DeepAI AI Chat
Log In Sign Up

The Stochastic Boolean Function Evaluation Problem for Symmetric Boolean Functions

by   Dimitrios Gkenosis, et al.
NYU college

We give two approximation algorithms solving the Stochastic Boolean Function Evaluation (SBFE) problem for symmetric Boolean functions. The first is an O(log n)-approximation algorithm, based on the submodular goal-value approach of Deshpande, Hellerstein and Kletenik. Our second algorithm, which is simple, is based on the algorithm solving the SBFE problem for k-of-n functions, due to Salloum, Breuer, and Ben-Dov. It achieves a (B-1) approximation factor, where B is the number of blocks of 0's and 1's in the standard vector representation of the symmetric Boolean function. As part of the design of the first algorithm, we prove that the goal value of any symmetric Boolean function is less than n(n+1)/2. Finally, we give an example showing that for symmetric Boolean functions, minimum expected verification cost and minimum expected evaluation cost are not necessarily equal. This contrasts with a previous result, given by Das, Jafarpour, Orlitsky, Pan and Suresh, which showed that equality holds in the unit-cost case.


page 1

page 2

page 3

page 4


Minimum Cost Adaptive Submodular Cover

We consider the problem of minimum cost cover of adaptive-submodular fun...

Adaptivity Gaps for the Stochastic Boolean Function Evaluation Problem

We consider the Stochastic Boolean Function Evaluation (SBFE) problem wh...

On Blockwise Symmetric Matchgate Signatures and Higher Domain #CSP

For any n≥ 3 and q≥ 3, we prove that the Equality function (=_n) on n ...

Two 6-approximation Algorithms for the Stochastic Score Classification Problem

We study the arbitrary cost case of the unweighted Stochastic Score Clas...

Level-p-complexity of Boolean functions using Thinning, Memoization, and Polynomials

This paper describes a purely functional library for computing level-p-c...

Approximating minimum representations of key Horn functions

Horn functions form a subclass of Boolean functions and appear in many d...

A Canonical-based NPN Boolean Matching Algorithm Utilizing Boolean Difference and Cofactor Signature

This paper presents a new compact canonical-based algorithm to solve the...