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Generalized Graph Colorability and Compressibility of Boolean Formulae [chapter]

Richard Nock, Pascal Jappy, Jean Sallantin
1998 Lecture Notes in Computer Science  
We prove that approximating the minimally consistent 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] .  ... 
doi:10.1007/3-540-49381-6_26 fatcat:wt63bayrozakbljpf6yloto42y

Switch lists in the landscape of knowledge representation languages

Ondrej Cepek
2022 Proceedings of the ... International Florida Artificial Intelligence Research Society Conference  
A switch-list representation (SLR) of a Boolean function is a 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  ... 
doi:10.32473/flairs.v35i.130700 fatcat:ldrg6y3blna6dbbkxan3ettova

The DNF exception problem

Dhruv Mubayi, György Turán, Yi Zhao
2006 Theoretical Computer Science  
Given a disjunctive normal form (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).  ... 
doi:10.1016/j.tcs.2005.10.038 fatcat:mbf2f5fcwfbjtka7ve7wh67wja

Knowledge compilation from DNF to switch-list representations

Ondrej Cepek, Radek Husek
2016 International Symposium on Artificial Intelligence and Mathematics  
a switch-listl representation, 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.  ... 
dblp:conf/isaim/CepekH16 fatcat:6xptnpyedbdfbn3drfppexmdji

PAC-learnability of determinate logic programs

Sašo Džeroski, Stephen Muggleton, Stuart Russell
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 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].  ... 
doi:10.1145/130385.130399 dblp:conf/colt/DzeroskiMR92 fatcat:znvsqnaubzgnrlgmgsxmdngxmq

On the orthogonalization of arbitrary Boolean formulae

Renato Bruni
2005 Journal of Applied Mathematics and Decision Sciences  
Moreover, such problem is strongly connected with the well-known 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.  ... 
doi:10.1155/jamds.2005.61 fatcat:a5msnmaal5bydhknimwctjx4ja

Properties of Switch-List Representations of Boolean Functions

Miloš Chromý, Ondřej Čepek
2020 The Journal of Artificial Intelligence Research  
First, we compare switch-list representations with a number of standard representations (such as CNF, 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.  ... 
doi:10.1613/jair.1.12199 fatcat:q64uhgufdvbndpa3xzt6vaom6a

Importing SMT and Connection proofs as expansion trees

Giselle Reis
2015 Electronic Proceedings in Theoretical Computer Science  
By representing the 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).  ... 
doi:10.4204/eptcs.186.3 fatcat:frjp276fq5amfcljaic4z44oii

The Complexity of Propositional Proofs

Nathan Segerlind
2007 Bulletin of Symbolic Logic  
AbstractPropositional 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.  ... 
doi:10.2178/bsl/1203350879 fatcat:mzffx4yqzfcg7ell47v452f2eu

Measuring logic complexity can guide pattern discovery in empirical systems [article]

Marco Gherardi, Pietro Rotondo
2016 arXiv   pre-print
We demonstrate its utility by measuring it in empirical data on gene regulation, digital circuitry, 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.  ... 
arXiv:1603.03337v1 fatcat:xa7f6k6p7rgglmx47a47cytxsu

Belief Revision in Sentential Decision Diagrams [article]

Lilith Mattei and Alessandro Facchini and Alessandro Antonucci
2022 arXiv   pre-print
Classical belief revision schemes have been already specialised to binary decision diagrams (BDDs), the classical formalism to compactly represent 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.  ... 
arXiv:2201.08112v1 fatcat:e2q6ftgpgrbbljwvdinj4bku4e

Phase Transitions and Stochastic Local Search in k-Term DNF Learning [chapter]

Ulrich Rückert, Stefan Kramer, Luc De Raedt
2002 Lecture Notes in Computer Science  
In the past decade, there has been a lot of interest in phase transitions within artificial intelligence, 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.  ... 
doi:10.1007/3-540-36755-1_34 fatcat:p4actxzprzervmf54x2lwx6n3m

The problem of Π 2 -cut-introduction

Alexander Leitsch, Michael Lettmann
2018 Theoretical Computer Science  
We describe an algorithmic method of 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| ♦ ≤  ... 
doi:10.1016/j.tcs.2017.10.003 fatcat:wfe6si3ooravroe6t2udgfcnlm

Approximation Properties of Inverse Fuzzy Transforms over the Residuated Lattice

Martina Danková, Martin Stepnicka
2009 European Society for Fuzzy Logic and Technology  
Perfilieva 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.  ... 
dblp:conf/eusflat/DankovaS09 fatcat:qs2gf7f6fbctxf2gkeuo5gseqy

Measuring logic complexity can guide pattern discovery in empirical systems

Marco Gherardi, Pietro Rotondo
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.  ... 
doi:10.1002/cplx.21819 fatcat:hejkgjnncrbxxecln2ca22l5fy
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