Cohesiveness in promise problems
Brandt, Ulrike ; Walter, Hermann K.-G.
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 47 (2013), p. 351-369 / Harvested from Numdam
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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.

Publié le : 2013-01-01
DOI : https://doi.org/10.1051/ita/2013042
Classification:  68Q45 
@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},
     volume = {47},
     year = {2013},
     pages = {351-369},
     doi = {10.1051/ita/2013042},
     mrnumber = {3132296},
     zbl = {1286.68274},
     language = {en},
     url = {http://dml.mathdoc.fr/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, Tome 47 (2013) pp. 351-369. doi : 10.1051/ita/2013042. http://gdmltest.u-ga.fr/item/ITA_2013__47_4_351_0/

[1] K. Ambos-Spies, U. Brandt and M. Ziegler, Real Benefit of Promises and Advice, accepted for presentation at CiE 2013 in vol. 7921 of Lect. Notes Comput. Sci. Springer (2013) 1-11. | Zbl pre06194917

[2] R.V. Book, D.-Z. Du, The Existence and Density of Generalized Complexity Cores, in J. ACM 34 (1987) 718-730. | MR 904201

[3] J.L. Balcazar, J. Diaz and J. Gabarro, Structural Complexity I, EATCS Monographs on Theoretical Computer Science. Springer Verlag, Heidelberg (1988). | MR 1047862 | Zbl 0826.68048

[4] S. Even, A.L. Selman and Y. Yacobi, The Complexity of Promise Problems with Applications to Public-Key Cryptography. Information and Control 61 (1984) 159-173. | MR 772678 | Zbl 0592.94012

[5] O. Goldreich, On Promise-Problems, A Survey in Memory of Shimon Even. Dep. Comp. Science, Weizmann Institute of Science (2005). | MR 2248667

[6] M.A. Harrison, Introduction to Formal Language Theory. Addison-Wesley Publishing Company (1978). | MR 526397 | Zbl 0411.68058

[7] G. Rozenberg and A. Salomaa, Word, Language, Grammar, in vol. 1 of Handbook of Formal Languages. Springer Verlag (1997). | MR 1469992

[8] H.R. Jun, Theory of Recursive Functions and Effective Computability. MacGraw-Hill Book Company (1967). | MR 224462 | Zbl 0183.01401

[9] R.I. Soare, Recursively enumerable Sets and Degrees. Springer Verlag (1987). | MR 882921 | Zbl 0667.03030