Combinatorics of Monotone Computations

Combinatorics of Monotone Computations (1998)

by Stasys Jukna

Venue:	Combinatorica
Citations:	6 - 0 self

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Datum	Value	Source
TITLE	Combinatorics of Monotone Computations	user correction - Legacy Corrections
AUTHOR NAME	Stasys Jukna	SVM HeaderParse 0.1
AUTHOR AFFIL	y	SVM HeaderParse 0.2
ABSTRACT	Our main result is a combinatorial lower bounds criterion for a general model of monotone circuits, where we allow as gates: (i) arbitrary monotone Boolean functions whose minterms or maxterms (or both) have length 6 d, and (ii) arbitrary real-valued non-decreasing functions on 6 d variables. This resolves a problem, raised by Razborov in 1986, and yields, in a uniform and easy way, non-trivial lower bounds for circuits computing explicit functions even when d !1. The proof is relatively simple and direct, and combines the bottlenecks counting method of Haken with the idea of finite limit due to Sipser. We demonstrate the criterion by super-polynomial lower bounds for explicit Boolean functions, associated with bipartite Paley graphs and partial t-designs. We then derive exponential lower bounds for clique-like graph functions of Tardos, thus establishing an exponential gap between the monotone real and non-monotone Boolean circuit complexities. Since we allow real gates, the criterion...	user correction - Legacy Corrections
YEAR	1998	user correction - Legacy Corrections
VENUE	Combinatorica	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	65--85	INFERENCE
VOLUME	19	INFERENCE
CITATIONS	27 found	ParsCit 1.0