in first-order with arbitrary numerical predicates (${\bf FO}[\mathit{Arb}]$) is in fact FO [ We develop an algebraic point of view on the Crane Beach properties using the program over monoid formalism which has proved of importance in circuit complexity. Using recent communication complexity results we establish a number of Crane Beach results for programs over specific classes of monoids. These can be viewed as Crane Beach theorems for classes of bounded-width branching programs. We also apply this to a standard extension of FO using modular-counting quantifiers and show that the boolean closure of this logic’s Σ1 fragment has the CBP.