The Opacity of Backbones

Hemaspaandra, Lane A.; Narváez, David E.

doi:10.1609/aaai.v31i1.11134

Cited by 8 publications

(4 citation statements)

References 9 publications

(10 reference statements)

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“…Third, natural is in the eye of the beholder; although the election-attack problems used in the result are the standard, natural ones, the election systems used are indirectly specified by the hypothesized sets in (NP ∩ coNP) − P, and so are likely not very natural. And fourth and finally, this entire approach then found application in a different area of AI, namely, the study of backbones and backdoors of Boolean formulas, where it was shown for example that if P = NP ∩ coNP, then search versus decision separations occur for backbones (Hemaspaandra and Narváez 2017a;2017b).…”

Section: Search Versus Decision For Np Problemsmentioning

confidence: 99%

Computational Social Choice and Computational Complexity: BFFs?

Hemaspaandra

2018

AAAI

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We discuss the connection between computational social choice (comsoc) and computational complexity. We stress the work so far on, and urge continued focus on, two less-recognized aspects of this connection. Firstly, this is very much a two-way street: Everyone knows complexity classification is used in comsoc, but we also highlight benefits to complexity that have arisen from its use in comsoc. Secondly, more subtle, less-known complexity tools often can be very productively used in comsoc.

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Section: Search Versus Decision For Np Problemsmentioning

confidence: 99%

Computational Social Choice and Computational Complexity: BFFs?

Hemaspaandra

2018

AAAI

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“…Given that our hypothesis is that combinatorial problems provide hard instances of SAT problems, we wish to study these structures closely and determine the role they play in the instances we are interested in. In (Hemaspaandra and Narváez 2017a) we looked at a separation in the complexity of finding a backbone versus that of finding the value to which that backbone must be set in order to find a satisfying assignment. This separation is true under the widely-believed assumption that P = NP ∩ coNP.…”

Section: Backbones and Backdoors In Satisfiabilitymentioning

confidence: 99%

Constraint Satisfaction Techniques for Combinatorial Problems

Narváez

2018

AAAI

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The last two decades have seen extraordinary advances in industrial applications of constraint satisfaction techniques, while combinatorial problems have been pushed to the sidelines. We propose a comprehensive analysis of the state of the art in constraint satisfaction problems when applied to combinatorial problems in areas such as graph theory, set theory, algebra, among others. We believe such a study will provide us with a deeper understanding about the limitations we still face in constraint satisfaction problems.

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“…A large drawback of SBSes and their variants is that in the general case, the problem of finding such a backdoor is computationally hard. A number of results that fit these issues into the context of Structural Complexity can be found in (Kilby et al 2005;Hemaspaandra and Narváez 2017, 2019. The works (Fichte and Szeider 2011;Gaspers and Szeider 2012a,b,c;Misra et al 2013) demonstrate the relationship between backdoors and basic concepts of Parameterized Complexity.…”

Section: Introductionmentioning

confidence: 97%

On Probabilistic Generalization of Backdoors in Boolean Satisfiability

Семенов

Pavlenko

Chivilikhin

et al. 2022

AAAI

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The paper proposes a probabilistic generalization of the well-known Strong Backdoor Set (SBS) concept applied to the Boolean Satisfiability Problem (SAT). We call a set of Boolean variables B a ρ-backdoor, if for a fraction of at least ρ of possible assignments of variables from B, assigning their values to variables in a Boolean formula in Conjunctive Normal Form (CNF) results in polynomially solvable formulas. Clearly, a ρ-backdoor with ρ=1 is an SBS. For a given set B it is possible to efficiently construct an (ε, δ)-approximation of parameter ρ using the Monte Carlo method. Thus, we define an (ε, δ)-SBS as such a set B for which the conclusion "parameter ρ deviates from 1 by no more than ε" is true with probability no smaller than 1 - δ. We consider the problems of finding the minimum SBS and the minimum (ε, δ)-SBS. To solve the former problem, one can use the algorithm described by R. Williams, C. Gomes and B. Selman in 2003. In the paper we propose a new probabilistic algorithm to solve the latter problem, and show that the asymptotic estimation of the worst-case complexity of the proposed algorithm is significantly smaller than that of the algorithm by Williams et al. For practical applications, we suggest a metaheuristic optimization algorithm based on the penalty function method to seek the minimal (ε, δ)-SBS. Results of computational experiments show that the use of (ε, δ)-SBSes found by the proposed algorithm allows speeding up solving of test problems related to equivalence checking and hard crafted and combinatorial benchmarks compared to state-of-the-art SAT solvers.

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The Opacity of Backbones

Cited by 8 publications

References 9 publications

Computational Social Choice and Computational Complexity: BFFs?

Computational Social Choice and Computational Complexity: BFFs?

Constraint Satisfaction Techniques for Combinatorial Problems

On Probabilistic Generalization of Backdoors in Boolean Satisfiability

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