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The difficulty in solving such problems is thus in identifying the minimal unsatisfiable subset from the many irrelevant clauses.
Indeed, hard problems in the variable region often contain a small and unique minimal unsatisfiable subset or reduce at an early stage in search to a hard unsatisfiable subproblem with a small and unique minimal unsatisfiable subset.
This applies for example to the computation of a minimal unsatisfiable subset (MUS) for CNF formulas, but also to the computation of prime implicants and implicates, with immediate application in a number of AI settings.
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The existence of a constraint gap greatly hinders our ability to find such minimal unsatisfiable subsets.
Concrete examples include computing minimal unsatisfiable subsets, minimal correction subsets, prime implicates and implicants, minimal models, backbone literals, and autarkies, among several others.
The papers are organized in topical sections on complexity analysis, binary decision diagrams, theoretical analysis, extraction of minimal unsatisfiable subsets, SAT algorithms, quantified Boolean formulae, model enumeration and local search, and empirical evaluation.
Previous work on MES computation proposes a simple algorithm based on iterative application of the definition of a redundant clause, similar to the well-known deletion-based approach for the computation of Minimal Unsatisfiable Subformulas (MUSes).
Therefore, we ranked chromatin regulators and TFs to find a minimal optimal subset, which can be used to optimally distinguish SEs from TEs.
Remark that each component (S_i) intersects just one minimal hereditary subset (W_i).
Then Theorem 3.8 ensures the existence of a minimal compact subset of such that (3.15).
Theorem 3.5 For each w ∈ M, every minimal essential subset of S ( w ) is connected.
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