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On converting CNF to DNF

2003
*
BRICS Report Series
*

We study how big the blow-up in size can be when

doi:10.7146/brics.v10i45.21817
fatcat:a7qm36sxyjcadj4hebymr2xfry
*one*switches between the*CNF*and*DNF*representations of boolean functions. ... For a function f : {0,1}^n -> {0,1}, cnfsize(f) denotes the minimum number of clauses in a*CNF*for f; similarly, dnfsize(f) denotes the minimum number of terms in a*DNF*for f. ... Acknowledgements An earlier version of this paper was submitted*to*the conference*on*Mathematical Foundations of Computer Science (MFCS). ...##
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On converting CNF to DNF

2005
*
Theoretical Computer Science
*

We study how big the blow-up in size can be when

doi:10.1016/j.tcs.2005.07.029
fatcat:3neoxlxp4rbvjakm6y7cjtrt4a
*one*switches between the*CNF*and*DNF*representations of Boolean functions. ... For a function f : {0, 1} n → {0, 1}, cnfsize(f ) denotes the minimum number of clauses in a*CNF*for f; similarly, dnfsize(f ) denotes the minimum number of terms in a*DNF*for f. ... Acknowledgements An earlier version of this paper was submitted*to*the conference*on*Mathematical Foundations of Computer Science (MFCS). ...##
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On Converting CNF to DNF
[chapter]

2003
*
Lecture Notes in Computer Science
*

We study how big the blow-up in size can be when

doi:10.1007/978-3-540-45138-9_55
fatcat:6zcxfdpl4nedhjsmgj3mgfu524
*one*switches between the*CNF*and*DNF*representations of Boolean functions. ... For a function f : {0, 1} n → {0, 1}, cnfsize(f ) denotes the minimum number of clauses in a*CNF*for f; similarly, dnfsize(f ) denotes the minimum number of terms in a*DNF*for f. ... Acknowledgements An earlier version of this paper was submitted*to*the conference*on*Mathematical Foundations of Computer Science (MFCS). ...##
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Recursive optimization on converting CNF to DNF using grid computing

2015
*
CSI Transactions on ICT
*

A NP hard problem

doi:10.1007/s40012-015-0070-z
fatcat:42j7nfpyyjckvj75phgoygxwtu
*CNF**to**DNF*conversion is a vast area of research for AI, circuit design, FPGA's (Miltersen et al. in*On**converting**CNF**To**DNF*, 2003), PLA's, etc. ... The*CNF**converted*data is then been applied*on*grid system for*converting*it*to**DNF*. ... The*CNF**to**DNF*conversion process is considered*to*be as the most accurate and optimizing. ...##
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Normal forms for inductive logic programming
[chapter]

1997
*
Lecture Notes in Computer Science
*

First, we show that in the propositional case induction from complete evidence can be seen as an equivalence-preserving transformation from

doi:10.1007/3540635149_43
fatcat:57kpgrgsnfhxxaaiq7sdx5y3r4
*DNF**to**CNF*. ... We define evidence normal form (ENF), which is Skolemised existential*DNF*under a Consistent Naming Assumption. ... ∧human ∨ ¬woman∧¬man∧¬human The reformulation task is then*to**convert*this*DNF*formula*to**CNF*, followed by a minimisation step. ...##
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On the gap between ess(f) and cnf_size(f)

2013
*
Discrete Applied Mathematics
*

Although ess(f ) is clearly a lower bound

doi:10.1016/j.dam.2012.07.004
fatcat:sje3ajdbn5eovcmiumlxlr2wgi
*on**cnf*_size(f ) (the minimum number of clauses in a*CNF*formula for f ),Cepek et al. showed it is not, in general, a tight lower bound [6]. ... They gave examples of functions f for which there is a small gap between ess(f ) and*cnf*_size(f ). We demonstrate significantly larger gaps. ... We can*convert*the partial functionf*to*a total functiong according*to*the construction detailed in Section 4.1. ...##
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On the gap between ess(f) and cnf_size(f)
[article]

2011
*
arXiv
*
pre-print

Although ess(f) is clearly a lower bound

arXiv:1106.4247v1
fatcat:b5xxa4zserdx3gpm5v67pj6y34
*on*cnf_size(f) (the minimum number of clauses in a*CNF*formula for f), Cepek et al. showed that it is not, in general, a tight lower bound. ... We can*convert*the partial functionf*to*a total functiong according*to*the construction detailed in Section 4.1. ... We can*convert*the partial functionf (x)*to*a total functiong(x) just as done in the previous section. The arguments regarding*DNF*-size and ess d (g) remain the same. ...##
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Efficient dualization of O(logn)-term monotone disjunctive normal forms

2003
*
Discrete Applied Mathematics
*

This improves upon the trivial result that k-term monotone

doi:10.1016/s0166-218x(02)00204-4
fatcat:p7nru7ujo5hjpjsms46mr2wndq
*DNFs*can be dualized in polynomial time, where k is bounded by some constant. ? ... This paper shows that O(log n)-term monotone disjunctive normal forms (*DNFs*) ' can be dualized in incremental polynomial time, where n is the number of variables in '. ... A negative*DNF*(resp.,*CNF*) is a*DNF*(resp.,*CNF*) consisting of only negative literals. ...##
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Generating all maximal independent sets of bounded-degree hypergraphs

