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Generalized Graph Colorability and Compressibility of Boolean Formulae
[chapter]

1998
*
Lecture Notes in Computer Science
*

We prove that approximating the minimally consistent

doi:10.1007/3-540-49381-6_26
fatcat:wt63bayrozakbljpf6yloto42y
*DNF*formula,*and*a generalization of graph colorability, is very hard. ... An Occam's razor is an algorithm which*compresses*the knowledge of observations (examples) in small formulae. ... success of the production system paradigm*and*of Horn clause*logics*" [35] . ...##
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Switch lists in the landscape of knowledge representation languages

2022
*
Proceedings of the ... International Florida Artificial Intelligence Research Society Conference
*

A switch-list representation (SLR) of a Boolean function is a

doi:10.32473/flairs.v35i.130700
fatcat:ldrg6y3blna6dbbkxan3ettova
*compressed*truth table representation of a Boolean function in which only the function value of the first row in the truth table*and*an ordered ... In this short paper we outline scenarios under which SLRs constitute a better representation language than standard representation languages such as CNFs*and*OBDDs. ... Acknowledgements The authors gratefully acknowledge a support by Czech Science Foundation (Grant 19-19463S)*and*by TAILOR, a project funded by EU Horizon 2020 research*and*innovation programme under GA ...##
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The DNF exception problem

2006
*
Theoretical Computer Science
*

Given a disjunctive normal form (

doi:10.1016/j.tcs.2005.10.038
fatcat:mbf2f5fcwfbjtka7ve7wh67wja
*DNF*) expression*and*a set A of vectors satisfying the expression, called the set of exceptions, we would like to update to get a new*DNF*which is false on A,*and*otherwise ... Is there an algorithm with running time polynomial in the number of variables, the size of the original formula*and*the number of exceptions, which produces an updated formula of size bounded by a certain ... We consider this question in the context of*propositional**logic*, by looking at the basic case of disjunctive normal forms (*DNFs*). ...##
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Knowledge compilation from DNF to switch-list representations

2016
*
International Symposium on Artificial Intelligence and Mathematics
*

a switch-listl representation,

dblp:conf/isaim/CepekH16
fatcat:6xptnpyedbdfbn3drfppexmdji
*and*(2) a knowledge*compression*problem, i.e. a problem of finding the most compact switch-list representation among those which represent the same function. ... We will summarize known results about these two problems*and*present a new one about the compilation problem. ...*DNF*minimization (optimal*compression*) is a notoriously hard problem. ...##
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PAC-learnability of determinate logic programs

1992
*
Proceedings of the fifth annual workshop on Computational learning theory - COLT '92
*

Acknowledgements Szulo Diieroski is on leave from Institut Joief Stefan, Ljubljana, Slovenia

doi:10.1145/130385.130399
dblp:conf/colt/DzeroskiMR92
fatcat:znvsqnaubzgnrlgmgsxmdngxmq
*and*is supported by a scholarship from the British Council*and*the Slovene Ministry of Science*and*Technology ... Stuart Russell is on sabbatical from the Computer Science Division, University of California, Berkeley*and*is supported by a Visiting Fellowship from the UK Science*and*Engineering Research Council*and*...*Proof*: After transforming the problem to a proposi- tional form, we use the algorithm for learning monotone k-term-*DNF*described in [Li*and*Vitanyi 1991]. ...##
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On the orthogonalization of arbitrary Boolean formulae

2005
*
Journal of Applied Mathematics and Decision Sciences
*

Moreover, such problem is strongly connected with the well-known

doi:10.1155/jamds.2005.61
fatcat:a5msnmaal5bydhknimwctjx4ja
*propositional*satisfiability problem. Therefore, important complexity issues are involved. ... A general procedure for transforming an arbitrary CNF or*DNF*to an orthogonal one is proposed. Such procedure is tested on randomly generated Boolean formulae. ... Hammer*and*Endre Boros for introducing the discussed problems to his attention. ...##
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Properties of Switch-List Representations of Boolean Functions

2020
*
The Journal of Artificial Intelligence Research
*

First, we compare switch-list representations with a number of standard representations (such as CNF,

doi:10.1613/jair.1.12199
fatcat:q64uhgufdvbndpa3xzt6vaom6a
*DNF*,*and*OBDD) with respect to their relative succinctness. ... As a by-product of this analysis, we also give a short*proof*of a longstanding open question proposed by Darwiche*and*Marquis, namely the incomparability of MODS (models)*and*PI (prime implicates) representations ... 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. ...##
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Importing SMT and Connection proofs as expansion trees

