scholarly journals Prioritizing MCDC test cases by spectral analysis of Boolean functions

2017 ◽  
Vol 27 (7) ◽  
pp. e1641
Author(s):  
Tolga Ayav
Keyword(s):  
Spectral Analysis ◽  
Boolean Functions ◽  
Test Cases ◽  
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.

scholarly journals An Orthogonal Basis for Functions over a Slice of the Boolean Hypercube

10.37236/4567 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Yuval Filmus
Keyword(s):  
Symmetric Group ◽  
Boolean Functions ◽  
Orthogonal Basis ◽  
Point Of View ◽  
Fundamental Result ◽  
Orthogonal Representation ◽  
Low Degree ◽  
Total Influence ◽  
Multilinear Polynomials ◽  
Analysis Of Boolean Functions

We present a simple, explicit orthogonal basis of eigenvectors for the Johnson and Kneser graphs, based on Young's orthogonal representation of the symmetric group. Our basis can also be viewed as an orthogonal basis for the vector space of all functions over a slice of the Boolean hypercube (a set of the form $\{(x_1,\ldots,x_n) \in \{0,1\}^n : \sum_i x_i = k\}$), which refines the eigenspaces of the Johnson association scheme; our basis is orthogonal with respect to any exchangeable measure. More concretely, our basis is an orthogonal basis for all multilinear polynomials $\mathbb{R}^n \to \mathbb{R}$ which are annihilated by the differential operator $\sum_i \partial/\partial x_i$. As an application of the last point of view, we show how to lift low-degree functions from a slice to the entire Boolean hypercube while maintaining properties such as expectation, variance and $L^2$-norm.As an application of our basis, we streamline Wimmer's proof of Friedgut's theorem for the slice. Friedgut's theorem, a fundamental result in the analysis of Boolean functions, states that a Boolean function on the Boolean hypercube with low total influence can be approximated by a Boolean junta (a function depending on a small number of coordinates). Wimmer generalized this result to slices of the Boolean hypercube, working mostly over the symmetric group, and utilizing properties of Young's orthogonal representation. Using our basis, we show how the entire argument can be carried out directly on the slice.

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