Evaluation of Monotone DNF Formulas

Sarah R. Allen; Lisa Hellerstein; Devorah Kletenik; Tonguç Ünlüyurt

doi:10.1007/s00453-015-0092-9

Evaluation of Monotone DNF Formulas

Sarah R. Allen, Lisa Hellerstein, Devorah Kletenik, Tonguç Ünlüyurt

Research output: Contribution to journal › Article › peer-review

Abstract

Stochastic boolean function evaluation (SBFE) is the problem of determining the value of a given boolean function f on an unknown input x, when each bit x_i of x can only be determined by paying a given associated cost c_i. Further, x is drawn from a given product distribution: for each x_i, Pr[ x_i= 1 ] = p_i and the bits are independent. The goal is to minimize the expected cost of evaluation. In this paper, we study the complexity of the SBFE problem for classes of DNF formulas. We consider both exact and approximate versions of the problem for subclasses of DNF, for arbitrary costs and product distributions, and for unit costs and/or the uniform distribution.

Original language	English (US)
Pages (from-to)	661-685
Number of pages	25
Journal	Algorithmica
Volume	77
Issue number	3
DOIs	https://doi.org/10.1007/s00453-015-0092-9
State	Published - Mar 1 2017

Keywords

Approximation algorithms
DNF formulas
Sequential testing
Stochastic boolean function evaluation

ASJC Scopus subject areas

General Computer Science
Computer Science Applications
Applied Mathematics

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10.1007/s00453-015-0092-9

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title = "Evaluation of Monotone DNF Formulas",

abstract = "Stochastic boolean function evaluation (SBFE) is the problem of determining the value of a given boolean function f on an unknown input x, when each bit xi of x can only be determined by paying a given associated cost ci. Further, x is drawn from a given product distribution: for each xi, Pr[ xi= 1 ] = pi and the bits are independent. The goal is to minimize the expected cost of evaluation. In this paper, we study the complexity of the SBFE problem for classes of DNF formulas. We consider both exact and approximate versions of the problem for subclasses of DNF, for arbitrary costs and product distributions, and for unit costs and/or the uniform distribution.",

keywords = "Approximation algorithms, DNF formulas, Sequential testing, Stochastic boolean function evaluation",

author = "Allen, {Sarah R.} and Lisa Hellerstein and Devorah Kletenik and Tongu{\c c} {\"U}nl{\"u}yurt",

note = "Funding Information: Sarah R. Allen was partially supported by an NSF Graduate Research Fellowship under Grant 0946825 and by NSF Grant CCF-1116594. Lisa Hellerstein was partially supported by NSF Grants 1217968 and 0917153. Devorah Kletenik was partially supported by NSF Grant 0917153. Tongu{\c c} {\"U}nl{\"u}yurt was partially supported by TUBITAK 2219 programme. Part of this research was performed while Tongu{\c c} {\"U}nl{\"u}yurt was visiting faculty at the NYU School of Engineering and Sarah Allen and Devorah Kletenik were students there. We thank anonymous referees for their helpful suggestions. Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media New York.",

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AU - Ünlüyurt, Tonguç

N1 - Funding Information: Sarah R. Allen was partially supported by an NSF Graduate Research Fellowship under Grant 0946825 and by NSF Grant CCF-1116594. Lisa Hellerstein was partially supported by NSF Grants 1217968 and 0917153. Devorah Kletenik was partially supported by NSF Grant 0917153. Tonguç Ünlüyurt was partially supported by TUBITAK 2219 programme. Part of this research was performed while Tonguç Ünlüyurt was visiting faculty at the NYU School of Engineering and Sarah Allen and Devorah Kletenik were students there. We thank anonymous referees for their helpful suggestions. Publisher Copyright: © 2015, Springer Science+Business Media New York.

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N2 - Stochastic boolean function evaluation (SBFE) is the problem of determining the value of a given boolean function f on an unknown input x, when each bit xi of x can only be determined by paying a given associated cost ci. Further, x is drawn from a given product distribution: for each xi, Pr[ xi= 1 ] = pi and the bits are independent. The goal is to minimize the expected cost of evaluation. In this paper, we study the complexity of the SBFE problem for classes of DNF formulas. We consider both exact and approximate versions of the problem for subclasses of DNF, for arbitrary costs and product distributions, and for unit costs and/or the uniform distribution.

AB - Stochastic boolean function evaluation (SBFE) is the problem of determining the value of a given boolean function f on an unknown input x, when each bit xi of x can only be determined by paying a given associated cost ci. Further, x is drawn from a given product distribution: for each xi, Pr[ xi= 1 ] = pi and the bits are independent. The goal is to minimize the expected cost of evaluation. In this paper, we study the complexity of the SBFE problem for classes of DNF formulas. We consider both exact and approximate versions of the problem for subclasses of DNF, for arbitrary costs and product distributions, and for unit costs and/or the uniform distribution.

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Evaluation of Monotone DNF Formulas

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