2015
*
Electronic Proceedings in Theoretical Computer Science
*

By representing the

doi:10.4204/eptcs.186.3
fatcat:frjp276fq5amfcljaic4z44oii
*proofs*in the same framework, all the algorithms*and*tools available for expansion trees (*compression*, visualization, sequent calculus*proof*construction,*proof*checking, etc.) can ... To understand*and*analyze these objects, one needs to study the corresponding*proof*theory,*and*then study the language used to represent*proofs*, on a prover by prover basis. ...*DNF*). ...##
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The Complexity of Propositional Proofs

2007
*
Bulletin of Symbolic Logic
*

AbstractPropositional

doi:10.2178/bsl/1203350879
fatcat:mzffx4yqzfcg7ell47v452f2eu
*proof*complexity is the study of the sizes of*propositional**proofs*,*and*more generally, the resources necessary to certify*propositional*tautologies. ... Questions about*proof*sizes have connections with computational complexity, theories of arithmetic,*and*satisfiability algorithms. ... On August 5th, 2006,*propositional**proof*complexity lost one of its leading young contributors when Misha Alekhnovich was killed in a kayaking accident in Russia. ...##
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Measuring logic complexity can guide pattern discovery in empirical systems
[article]

2016
*
arXiv
*
pre-print

We demonstrate its utility by measuring it in empirical data on gene regulation, digital circuitry,

arXiv:1603.03337v1
fatcat:xa7f6k6p7rgglmx47a47cytxsu
*and**propositional*calculus.*Logic*complexity is exceptionally low in these systems. ... The asymmetry between "on"*and*"off" states in the data correlates with the complexity in a non-null way; a model of random Boolean networks clarifies this trend*and*indicates a common hierarchical architecture ... We also acknowledge discussions with Bruno Bassetti*and*Jacopo Grilli. ...##
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Belief Revision in Sentential Decision Diagrams
[article]

2022
*
arXiv
*
pre-print

Classical belief revision schemes have been already specialised to binary decision diagrams (BDDs), the classical formalism to compactly represent

arXiv:2201.08112v1
fatcat:e2q6ftgpgrbbljwvdinj4bku4e
*propositional*knowledge. ... A specialised procedure for*DNFs*is also presented. Preliminary experiments performed with randomly generated knowledge bases show the advantages of directly perform revision within SDD formalism. ... Again, a*compression*is made on the currently processed node. Thus the worst-case running time of the algorithm is O(|S|).*Proof*of Theorem 2. ...##
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Phase Transitions and Stochastic Local Search in k-Term DNF Learning
[chapter]

2002
*
Lecture Notes in Computer Science
*

In the past decade, there has been a lot of interest in phase transitions within artificial intelligence,

doi:10.1007/3-540-36755-1_34
fatcat:p4actxzprzervmf54x2lwx6n3m
*and*more recently, in machine learning*and*inductive*logic*programming. ... We compare several variants that first reduce k-term*DNF*to SAT*and*then apply well-known SLS algorithms, such as GSAT*and*WalkSAT. ... In this paper, we study an important class of boolean formulae, i.e. k-term*DNF*,*and*show that phase transitions also occur in this*propositional*framework. ...##
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The problem of Π 2 -cut-introduction

2018
*
Theoretical Computer Science
*

We describe an algorithmic method of

doi:10.1016/j.tcs.2017.10.003
fatcat:wfe6si3ooravroe6t2udgfcnlm
*proof**compression*based on the introduction of Pi_2-cuts into a cut-free LK-*proof*. ... It is shown that, by this algorithm, we can achieve an exponential*proof**compression*. ... Let π be a minimal*proof*of S n in terms of quantifier,*logical*, or symbol complexity*and*π ′ a minimal*proof*of S ′ n in terms of quantifier,*logical*,*and*symbol complexity, respectively then |π| ♦ ≤ ...##
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Approximation Properties of Inverse Fuzzy Transforms over the Residuated Lattice

2009
*
European Society for Fuzzy Logic and Technology
*

Perfilieva

dblp:conf/eusflat/DankovaS09
fatcat:qs2gf7f6fbctxf2gkeuo5gseqy
*and*their approximation properties. We will try to reduce some requirements used in the original work to prove Approximation theorem. ... Acknowledgment We gratefully acknowledge partial support of the projects MSM6198898701*and*1M0572 of the M ŠMT ČR. ... In the following*proposition*, we are going to show that the combinations of {*DNF*D f , CNF C f }*and*{CNF D f ,*DNF*C f } have this property. ...##
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Measuring logic complexity can guide pattern discovery in empirical systems

2016
*
Complexity
*

*Logic*complexity is exceptionally low in these systems,

*and*the asymmetry between "on"

*and*"off" states in the data correlates with the complexity in a non-null way. ... A definition of complexity based on

*logic*functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science was explored. ... Formal

*Logic*The relations between

*logic*functions

*and*expressions constitute the branch of

*logic*known as

*propositional*calculus. ...

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