On finding solutions for extended Horn formulas

Schlipf, John S.; Annexstein, Fred S.; Franco, John; Swaminathan, Ram

doi:10.1016/0020-0190(95)00019-9

Cited by 56 publications

(29 citation statements)

References 2 publications

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“…This class was developed in [89] as a generalization of other classes including Horn, extended Horn [18], simple extended Horn [92], and CC-balanced expressions [25]. It is peculiar in that it is defined based on an algorithm rather than on properties of expressions.…”

Section: Definition 8 a Cnf Expression Is A Member Of The Class Slur mentioning

confidence: 99%

“…Those results have been used, for example, to show how limited most succinctly defined polynomial-time classes of SAT are. Notable examples of such classes are Horn [33,58], renameable Horn [73], q-Horn [16,15], extended Horn [18], SLUR [89], balanced [25], and matched [46], to name a few. These classes have been studied partly in the belief that they will yield some distinction between hard and easy problems.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic Analysis of Satisfiability Algorithms

Franco¹,

Crama²,

Hammer³

2010

Boolean Models and Methods in Mathematics, Computer Science, and Engineering

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Section: Definition 8 a Cnf Expression Is A Member Of The Class Slur mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Probabilistic Analysis of Satisfiability Algorithms

Franco¹,

Crama²,

Hammer³

2010

Boolean Models and Methods in Mathematics, Computer Science, and Engineering

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“…Note also that, in some special cases of peptide analysis, one may be able to obtain polynomially solvable formulae by imposing syntactical limitations on the structure of the generated clauses (see e.g. [3,8,12,20]). For instance, when considering only b-ion and y-ion as the possible types of fragments, and only single charged ions, we obtain Quadratic formulae [1], which are polynomially solvable.…”

Section: Theorem 55mentioning

confidence: 99%

A Logic-Based Approach to Polymer Sequence Analysis

Bruni

2010

J Math Model Algor

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Polymers are compounds formed by the joining of smaller, often repeating, units linked by covalent bonds. The analysis of their sequence is a fundamental issue in many areas of chemistry, medicine and biology. Nowadays, the prevalent approach to this problem consists in using a mass spectrometry analysis that gives information about the molecular weights of the polymer and of its fragments. This information should be used in order to obtain the sequence. This is however a difficult mathematical problem, and several approaches have been proposed for it. In particular, a promising one is based on a propositional logic modeling of the problem. This paper presents conceptual improvements in this approach, principally the off-line computation of a database that substantially speeds-up the sequencing operations. This is obtained by finding a correspondence between sequences and natural numbers, so that all sequences up to a certain molecular weight can be implicitly considered in the above database, and explicitly computed only when needed. Results on real-world problems show the effectiveness of this approach.

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“…The sets UC k of all clause-sets F with hd(F ) ≤ k yield the basic hierarchy, and we have SAT decision in time O(n(F ) 2 hd(F )−2 · (F )). The special case UC 1 = UC was introduced in [59] for the purpose of Knowledge Compilation (KC), and in [30,33] it is shown that UC = SLUR holds, where SLUR is the class introduced in [54] as an umbrella class for polynomial-time SAT solving. By [6,33] we get that membership decision for UC k with k ≥ 1 is coNP-complete.…”

Section: Introductionmentioning

confidence: 99%

Unified Characterisations of Resolution Hardness Measures

Beyersdorff

Kullmann

2014

Lecture Notes in Computer Science

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Abstract. Various "hardness" measures have been studied for resolution, providing theoretical insight into the proof complexity of resolution and its fragments, as well as explanations for the hardness of instances in SAT solving. In this paper we aim at a unified view of a number of hardness measures, including different measures of width, space and size of resolution proofs. Our main contribution is a unified game-theoretic characterisation of these measures. As consequences we obtain new relations between the different hardness measures. In particular, we prove a generalised version of Atserias and Dalmau's result on the relation between resolution width and space from [5].

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On finding solutions for extended Horn formulas

Cited by 56 publications

References 2 publications

Probabilistic Analysis of Satisfiability Algorithms

Probabilistic Analysis of Satisfiability Algorithms

A Logic-Based Approach to Polymer Sequence Analysis

Unified Characterisations of Resolution Hardness Measures

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