Cohesiveness in promise problems∗
Fachbereich Informatik, Technische
Universität Darmstadt, Germany .
Accepted: 22 August 2013
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 and language families. We show, that cores of unsolvability are completely determined by partitions of cohesive sets. We prove the existence of cores in unsolvable promise problems assuming certain closure properties for the given set family. Connections to immune sets and complexity cores are presented. Furthermore, results about cohesiveness with respect to the language families from the Chomsky hierarchy are given.
Mathematics Subject Classification: 68Q45
Key words: Promise problems / set and language families / cores of unsolvability / complexity cores / cohesive sets
© EDP Sciences 2013