# 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…

## 8 Citations

### Minimal sets on propositional formulae. Problems and reductions

- Computer Science, MathematicsArtif. Intell.
- 2017

### On the Query Complexity of Selecting Few Minimal Sets

- Computer Science, MathematicsElectron. Colloquium Comput. Complex.
- 2014

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.

### On the query complexity of selecting minimal sets for monotone predicates

- Computer Science, MathematicsArtif. Intell.
- 2016

### A MaxSAT Algorithm Using Cardinality Constraints of Bounded Size

- Computer ScienceIJCAI
- 2015

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

- Computer Science2013 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

- Computer SciencePMAI@IJCAI
- 2022

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

- Computer ScienceElectron. 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

- Computer Science, MathematicsSAT
- 2016

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.

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