Spectral analysis of Boolean functions as a graph eigenvalue problem

1999 ◽  
Vol 48 (3) ◽  
pp. 345-351 ◽  
Author(s):  
A. Bernasconi ◽  
B. Codenotti
Keyword(s):  
Spectral Analysis ◽  
Eigenvalue Problem ◽  
Boolean Functions ◽  
Analysis Of Boolean Functions

scholarly journals Analysis of Boolean functions based on interaction graphs and their influence in system biology

2019 ◽  
Vol 32 (12) ◽  
pp. 7803-7821
Author(s):  
Ranjeet Kumar Rout ◽  
Santi P. Maity ◽  
Pabitra Pal Choudhury ◽  
Jayanta Kumar Das ◽  
Sk. Sarif Hassan ◽  
...  
Keyword(s):  
Boolean Functions ◽  
System Biology ◽  
Interaction Graphs ◽  
Analysis Of Boolean Functions

scholarly journals FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraints

2020 ◽  
Vol 34 (02) ◽  
pp. 1552-1560
Author(s):  
Anastasios Kyrillidis ◽  
Anshumali Shrivastava ◽  
Moshe Vardi ◽  
Zhiwei Zhang
Keyword(s):  
Boolean Functions ◽  
Continuous Optimization ◽  
Conjunctive Normal Form ◽  
Cardinality Constraints ◽  
Sat Solvers ◽  
Boolean Satisfiability Problem ◽  
Algebraic Framework ◽  
Clause Learning ◽  
Sat Solver ◽  
Analysis Of Boolean Functions

The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side—especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT solvers—has been remarkable. Yet, while SAT solvers, aimed at solving industrial-scale benchmarks in Conjunctive Normal Form (CNF), have become quite mature, SAT solvers that are effective on other types of constraints (e.g., cardinality constraints and XORs) are less well-studied; a general approach to handling non-CNF constraints is still lacking. In addition, previous work indicated that for specific classes of benchmarks, the running time of extant SAT solvers depends heavily on properties of the formula and details of encoding, instead of the scale of the benchmarks, which adds uncertainty to expectations of running time.To address the issues above, we design FourierSAT, an incomplete SAT solver based on Fourier analysis of Boolean functions, a technique to represent Boolean functions by multilinear polynomials. By such a reduction to continuous optimization, we propose an algebraic framework for solving systems consisting of different types of constraints. The idea is to leverage gradient information to guide the search process in the direction of local improvements. Empirical results demonstrate that FourierSAT is more robust than other solvers on certain classes of benchmarks.

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