• Corpus ID: 17674889

Computing Minimal Sets on Propositional Formulae I: Problems & Reductions

@article{MarquesSilva2014ComputingMS,
  title={Computing Minimal Sets on Propositional Formulae I: Problems \& Reductions},
  author={Joao Marques-Silva and Mikol{\'a}{\vs} Janota},
  journal={ArXiv},
  year={2014},
  volume={abs/1402.3011}
}
Boolean Satisfiability (SAT) is arguably the archetypical NP-complete decision problem. Progress in SAT solving algorithms has motivated an ever increasing number of practical applications in recent years. However, many practical uses of SAT involve solving function as opposed to decision problems. Concrete examples include computing minimal unsatisfiable subsets, minimal correction subsets, prime implicates and implicants, minimal models, backbone literals, and autarkies, among several others… 

Tables from this paper

On the Query Complexity of Selecting Few Minimal Sets

This paper develops tighter upper bounds on the query complexity of solving several function problems defined on propositional formulas, including computing the backbone of a formula and computing the set of independent variables of a formulas.

A MaxSAT Algorithm Using Cardinality Constraints of Bounded Size

A new core-guided algorithm is introduced that adds cardinality constraints for each detected core, but also limits the number of literals in each constraint in order to control thenumber of refutations in subsequent satisfiability checks.

Extracting unsatisfiable cores for LTL via temporal resolution

  • Viktor Schuppan
  • Computer Science
    2013 20th International Symposium on Temporal Representation and Reasoning
  • 2013
This article constructs and optimize resolution graphs for temporal resolution as implemented in the temporal resolution-based solver TRP++, and uses them to extract UCs for propositional LTL, and produces more fine-grained UCs than competing tools.

Computing unsatisfiable cores for LTLf specifications

This paper provides four algorithms for extracting an unsatisfiable core in LTLf specifications leveraging the adaptation of state-of-the-art approaches to LTLF satisfiability checking and implements the different approaches within the respective tools.

Tight bounds on The Fourier Spectrum of AC0

  • Avishay Tal
  • Computer Science
    Electron. Colloquium Comput. Complex.
  • 2014
It is shown that AC0 circuits on n variables with depth d and size m have at most 2−Ω(k/logd−1m) of their Fourier mass at level k or above, and the result is tight up to the factor 3 in the exponent.

MCS Extraction with Sublinear Oracle Queries

Novel algorithms for computing MCSes which, in specific settings, are guaranteed to require asymptotically fewer than linear calls to a SAT oracle, where the oracle calls can be viewed as simple.

References

SHOWING 1-10 OF 115 REFERENCES

Minimal Sets over Monotone Predicates in Boolean Formulae

All computational problems related with Boolean formulas can be viewed as computing a minimal set subject to a monotone predicate, i.e. the MSMP problem, and a new algorithm is developed, that is asymptotically optimal, for this problem.

Solving satisfiability problems with preferences

This paper shows how dll can be extended in order to return one or all optimal models of ψ (once converted in clauses and assuming ψ is satisfiable), and how the same procedures can be used to compute optimal models wrt a qualitative preference on formulas and/or a quantitative preference on literals or formulas.

Algorithms for computing backbones of propositional formulae

This article overviews existing algorithms for backbone computation and introduces two novel ones, and demonstrates that one of the novel algorithms significantly outperforms the existing ones.

On Computing Minimal Equivalent Subformulas

A new class of algorithms that are based on the iterative analysis of subsets of clauses that can be adapted to the computation of MESes, and the experimental results confirm the effectiveness of the proposed algorithms.

Constraint Satisfaction Problems in Clausal Form II: Minimal Unsatisfiability and Conflict Structure

The combinatorial properties of non-boolean conjunctive normal forms (clause-sets), allowing arbitrary (but finite) sets of values for variables, while literals express that some variable shall not get some (given) value, are studied.

Minimal Unsatisfiability and Autarkies

The second part of this chapter provides a solid foundation of the basic ideas and results of autarky theory: the basic algorithmic problems, the algebra involved, and relations to various combinatorial theories (e.g., matching theory, linear programming, graph theory, the theory of permanents).

Minimal Assignments for Bounded Model Checking

This work forms the extraction of a succinct counterexample as the problem of finding a minimal assignment that, together with the Boolean formula describing the model, implies an objective.

Computers and Intractability: A Guide to the Theory of NP-Completeness

It is proved here that the number ofrules in any irredundant Horn knowledge base involving n propositional variables is at most n 0 1 times the minimum possible number of rules.

Optimizing with minimum satisfiability

Using heuristics to find minimal unsatisfiable subformulas in satisfiability problems

Efficient algorithms to extract minimal unsatisfiable subsets of clauses or variables in unsatisfiable propositional formulas, based on heuristics, are proposed and it is shown that, in some cases, the minimality of the subformulas can be proven with these algorithms.
...