Filters








1,014 Hits in 3.9 sec

On converting CNF to DNF

Peter Bro Miltersen, Jaikumar Radhakrishnan, Ingo Wegener
2003 BRICS Report Series  
We study how big the blow-up in size can be when 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).  ... 
doi:10.7146/brics.v10i45.21817 fatcat:a7qm36sxyjcadj4hebymr2xfry

On converting CNF to DNF

Peter Bro Miltersen, Jaikumar Radhakrishnan, Ingo Wegener
2005 Theoretical Computer Science  
We study how big the blow-up in size can be when 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).  ... 
doi:10.1016/j.tcs.2005.07.029 fatcat:3neoxlxp4rbvjakm6y7cjtrt4a

On Converting CNF to DNF [chapter]

Peter Bro Miltersen, Jaikumar Radhakrishnan, Ingo Wegener
2003 Lecture Notes in Computer Science  
We study how big the blow-up in size can be when 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).  ... 
doi:10.1007/978-3-540-45138-9_55 fatcat:6zcxfdpl4nedhjsmgj3mgfu524

Recursive optimization on converting CNF to DNF using grid computing

Mayuresh S. Pardeshi
2015 CSI Transactions on ICT  
A NP hard problem 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.  ... 
doi:10.1007/s40012-015-0070-z fatcat:42j7nfpyyjckvj75phgoygxwtu

Normal forms for inductive logic programming [chapter]

Peter A. Flach
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 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.  ... 
doi:10.1007/3540635149_43 fatcat:57kpgrgsnfhxxaaiq7sdx5y3r4

On the gap between ess(f) and cnf_size(f)

Lisa Hellerstein, Devorah Kletenik
2013 Discrete Applied Mathematics  
Although ess(f ) is clearly a lower bound 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.  ... 
doi:10.1016/j.dam.2012.07.004 fatcat:sje3ajdbn5eovcmiumlxlr2wgi

On the gap between ess(f) and cnf_size(f) [article]

Lisa Hellerstein, Devorah Kletenik
2011 arXiv   pre-print
Although ess(f) is clearly a lower bound 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.  ... 
arXiv:1106.4247v1 fatcat:b5xxa4zserdx3gpm5v67pj6y34

Efficient dualization of O(logn)-term monotone disjunctive normal forms

Kazuhisa Makino
2003 Discrete Applied Mathematics  
This improves upon the trivial result that k-term monotone 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.  ... 
doi:10.1016/s0166-218x(02)00204-4 fatcat:p7nru7ujo5hjpjsms46mr2wndq

Generating all maximal independent sets of bounded-degree hypergraphs

Nina Mishra, Leonard Pitt
1997 Proceedings of the tenth annual conference on Computational learning theory - COLT '97  
We show that any monotone function with a read-k 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.  ... 
doi:10.1145/267460.267500 dblp:conf/colt/MishraP97 fatcat:qfprhmtc3jakbb4tsgw3th5c6q

Applying Variable Minimal Unsatisfiability in Model Checking

Zhen-Yu CHEN
2008 Journal of Software (Chinese)  
A mathematical definition of variable minimal unsatisfiability (VMU) is introduced 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.  ... 
doi:10.3724/sp.j.1001.2008.00039 fatcat:aucua72onzhbtbe6z5r6wv25gm

A Knowledge Compilation Map

A. Darwiche, P. Marquis
2002 The Journal of Artificial Intelligence Research  
We also go beyond classical, flat target compilation languages based 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.  ... 
doi:10.1613/jair.989 fatcat:qq2to3nr2bau3idwbnup6lfrgm

Polyhedrons and Perceptrons Are Functionally Equivalent [article]

Daniel Crespin
2013 arXiv   pre-print
Perceptron networks in disjunctive normal form (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 .  ... 
arXiv:1311.1090v1 fatcat:tmpbamvfl5gkhb4cqd32s3gywa

A Solution of the P versus NP Problem [article]

Norbert Blum
2017 arXiv   pre-print
Berg and Ulfberg and Amano and Maruoka have used 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.  ... 
arXiv:1708.03486v2 fatcat:qazjea2sxbe63hck4jpfp64uny

The exp-log normal form of types [article]

Danko Ilik
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 → CNFCNF with DNF : Set := | two : CNFCNFDNF | dis : CNFDNFDNF with Base : Set := | prp : Proposition → Base | bd : DNF → Base.  ... 
arXiv:1502.04634v3 fatcat:6fx7n53vrbejflrzqgywihisji

Model Counting meets F0 Estimation [article]

A. Pavan and N.V. Vinodchandran and Arnab Bhattacharyya and Kuldeep S. Meel
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.  ... 
arXiv:2105.00639v1 fatcat:4exegyfj35c5fnem7sewzwzime
« Previous Showing results 1 — 15 out of 1,014 results