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Algorithms for computing backbones of propositional formulae

Mikoláš Janota, Inês Lynce, Joao Marques-Silva
2015 AI Communications  
This article overviews existing algorithms for backbone computation and introduces two novel ones. Further, an extensive evaluation of the algorithms is presented.  ...  Often, some other properties of the formula need to be computed.  ...  Implicant Enumeration An algorithm for computing the backbone of a propositional formula based on implicant enumeration is shown in Algorithm 1.  ... 
doi:10.3233/aic-140640 fatcat:r3cvfiqrkfcnbc2uxhk74fzpay

Algorithm for Computing Backbones of Propositional Formulae Based on Solved Backbone Information

Zipeng Wang, Yiping Bao, Junhao Xing, Xinyu Chen, Sihan Liu
2016 Proceedings of the 2016 International Conference on Applied Mathematics, Simulation and Modelling   unpublished
Based on this idea, we bring up a new algorithm for computing backbone of propositional formulae using solved backbone information.  ...  First of all, this article reviews three existing algorithms for computing backbone, finding that no algorithm uses solved backbone as information.  ...  ALGORITHM FOR COMPUTING BACKBONES OF PROPOSITIONAL FORMULAE BASED ON SOLVED BACKBONE INFORMATION According to the proposition 1 we can get a more efficient algorithm based on solved backbone information  ... 
doi:10.2991/amsm-16.2016.8 fatcat:5rrruvc665edndvw4rte2o43e4

On Computing Generalized Backbones

Alessandro Previti, Alexey Ignatiev, Matti Jarvisalo, Joao Marques-Silva
2017 2017 IEEE 29th International Conference on Tools with Artificial Intelligence (ICTAI)  
satisfiability (SAT), motivating the development of efficient algorithms for determining the set of backbone variables of a given propositional formula.  ...  two generic algorithms for determining the backbone in this general context.  ...  algorithms for determining the set of backbone variables of a given propositional formula have been recently developed [20] .  ... 
doi:10.1109/ictai.2017.00161 dblp:conf/ictai/PrevitiIJM17 fatcat:5xdatyck4zddjkmwi4wvtlfvoi

A preference-based approach to backbone computation with application to argumentation

Alessandro Previti, Matti Järvisalo
2018 Proceedings of the 33rd Annual ACM Symposium on Applied Computing - SAC '18  
Algorithms for determining the backbone of propositional formulas, i.e., Boolean satisfiability (SAT) instances, find various real-world applications.  ...  We also show empirically that the proposed approach is specifically effective in computing the ideal semantics of argumentation frameworks, noticeably outperforming an other state-of-the-art backbone solver  ...  ACKNOWLEDGMENTS The authors thank Mikolas Janota for advice on MiniBones, and Andreas Niskanen for discussion and advice on the AFGen and CNFGen generators.  ... 
doi:10.1145/3167132.3167230 dblp:conf/sac/PrevitiJ18 fatcat:lj7lvloyyjaujgirxeqia5saku

Computing Minimal Sets on Propositional Formulae I: Problems & Reductions [article]

Joao Marques-Silva, Mikolas Janota
2014 arXiv   pre-print
Moreover, this exercise motivates the development of more efficient algorithms for the MSMP problem.  ...  This paper addresses a number of representative function problems defined on Boolean formulas, and shows that all these function problems can be reduced to a generic problem of computing a minimal set  ...  FBB is the function problem of computing the backbone of F ∈ F. In practice, algorithms for computing the backbone of a formula often start from a reference model [70] .  ... 
arXiv:1402.3011v2 fatcat:ia3domcftjdyhjjzjpq2lnqwru

Local Backbones [chapter]

Ronald de Haan, Iyad Kanj, Stefan Szeider
2013 Lecture Notes in Computer Science  
The notion of backbones for CNF formulas has been studied in various contexts. In this paper, we introduce local variants of backbones, and study the computational complexity of detecting them.  ...  A backbone of a propositional CNF formula is a variable whose truth value is the same in every truth assignment that satisfies the formula.  ...  Introduction A backbone of a propositional formula ϕ is a variable whose truth value is the same for all satisfying assignments of ϕ.  ... 
doi:10.1007/978-3-642-39071-5_28 fatcat:hamlrphmubc5berc4qwrcoycja

Improving SAT-solving with Machine Learning

Haoze Wu
2017 Proceedings of the 2017 ACM SIGCSE Technical Symposium on Computer Science Education - SIGCSE '17  
We first used a logistic regression model to predict the satisfiability of propositional boolean formulae after fixing the values of a certain fraction of the variables in each formula.  ...  Excluding the preprocessing time, compared with the default setting of Minisat, the runtime of Minisat for satisfiable formulae decreased by 23%.  ...  formulae, for varying values of n.  ... 
doi:10.1145/3017680.3022464 dblp:conf/sigcse/Wu17 fatcat:inj42rvytvfz5pbhzwikrw57pu

Abstract Solvers for Computing Cautious Consequences of ASP programs

GIOVANNI AMENDOLA, CARMINE DODARO, MARCO MARATEA
2019 Theory and Practice of Logic Programming  
By doing so, we also formally show that the algorithms for solving cautious reasoning tasks in ASP are strongly related to those for computing backbones of Boolean formulas.  ...  We show how to improve the current abstract solvers for cautious reasoning in ASP with new techniques borrowed from backbone computation in SAT, in order to design new solving algorithms.  ...  Such advanced techniques have been borrowed from the computation of backbones of propositional formulas.  ... 
doi:10.1017/s1471068419000164 fatcat:cg55bnqd4vagxcf53wkn2b26q4

