Minimal unsatisfiability and deficiency: recent developments

TL;DR

This paper reviews recent theoretical advances in understanding minimal unsatisfiability and deficiency in clause-sets, focusing on the structural properties and significance of the deficiency measure.

Contribution

It provides a comprehensive overview of recent developments related to the deficiency and minimal unsatisfiability in clause-sets, highlighting new structural insights.

Findings

Deficiency delta(F) = c(F) - n(F) is crucial in minimal unsatisfiability studies.

Recent results deepen understanding of the structure of minimally unsatisfiable clause-sets.

The overview connects historical and recent research developments.

Abstract

Starting with Aharoni and Linial in 1986, the deficiency delta(F) = c(F) - n(F) >= 1 for minimally unsatisfiable clause-sets F, the difference of the number of clauses and the number of variables, is playing an important role in investigations into the structure of minimal unsatisfiability. The talk belonging to this extended abstract, available at http://cs.swan.ac.uk/~csoliver/papers.html#BORDEAUX2016 , gives a high-level overview on recent developments.