The complexity of facets resolved

Papadimitriou, Christos H.; Wolfe, David

doi:10.1016/0022-0000(88)90042-6

Cited by 168 publications

(81 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Lean denotes the class of lean formulas. It is not difficult to see that In [9], M U is shown to be D P -complete, where D P is the class which can be described as the difference between two N P problems. A D P -complete problem is equivalent to solving a SAT -U N SAT problem defined as: given two formulas F and F , is it the case that F is satisfiable and F is unsatisfiable?…”

Section: Definition 1 (Variable Minimal Unsatisfiability) V Mu := {F mentioning

confidence: 99%

“…It is strongly conjectured that D P is different from N P and from coN P . M U is D P -complete [9] and U N SAT is coN P -complete. Due to an observation by Stefan Szeider, each class between M U and U N SAT is coN P -hard [17].…”

Section: Definition 1 (Variable Minimal Unsatisfiability) V Mu := {F mentioning

confidence: 99%

“…Consider a propositional formula F in conjunctive normal form (CNF), F is minimal unsatisfiable if and only if the formula is unsatisfiable and any proper subformula is satisfiable. There are many existing work on theoretical results [8,9,10,11,12,13,14] and experimental results [15,16] of minimal unsatisfiability. The class of minimal unsatisfiable formulas is denoted as M U and shown to be D P -complete [9].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Variable Minimal Unsatisfiability

Chen

Ding

2006

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. In this paper, we present variable minimal unsatisfiability (VMU), which is a generalization of minimal unsatisfiability (MU). A characterization of a VMU formula F is that every variable of F is used in every resolution refutation of F . We show that the class of VMU formulas is D P -complete. For fixed deficiency (the difference of the number of clauses and the number of variables), the VMU formulas can be solved in polynomial time. Furthermore, we investigate more subclasses of VMU formulas. Although the theoretic results on VMU and MU are similar, some observations are shown that the extraction of VMU may be more practical than MU in some cases.

show abstract

Section: Definition 1 (Variable Minimal Unsatisfiability) V Mu := {F mentioning

confidence: 99%

Section: Definition 1 (Variable Minimal Unsatisfiability) V Mu := {F mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Variable Minimal Unsatisfiability

Chen

Ding

2006

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…A formula is minimal unsatisfiable if it is unsatisfiable but omitting any of its clauses makes it satisfiable. Recognition of minimal unsatisfiable formulas is computationally hard, shown to be D P -complete by Papadimitriou and Wolfe [24] (D P -sometimes denoted as DP-is the class of problems that can be considered as the difference of two NP-problems; D P is located at the second level of the Boolean Hierarchy and contains all NP and all co-NP problems; see, e.g., [23]). …”

Section: Introductionmentioning

confidence: 99%

Minimal Unsatisfiable Formulas with Bounded Clause-Variable Difference are Fixed-Parameter Tractable

Szeider

2003

Lecture Notes in Computer Science

View full text Add to dashboard Cite

“…This is understandable, to be sure, because checking minimal unsatisfiability is a hard problem known to be D P -complete 1 [20].…”

Section: Introductionmentioning

confidence: 99%

MUP: a minimal unsatisfiability prover

Huang

Proceedings of the ASP-DAC 2005. Asia and South Pacific Design Automation Conference, 2005.

View full text Add to dashboard Cite

Abstract-After establishing the unsatisfiability of a SAT instance encoding a typical design task, there is a practical need to identify its minimal unsatisfiable subsets, which pinpoint the reasons for the infeasibility of the design. Due to the potentially expensive computation, existing tools for the extraction of unsatisfiable subformulas do not guarantee the minimality of the results. This paper describes a practical algorithm that decides the minimal unsatisfiability of any CNF formula through BDD manipulation. This algorithm has a worse-case complexity that is exponential only in the treewidth of the CNF formula. We provide an empirical evaluation of the algorithm, highlighting its efficiency on a set of hard problems as well as its ability to work with existing subformula extraction tools to achieve optimal results.

show abstract

The complexity of facets resolved

Cited by 168 publications

References 7 publications

Variable Minimal Unsatisfiability

Variable Minimal Unsatisfiability

Minimal Unsatisfiable Formulas with Bounded Clause-Variable Difference are Fixed-Parameter Tractable

MUP: a minimal unsatisfiability prover

Contact Info

Product

Resources

About