Blocked Clause Decomposition [chapter]

Marijn J. H. Heule, Armin Biere
2013 Lecture Notes in Computer Science  
We demonstrate that it is fairly easy to decompose any propositional formula into two subsets such that both can be solved by blocked clause elimination.  ...  We present algorithms and heuristics to obtain unbalanced decompositions efficiently. Our techniques have been implemented in the state-of-the-art solver Lingeling.  ...  For random formulas, the backbone of a formula is fragile [6] : i.e., removal of a few clauses reduces the size of the backbone.  ... 
doi:10.1007/978-3-642-45221-5_29 fatcat:72naebvkpfd6jf6ddslmjiifnu

Backbone Guided Local Search for the Weighted Maximum Satisfiability Problem [chapter]

He Jiang, Jifeng Xu
2009 Evolutionary Computation  
In this chapter we investigated the computational complexity of the backbone for weighted MAX-SAT and developed a backbone guided local search (BGLS) algorithm.  ...  Given a set of Boolean variables 1 2 { , . , } n V x x x = , a propositional formula φ is a conjunction on a set of m clauses 1 2 { , . , } m C C C C = .  ... 
doi:10.5772/9610 fatcat:jkx7xzn6jbeqpcbvlpjbplsgze

A Logic-Based Approach to Solve the Steiner Tree Problem [chapter]

Mohamed El Bachir Menai
2009 IFIP Advances in Information and Communication Technology  
The algorithm is tested on a well known set of benchmark instances.  ...  In this paper, we propose to solve the STP by formulating it as a variation of SAT, and to solve it using a heuristic search method guided by the backbone of the problem.  ...  Introduction The satisfiability problem in propositional logic (SAT) is the task to decide for a given propositional formula in conjunctive normal form (CNF) whether it has a model.  ... 
doi:10.1007/978-1-4419-0221-4_10 fatcat:7jeob3fugzgzna2aw5utiby6zm

Discovering Cyclic Causal Models with Latent Variables: A General SAT-Based Procedure [article]

Antti Hyttinen, Patrik O. Hoyer, Frederick Eberhardt, Matti Jarvisalo
2013 arXiv   pre-print
The procedure allows for both directed cycles (feedback loops) and the presence of latent variables.  ...  Simulations illustrate the effect of these assumptions on discovery and how the present algorithm scales.  ...  SAT AND BACKBONES Our algorithm for causal structure discovery is based on computing the so-called backbone of a given formula in propositional logic.  ... 
arXiv:1309.6836v1 fatcat:wde2vqsucbcnjpgekmmehc4jaa

Semantics based verification and synthesis of BPEL4WS abstract processes

Ziyang Duan, A. Bernstein, P. Lewis, Shiyong Lu
2004 Proceedings. IEEE International Conference on Web Services, 2004.  
We then sketch an algorithm that automatically synthesizes a workflow given its specification and a task library.  ...  Based on the model, we present a set of inference rules to deduce the strongest postcondition and weakest precondition of a workflow and demonstrate that automatic workflow verification is possible due  ...  Hence a state assigns a subset of literals in U Boolean values. Assertion: An assertion is a well-formed formula (wff) defined on U. A well-formed formula (wff) is a sentence in propositional logic.  ... 
doi:10.1109/icws.2004.1314805 dblp:conf/icws/DuanBLL04 fatcat:2el6zwjfijdlbjkfpgf4w4jawq

Spines of random constraint satisfaction problems: definition and connection with computational complexity

Gabriel Istrate, Stefan Boettcher, Allon G. Percus
2005 Annals of Mathematics and Artificial Intelligence  
We study the connection between the order of phase transitions in combinatorial problems and the complexity of decision algorithms for such problems.  ...  Finally, we argue that it is the spine rather than the backbone parameter whose continuity has implications for the decision complexity of combinatorial problems, and we provide experimental evidence that  ...  Because of Proposition 1 and the fact that SAT(C) has a continuous spine, for every ǫ > 0, minimally unsatisfiable subformulas of a random formula Φ with constraint density c(ǫ) contain w.h.p. at most  ... 
doi:10.1007/s10472-005-7033-2 fatcat:u43fbvbrajczvmn5wmb4tkwwsm

Supporting Historical Photo Identification with Face Recognition and Crowdsourced Human Expertise (Extended Abstract)

Vikram Mohanty, David Thames, Sneha Mehta, Kurt Luther
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
In this paper, we focus on identifying portraits of soldiers who participated in the American Civil War (1861-65). Millions of these portraits survive, but only 10-20% are identified.  ...  Identifying people in historical photographs is important for interpreting material culture, correcting the historical record, and creating economic value, but it is also a complex and challenging task  ...  By doing so, we also formally show, through a uniform treatment, a strong relation among algorithms for solving cautious reasoning tasks in ASP and those for computing backbones of Boolean formulas.  ... 
doi:10.24963/ijcai.2020/652 dblp:conf/ijcai/AmendolaDM20 fatcat:ewc3j6xj7jhzhpiwy2w46ogs6q
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