A separator theorem for graphs of bounded genus
Journal of Algorithms
The Boolean formula value problem is in ALOGTIME
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The complexity of Boolean functions
The complexity of Boolean functions
A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
An optimal parallel algorithm for formula evaluation
SIAM Journal on Computing
Size-depth tradeoffs for Boolean formulae
Information Processing Letters
Size-Depth Tradeoffs for Algebraic Formulas
SIAM Journal on Computing
The Parallel Evaluation of General Arithmetic Expressions
Journal of the ACM (JACM)
Log Space Recognition and Translation of Parenthesis Languages
Journal of the ACM (JACM)
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
On Separators, Segregators and Time versus Space
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
The circuit value problem is log space complete for P
ACM SIGACT News
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
On determinism versus non-determinism and related problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
On determinism versus non-determinism and related problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Upper Bounds for Monotone Planar Circuit Value and Variants
Computational Complexity
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
Algebraic Complexity Theory
One-input-face MPCVP is hard for l, but in LogDCFL
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
The size and depth of layered boolean circuits
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Balancing bounded treewidth circuits
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Parameterized Complexity
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Spira [28] showed that any Boolean formula of size s can be simulated in depth O (logs ). We generalize Spira's theorem and show that any Boolean circuit of size s with segregators of size f (s ) can be simulated in depth O (f (s )logs ). If the segregator size is at least s ε for some constant ε 0, then we can obtain a simulation of depth O (f (s )). This improves and generalizes a simulation of polynomial-size Boolean circuits of constant treewidth k in depth O ( k 2 logn ) by Jansen and Sarma [17]. Since the existence of small balanced separators in a directed acyclic graph implies that the graph also has small segregators, our results also apply to circuits with small separators. Our results imply that the class of languages computed by non-uniform families of polynomial-size circuits that have constant size segregators equals non-uniform NC 1. Considering space bounded Turing machines to generate the circuits, for f (s )log2s -space uniform families of Boolean circuits our small-depth simulations are also f (s )log2s -space uniform. As a corollary, we show that the Boolean Circuit Value problem for circuits with constant size segregators (or separators) is in deterministic SPACE (log2n ). Our results also imply that the Planar Circuit Value problem, which is known to be P -Complete [16], can be solved in deterministic $SPACE (\sqrt{n} \log n)$ .