Finding Small Backdoors in SAT Instances

Li, Zijie; Beek, Peter van der

doi:10.1007/978-3-642-21043-3_33

Cited by 10 publications

(11 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Backdoor sets aim at exploiting hidden structures in real-world problem instances. The effectiveness of this approach has been investigated empirically in [31,42,59,85] and in many cases, small backdoor sets were found for large industrial instances.…”

Section: Resultsmentioning

confidence: 99%

Backdoors to Satisfaction

Gaspers

Szeider

2012

Lecture Notes in Computer Science

View full text Add to dashboard Cite

A backdoor set is a set of variables of a propositional formula such that fixing the truth values of the variables in the backdoor set moves the formula into some polynomial-time decidable class. If we know a small backdoor set we can reduce the question of whether the given formula is satisfiable to the same question for one or several easy formulas that belong to the tractable class under consideration. In this survey we review parameterized complexity results for problems that arise in the context of backdoor sets, such as the problem of finding a backdoor set of size at most k, parameterized by k. We also discuss recent results on backdoor sets for problems that are beyond NP.

show abstract

Section: Resultsmentioning

confidence: 99%

Backdoors to Satisfaction

Gaspers

Szeider

2012

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…Also there are some investigations done on detecting backdoors using AI algorithms, we have presented an innovative idea for backdoor detection [6].…”

Section: The Proposed Mrthodmentioning

confidence: 99%

Backdoor Detection System Using Artificial Neural Network and Genetic Algorithm

Salimi¹,

Arastouie

2011

2011 International Conference on Computational and Information Sciences

View full text Add to dashboard Cite

In this paper, we consider the issue of detecting a missing member of malicious codes named backdoors. We developed a novel approach for revealing them based on two clustered; system behavior and network traffic. Backdoors can easily be installed on the victim system aiming its exploit; detecting them requires considerable policies. Using Artificial Intelligence (AI) has revolutionized all security providing systems. Hence, our proposed method acquired a tunable idea using Artificial Neural Network (ANN) for classifying system features and predicting the percentage of backdoor existing probability and Genetic Algorithm (GA) in order to give a deterministic answer to the issue. Using ANN incorporation with the GA guarantees how precise our approach could be.

show abstract

“…either returns a satisfying assignment or concludes unsatisfiability of φ[τ ]. It appears that many instances in practice happen to have small "weak" or "strong" backdoors for different sub-solvers [20,26]. There has been an extensive theoretical study of backdoors to different sub-solvers in the realm of parameterized complexity [23,25,16].…”

Section: Introductionmentioning

confidence: 99%

Solving d-SAT via Backdoors to Small Treewidth

Fomin¹,

Lokshtanov²,

Misra³

et al. 2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

A backdoor set of a CNF formula is a set of variables such that fixing the truth values of the variables from this set moves the formula into a polynomial-time decidable class. In this work we obtain several algorithmic results for solving d-SAT, by exploiting backdoors to d-CNF formulas whose incidence graphs have small treewidth.For a CNF formula φ and integer t, a strong backdoor set to treewidth t is a set of variables such that each possible partial assignment τ to this set reduces φ to a formula whose incidence graph is of treewidth at most t. A weak backdoor set to treewidth t is a set of variables such that there is a partial assignment to this set that reduces φ to a satisfiable formula of treewidth at most t. Our main contribution is an algorithm that, given a d-CNF formula φ and an integer k, in time 2 O(k) |φ|,• either finds a satisfying assignment of φ, or• reports correctly that φ is not satisfiable, or• concludes correctly that φ has no weak or strong backdoor set to treewidth t of size at most k.As a consequence of the above, we show that d-SAT parameterized by the size of a smallest weak/strong backdoor set to formulas of treewidth t, is fixedparameter tractable. Prior to our work, such results were know only for the very special case of t = 1 (Gaspers and Szeider, ICALP 2012). Our result not only extends the previous work, it also improves the running time substantially. The running time of our algorithm is linear in the input size for every fixed k. Moreover, the exponential dependence on the parameter k is asymptotically optimal under Exponential Time Hypothesis (ETH). One of our main technical contributions is a linear time "protrusion replacer" improving over a O(n log 2 n)-time procedure of Fomin et al. (FOCS 2012). The new deterministic linear time protrusion replacer has several applications in kernelization and parameterized algorithms.

show abstract

Finding Small Backdoors in SAT Instances

Cited by 10 publications

References 7 publications

Backdoors to Satisfaction

Backdoors to Satisfaction

Backdoor Detection System Using Artificial Neural Network and Genetic Algorithm

Solving d-SAT via Backdoors to Small Treewidth

Contact Info

Product

Resources

About