A #SAT Algorithm for Small Constant-Depth Circuits with PTF gates.

Swapnam  Balaji; Vaibhav Krishan; Deepanshu  Kush; Nutan Limaye; Srikanth Srinivasan

doi:10.1007/s00453-021-00915-7

A #SAT Algorithm for Small Constant-Depth Circuits with PTF gates.

Swapnam Balaji
, Vaibhav Krishan
, Deepanshu Kush
, Nutan Limaye
, Srikanth Srinivasan

Algorithms

Indian Institute of Technology Bombay

Research output: Journal Article or Conference Article in Journal › Journal article › Research › peer-review

Abstract

We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit C made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of constant-degree polynomials), counts the number of satisfying assignments to C in significantly better than brute-force time.

Original language	English
Journal	Algorithmica
Volume	84
ISSN	0178-4617
DOIs	https://doi.org/10.1007/s00453-021-00915-7
Publication status	Published - 2022

Keywords

Circuit Satisfiability
Memoization
PTF circuits

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10.1007/s00453-021-00915-7

A #SAT Algorithm for Small Constant-Depth CircuitsOther version, 809 KB

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title = "A \#SAT Algorithm for Small Constant-Depth Circuits with PTF gates.",

abstract = "We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit C made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of constant-degree polynomials), counts the number of satisfying assignments to C in significantly better than brute-force time.",

keywords = "Circuit Satisfiability, Memoization, PTF circuits, Circuit Satisfiability, Memoization, PTF circuits",

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AU - Balaji, Swapnam

AU - Krishan, Vaibhav

AU - Kush, Deepanshu

AU - Limaye, Nutan

AU - Srinivasan, Srikanth

PY - 2022

Y1 - 2022

N2 - We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit C made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of constant-degree polynomials), counts the number of satisfying assignments to C in significantly better than brute-force time.

AB - We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit C made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of constant-degree polynomials), counts the number of satisfying assignments to C in significantly better than brute-force time.

KW - Circuit Satisfiability

KW - Memoization

KW - PTF circuits

KW - Circuit Satisfiability

KW - Memoization

KW - PTF circuits

U2 - 10.1007/s00453-021-00915-7

DO - 10.1007/s00453-021-00915-7

M3 - Journal article

SN - 0178-4617

VL - 84

JO - Algorithmica

JF - Algorithmica

ER -

A #SAT Algorithm for Small Constant-Depth Circuits with PTF gates.

Abstract

Keywords

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