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.
Mots-clés : 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}, pages = {351--369}, publisher = {EDP-Sciences}, volume = {47}, number = {4}, year = {2013}, doi = {10.1051/ita/2013042}, mrnumber = {3132296}, zbl = {1286.68274}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ita/2013042/} }
TY - JOUR AU - Brandt, Ulrike AU - Walter, Hermann K.-G. TI - Cohesiveness in promise problems JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2013 SP - 351 EP - 369 VL - 47 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita/2013042/ DO - 10.1051/ita/2013042 LA - en ID - ITA_2013__47_4_351_0 ER -
%0 Journal Article %A Brandt, Ulrike %A Walter, Hermann K.-G. %T Cohesiveness in promise problems %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2013 %P 351-369 %V 47 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita/2013042/ %R 10.1051/ita/2013042 %G en %F 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, Tome 47 (2013) no. 4, pp. 351-369. doi : 10.1051/ita/2013042. http://archive.numdam.org/articles/10.1051/ita/2013042/
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