A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
The Minimum Equivalent DNF Problem and Shortest Implicants

2001
*
Journal of computer and system sciences (Print)
*

We prove that

doi:10.1006/jcss.2001.1775
fatcat:pckny7ewpfhwnl7brlekfkd6fm
*the**Minimum**Equivalent**DNF**problem*is p 2 -complete, resolving a conjecture due to Stockmeyer. ... When*the*input is a formula,*the**Shortest**Implicant**problem*is p 2complete,*and*p 2 -hard to approximate to within an n 1=2? factor. ...*The**problem*of finding a*minimum**equivalent**DNF*then becomes exactly*the**problem*of finding*the**shortest**implicant*core of . ...##
###
The minimum equivalent DNF problem and shortest implicants

*
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
*

We prove that

doi:10.1109/sfcs.1998.743506
dblp:conf/focs/Umans98
fatcat:zeaa4hhiwbcitf3mcpy2y4jzdq
*the**Minimum**Equivalent**DNF**problem*is S P 2 -complete, resolving a conjecture due to Stockmeyer. ... We also consider*the*complexity*and*approximability of a related optimization*problem*in*the*second level of*the*polynomial hierarchy, that of finding*shortest**implicants*of a Boolean function. ... ACKNOWLEDGMENTS We thank Christos Papadimitriou for suggesting this*problem*,*and*many useful discussions. ...##
###
On the Complexity and Inapproximability of Shortest Implicant Problems
[chapter]

1999
*
Lecture Notes in Computer Science
*

We obtain inapproximability results for

doi:10.1007/3-540-48523-6_65
fatcat:xkrdnqrrazesdm7m6475tcp37m
*the**DNF**and*formula variants of*the**shortest**implicant**problem*that show that trivial approximation algorithms are optimal for these*problems*, up to lower order ... We investigate*the*complexity*and*approximability of a basic optimization*problem*in*the*second level of*the*Polynomial Hierarchy, that of nding*shortest**implicants*. ... in*the*reduction showing that*the**Minimum**Equivalent**DNF**problem*is p 2 -complete. ...##
###
Boolean functions with long prime implicants

2013
*
Information Processing Letters
*

Moreover, in case that

doi:10.1016/j.ipl.2013.07.001
fatcat:jep3g5m4rnhk3lvdwei44w7aoi
*the*answer is affirmative we present a polynomial time algorithm which outputs a*shortest**DNF*representation of*the*given function. ... In this short note we introduce a class of Boolean functions defined by a*minimum*length of its prime*implicants*. ... Finding a*minimum*(prime)*DNF*is then*equivalent*to finding a*minimum*set cover in an instance where truepoints are*the*elements of*the*base set*and*prime*implicates*correspond to*the*system of subsets ...##
###
Page 2057 of Mathematical Reviews Vol. , Issue 2003C
[page]

2003
*
Mathematical Reviews
*

2057
2003c:68099 68Q25 68Q15
Umans, Christopher (1-CA-CD; Berkeley, CA)

*The**minimum**equivalent**DNF**problem**and**shortest**implicants*. (English summary) Special issue on FOCS 98 (Palo Alto, CA). J. ...*Shortest**Implicant*for*DNF*formulas is complete for*the*complexity class in which*the*guess y has O(log’) length,*and*TAUTOLOGY is*the*verification subroutine. ...##
###
Bidual Horn functions and extensions

1999
*
Discrete Applied Mathematics
*

We also give characterizations of

doi:10.1016/s0166-218x(99)00033-5
fatcat:lttktdepcjhuhanxai65akxg5i
*shortest**DNF*expressions of a bidual Horn function f*and*show how to compute such an expression from a Horn*DNF*for f in polynomial time; for arbitrary Horn functions, ... Besides*the*extension*problem*, we study recognition of bidual Horn functions from Boolean formulas*and*properties of normal form expressions. ... Acknowledgements We would like to thank*the*participants of*the*Siena '96 Workshop on*the*Satisÿability*Problem*for comments on this work,*and**the*anonymous referees for their helpful suggestions which ...##
###
On connected Boolean functions

1999
*
Discrete Applied Mathematics
*

This paper studies

doi:10.1016/s0166-218x(99)00098-0
fatcat:kulhs5efyrgtpcuw6cbks4g5aa
*the*relationships between these properties*and**the**DNF*representations of*the*associated Boolean functions. ? (A. Kogan) 0166-218X/99/$ -see front matter ? ... This concept is further strengthened to that of convexity where every*shortest*path connecting two points of*the*same kind should consist of points of*the*same kind. ... Acknowledgements*The*authors gratefully acknowledge*the*partial support provided by*the*O ce of Naval Research (grant N00014-92J1375)*and**the*National Science Foundation (grant NSF-DMS-9806 389). ...##
###
A Boolean measure of similarity

2006
*
Discrete Applied Mathematics
*

We relate

doi:10.1016/j.dam.2006.04.011
fatcat:upgzbcrzlbajdaeholvkk3opvu
*the*similarity measure to one based on Hamming distance*and*we develop from this some ways of quantifying*the*'quality' of a dataset. ... We propose a way of measuring*the*similarity of a Boolean vector to a given set of Boolean vectors, motivated in part by certain data mining or machine learning*problems*. ... Martin Anthony's work is supported in part by*the*IST Programme of*the*European Community, under*the*PASCAL Network of Excellence, IST-2002-506778. ...##
###
Convexity and logical analysis of data

