Unsolvability Cores in Classification Problems

Cohesiveness in promise problems

Promise problems have been introduced in 1985 by S.Even e.a. as a generalization of decision problems. Using a very general approach we study solvability and unsolvability conditions for promise problems of set families and languages. We show, that cores of unsolvability are completely determined by partitions of cohesive sets. We prove the existence of cores in unsolvable promise problems assu...

Degrees of Unsolvability: A Tutorial

Given a problem P , one associates to P a degree of unsolvability, i.e., a quantity which measures the amount of algorithmic unsolvability which is inherent in P . We focus on two degree structures: the semilattice of Turing degrees, DT, and its completion, Dw = D̂T, the lattice of Muchnik degrees. We emphasize specific, natural degrees and their relationship to reverse mathematics. We show how ...

On the algorithmic unsolvability of some stability problems for hybrid systems

Cellular Automata and Intermediate Reachability Problems

We exhibit one-dimensional cellular automata whose reachability and confluence problems have arbitrary r.e. degree of unsolvability.

Finding Minimal Unsatis ̄able Subformulae in Satis ̄ability instances

A minimal unsatis ̄able subformula (MUS) of a given CNF is a set of clauses which is unsatis ̄able, but becomes satis ̄able as soon as we remove any of its clauses. In practical scenarios it is often useful to know, in addition to the unsolvability of an instance, which parts of the instance cause the unsolvability. An approach is here proposed to the problem of automatic detection of such a subfo...