Tradeoffs in the complexity of backdoors to satisfiability: dynamic sub-solvers and learning during search

Dilkina, Bistra; Gomes, Carla P.; Sabharwal, Ashish

doi:10.1007/s10472-014-9407-9

Cited by 9 publications

(10 citation statements)

References 37 publications

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“…A strong backdoor to a semantic class T is a subset S ⊆ X such that every complete assignment of the variables from S yields an instance whose language is in T . Note that assigning a variable involves no further inference (e.g., arc consistency); indeed doing so has been shown to make backdoors potentially much harder to detect [17]. There exist alternative forms of backdoors, such as weak backdoors [1] and partition backdoors [18], but we only consider strong backdoors throughout this paper so we may omit the word "strong" in proofs.…”

Section: Preliminariesmentioning

confidence: 99%

On Backdoors to Tractable Constraint Languages

Carbonnel

Cooper

Hébrard

2014

Lecture Notes in Computer Science

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In the context of CSPs, a strong backdoor is a subset of variables such that every complete assignment yields a residual instance guaranteed to have a specified property. If the property allows efficient solving, then a small strong backdoor provides a reasonable decomposition of the original instance into easy instances. An important challenge is the design of algorithms that can find quickly a small strong backdoor if one exists. We present a systematic study of the parameterized complexity of backdoor detection when the target property is a restricted type of constraint language defined by means of a family of polymorphisms. In particular, we show that under the weak assumption that the polymorphisms are idempotent, the problem is unlikely to be FPT when the parameter is either r (the constraint arity) or k (the size of the backdoor) unless P = NP or FPT = W[2]. When the parameter is k + r, however, we are able to identify large classes of languages for which the problem of finding a small backdoor is FPT.

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Section: Preliminariesmentioning

confidence: 99%

On Backdoors to Tractable Constraint Languages

Carbonnel

Cooper

Hébrard

2014

Lecture Notes in Computer Science

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“…A CNF formula is a conjunction of disjunctions, and the disjunctions are called the clauses of the formula. Following Dilkina, Gomes, and Sabharwal [DGS14], we define satisfiability of CNF formulas using the language of set theory. This is done by formalizing the intuition that, in order for an assignment to satisfy a CNF formula, it must set at least one literal in every clause to True.…”

Section: Results On Backdoors To Cnf Formulasmentioning

confidence: 99%

“…A either rejects the input F (this indicates that it declines to make a statement as to whether F is satisfiable) or determines F (i.e., A returns a satisfying assignment if F is satisfiable and A proclaims F 's unsatisfiability if F is unsatisfiable). Many examples of subsolvers can be found in the literature (for instance, in Table 1 of [DGS14]). The subsolver that is of particular relevance to this paper is the unit propagation subsolver, which focuses on unit clauses.…”

Section: Definition 32 (Subsolver [Wgs03]) a Polynomial-time Algorithmmentioning

confidence: 99%

“…Many examples of subsolvers can be found in the literature (for instance, in Table 1 of [DGS14]). The subsolver that is of particular relevance to this paper is the unit propagation subsolver, which focuses on unit clauses.…”

Section: Definition 33 (Strong Backdoor [Wgs03]mentioning

confidence: 99%

“…The complexity of decision problems associated with backdoors and backbones has been studied by Nishimura, Ragde, and Szeider [NRS04], Kilby, Slaney, Thiébaux, and Walsh [KSTW05], and Dilkina, Gomes, and Sabharwal [DGS14], among others.…”

Section: Introductionmentioning

confidence: 99%

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Existence Versus Exploitation: The Opacity of Backdoors and Backbones Under a Weak Assumption

Hemaspaandra

Narváez²

2019

SOFSEM 2019: Theory and Practice of Computer Science

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Backdoors and backbones of Boolean formulas are hidden structural properties. A natural goal, already in part realized, is that solver algorithms seek to obtain substantially better performance by exploiting these structures.However, the present paper is not intended to improve the performance of SAT solvers, but rather is a cautionary paper. In particular, the theme of this paper is that there is a potential chasm between the existence of such structures in the Boolean formula and being able to effectively exploit them. This does not mean that these structures are not useful to solvers. It does mean that one must be very careful not to assume that it is computationally easy to go from the existence of a structure to being able to get one's hands on it and/or being able to exploit the structure.For example, in this paper we show that, under the assumption that P = NP, there are easily recognizable families of Boolean formulas with strong backdoors that are easy to find, yet for which it is hard (in fact, NP-complete) to determine whether the formulas are satisfiable. We also show that, also under the assumption P = NP, there are easily recognizable sets of Boolean formulas for which it is hard (in fact, NP-complete) to determine whether they have a large backbone. * Work done in part while visiting ETH-Zürich and the University of Dusseldorf.

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Answer Set Solver Backdoors

Oikarinen

Järvisalo

2014

Logics in Artificial Intelligence

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Tradeoffs in the complexity of backdoors to satisfiability: dynamic sub-solvers and learning during search

Cited by 9 publications

References 37 publications

On Backdoors to Tractable Constraint Languages

On Backdoors to Tractable Constraint Languages

Existence Versus Exploitation: The Opacity of Backdoors and Backbones Under a Weak Assumption

Answer Set Solver Backdoors

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