2000
*
Theoretical Computer Science
*

We study

doi:10.1016/s0304-3975(98)00337-5
fatcat:f4nbs24hwnhixkjklds44fk76a
*the**problem*of uniqueness,*and*provide a polynomial algorithm for checking whether all k-convex extensions agree in a point outside*the*given data set. ... Given a set of true points*and*a set of false points,*the*central question of Logical Analysis of Data is*the*study of those Boolean functions whose values agree with those of*the*given points. ...*The*authors also express their gratitude to Endre Boros*and*Dan Roth for useful discussions,*and*to*the*anonymous referee for careful analysis*and*helpful suggestions. ...##
###
FPGA HW Accelerator of the First Step of Systematic Two-Level Minimization of Single-Output Boolean Function

2020
*
Acta Polytechnica Hungarica
*

normal form (

doi:10.12700/aph.17.7.2020.7.2
fatcat:5ig4zhe57vh47chxdfhxao5nsq
*DNF*)*and**the*conjunctive normal form (CNF), having defined*the*OFF*and*ON sets andalternativelyalso*the*DC ("don't care") set. ... Its advantages include an extremely short prime-*implicant*-generation time in*the*order of ns*and*/or tens of nsin case of Boolean functions with small amount of input variablesand*the*possibility to generate ... Table 3 3*Equivalence*of decadic*equivalents*(DE), ternary*equivalents*(TE)*and*prime*implicants*(PI) for both*the**DNF**and*CNF forms DE TE*DNF*PI description*DNF*PI CNF PI description CNF PI ...##
###
How Should We Solve Search Problems Privately?

2008
*
Journal of Cryptology
*

However, it is often

doi:10.1007/s00145-008-9032-z
fatcat:cypjrmnx5zcplergc3epeu7yye
*the*case that*the*parties executing a computation try to solve a search*problem*, where one input may have a multitude of correct answers -such as when*the*parties compute a*shortest*... Picking one output arbitrarily from*the*solution set has significant*implications*on*the*privacy of*the*algorithm. Beimel et al. ... We thank Rafi Ostrovsky*and**the*IPAM staff for inviting us to IPAM*and*making our stay pleasant*and*productive. ...##
###
Properties of Switch-List Representations of Boolean Functions

2020
*
The Journal of Artificial Intelligence Research
*

As a by-product of this analysis, we also give a short proof of a longstanding open question proposed by Darwiche

doi:10.1613/jair.1.12199
fatcat:q64uhgufdvbndpa3xzt6vaom6a
*and*Marquis, namely*the*incomparability of MODS (models)*and*PI (prime*implicates*) representations ... First, we compare switch-list representations with a number of standard representations (such as CNF,*DNF*,*and*OBDD) with respect to their relative succinctness. ... Acknowledgements*The*authors gratefully acknowledge a support by Czech Science Foundation (Grant 19-19463S), by SVV project number 260 575*and*by Charles University project UNCE/SCI/004. ...##
###
A Model of Interactive Teaching

1997
*
Journal of computer and system sciences (Print)
*

*The*learner makes only

*equivalence*queries

*and*all hypotheses are also

*DNF*formulas. ] 1997 Academic Press ... An important concept class that is not known to be learnable is

*DNF*formulas. We demonstrate

*the*power of our approach by providing a deterministic teacher

*and*learner for

*the*class of

*DNF*formulas. ... We also thank

*the*COLT '95 program committee. ...

##
###
Lower bounds on learning decision lists and trees
[chapter]

1995
*
Lecture Notes in Computer Science
*

ACKNOWLEDGMENTS We thank Martin Anthony

doi:10.1007/3-540-59042-0_102
fatcat:6zrph47mhjhp7j6c4w7q4ahzpe
*and*Ron Rivest for information about decision lists, Lisa Hellerstein for pointing out an omission in our proofs,*and**the*referees for their very careful reading ...*and*pointing out of numerous small errors. ...*The*result below on*DNF*easily follows from a reduction from*the*Graph Coloring*problem*to*the*approximation of*the*smallest consistent*DNF*given in [19] (see also [12] )*and**the*n = non-approximability ...##
###
Lower Bounds on Learning Decision Lists and Trees

1996
*
Information and Computation
*

ACKNOWLEDGMENTS We thank Martin Anthony

doi:10.1006/inco.1996.0040
fatcat:qf5rp4tg3badnlwkds3b43djl4
*and*Ron Rivest for information about decision lists, Lisa Hellerstein for pointing out an omission in our proofs,*and**the*referees for their very careful reading ...*and*pointing out of numerous small errors. ...*The*result below on*DNF*easily follows from a reduction from*the*Graph Coloring*problem*to*the*approximation of*the*smallest consistent*DNF*given in [19] (see also [12] )*and**the*n = non-approximability ...
« Previous

*Showing results 1 — 15 out of 261 results*