Concetti Chiave
Depth-3 circuit lower bounds and k-SAT algorithms are closely related, with implications for solving long-standing problems.
Sintesi
This paper explores the relationship between depth-3 circuit lower bounds and k-SAT algorithms, proposing a new problem ENUM(k, t) to reveal interactions between the two. The authors introduce a randomized algorithm for ENUM(k, t) and demonstrate its power by considering ENUM(3, n^2). By restricting to monotone CNFs, the problem becomes a hypergraph Turán problem. The analysis leads to improved circuit lower bounds and k-SAT algorithms.
The content discusses local search as a fundamental paradigm in solving the satisfiability problem. It delves into the connection between lower bounds and algorithms in the context of depth-3 circuits. The paper introduces a novel approach to analyzing enumeration problems for CNFs with bounded negations.
Statistiche
A simple construction shows that b(n, k, n^2 ) ≥ 2(1−O(log(k)/k))n.
The expected running time of our algorithm is 1.598n.
Σ3 3(Maj) ≥ 1.251n−o(n).
Citazioni
"Local search is a fundamental paradigm in solving the satisfiability problem."
"The former yields an unrestricted depth-3 lower bound of 2ω(√n), solving a long-standing open problem."