Cohesiveness in promise problems
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 47 (2013) no. 4, p. 351-369

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.

DOI : https://doi.org/10.1051/ita/2013042
Classification:  68Q45
Keywords: promise problems, set and language families, cores of unsolvability, complexity cores, cohesive sets
@article{ITA_2013__47_4_351_0,
     author = {Brandt, Ulrike and Walter, Hermann K.-G.},
     title = {Cohesiveness in promise problems},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {4},
     year = {2013},
     pages = {351-369},
     doi = {10.1051/ita/2013042},
     zbl = {1286.68274},
     mrnumber = {3132296},
     language = {en},
     url = {http://www.numdam.org/item/ITA_2013__47_4_351_0}
}
Brandt, Ulrike; Walter, Hermann K.-G. Cohesiveness in promise problems. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 47 (2013) no. 4, pp. 351-369. doi : 10.1051/ita/2013042. http://www.numdam.org/item/ITA_2013__47_4_351_0/

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