1997
*
Proceedings of the tenth annual conference on Computational learning theory - COLT '97
*

We show that any monotone function with a read-k

doi:10.1145/267460.267500
dblp:conf/colt/MishraP97
fatcat:qfprhmtc3jakbb4tsgw3th5c6q
*CNF*representation can be learned in terms of its*DNF*representation with membership queries alone in time polynomial in the*DNF*size and n (the number ... Our algorithm gives a solution for the bounded degree case and works even if the hypergraph is not input, but rather only queries are available as*to*which sets are independent. ... ACKNOWLEDGEMENTS We would like*to*thank Dan Oblinger for entertaining our numerous, random musings, and Heikki Mannila for his encouragement and for his comments*on*an earlier draft. ...##
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Applying Variable Minimal Unsatisfiability in Model Checking

2008
*
Journal of Software (Chinese)
*

A mathematical definition of variable minimal unsatisfiability (VMU) is introduced

doi:10.3724/sp.j.1001.2008.00039
fatcat:aucua72onzhbtbe6z5r6wv25gm
*to*drive this abstraction refinement process. ... The set of variables of VMU formula is a minimal*one*guaranteeing its unsatisfiability. Furthermore, the authors prove that VMU-driven refinement is valid and minimal by mathematical reasoning. ... Acknowledgement The authors would like*to*thank Prof. DING De-Cheng and Prof. XU Bao-Wen for their valuable discussions and thank the anonymous referees for their helpful comments and suggestions. ...##
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A Knowledge Compilation Map

2002
*
The Journal of Artificial Intelligence Research
*

We also go beyond classical, flat target compilation languages based

doi:10.1613/jair.989
fatcat:qq2to3nr2bau3idwbnup6lfrgm
*on**CNF*and*DNF*, and consider a richer, nested class based*on*directed acyclic graphs (such as OBDDs), which we show*to*include a relatively ... We propose a perspective*on*knowledge compilation which calls for analyzing different compilation approaches according*to*two key dimensions: the succinctness of the target compilation language, and the ... Acknowledgements We wish*to*thank Alvaro del Val, Mark Hopkins and Jérôme Lang for some suggestions, as well as Ingo Wegener for his help with some of the issues discussed in the paper. ...##
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Polyhedrons and Perceptrons Are Functionally Equivalent
[article]

2013
*
arXiv
*
pre-print

Perceptron networks in disjunctive normal form (

arXiv:1311.1090v1
fatcat:tmpbamvfl5gkhb4cqd32s3gywa
*DNF*) and conjunctive normal forms (*CNF*) are introduced. ... The main theme is that single output perceptron neural networks and characteristic functions of polyhedrons are*one*and the same class of functions. ... Schemes ∆ will be used*to*specify*DNF*and*CNF*polyhedrons over H. They will also define*DNF*and*CNF*networks. These are bit valued functions defined*on*R n . ...##
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A Solution of the P versus NP Problem
[article]

2017
*
arXiv
*
pre-print

Berg and Ulfberg and Amano and Maruoka have used

arXiv:1708.03486v2
fatcat:qazjea2sxbe63hck4jpfp64uny
*CNF*-*DNF*-approximators*to*prove exponential lower bounds for the monotone network complexity of the clique function and of Andreev's function. ... We show that these approximators can be used*to*prove the same lower bound for their non-monotone network complexity. This implies P not equal NP. ... During the construction of the approximators,*one**CNF*/*DNF*-and*one**DNF*/*CNF*-approximator switch are performed. ...##
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The exp-log normal form of types
[article]

2016
*
arXiv
*
pre-print

*on*terms. ... Second, it is not clear how

*to*decide when two types are essentially the same, i.e. isomorphic, in spite of the meta-theoretic results

*on*decidability of the isomorphism. ... Inductive

*CNF*: Set := | top | con :

*CNF*→ Base →

*CNF*→

*CNF*with

*DNF*: Set := | two :

*CNF*→

*CNF*→

*DNF*| dis :

*CNF*→

*DNF*→

*DNF*with Base : Set := | prp : Proposition → Base | bd :

*DNF*→ Base. ...

##
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Model Counting meets F0 Estimation
[article]

2021
*
arXiv
*
pre-print

*To*this end, we focus

*on*two foundational problems: model counting for CSP's and computation of zeroth frequency moments (F_0) for data streams. ... We next turn our attention

*to*viewing streaming from the lens of counting and show that framing F_0 estimation as a special case of #

*DNF*counting allows us

*to*obtain a general recipe for a rich class of ... We will use #

*CNF*

*to*refer

*to*the case when is a

*CNF*formula while #

*DNF*

*to*refer

*to*the case when is a

*DNF*formula. ...

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