Cohesiveness in promise problems

Ulrike Brandt; Hermann K.-G. Walter

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2013)

  • Volume: 47, Issue: 4, page 351-369
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Brandt, Ulrike, and Walter, Hermann K.-G.. "Cohesiveness in promise problems." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 47.4 (2013): 351-369. <http://eudml.org/doc/273055>.

@article{Brandt2013,
abstract = {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.},
author = {Brandt, Ulrike, Walter, Hermann K.-G.},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {promise problems; set and language families; cores of unsolvability; complexity cores; cohesive sets},
language = {eng},
number = {4},
pages = {351-369},
publisher = {EDP-Sciences},
title = {Cohesiveness in promise problems},
url = {http://eudml.org/doc/273055},
volume = {47},
year = {2013},
}

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
PB - EDP-Sciences
VL - 47
IS - 4
SP - 351
EP - 369
AB - 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.
LA - eng
KW - promise problems; set and language families; cores of unsolvability; complexity cores; cohesive sets
UR - http://eudml.org/doc/273055
ER -

References

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  1. [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. Zbl1315.03066
  2. [2] R.V. Book, D.-Z. Du, The Existence and Density of Generalized Complexity Cores, in J. ACM34 (1987) 718–730. MR904201
  3. [3] J.L. Balcazar, J. Diaz and J. Gabarro, Structural Complexity I, EATCS Monographs on Theoretical Computer Science. Springer Verlag, Heidelberg (1988). Zbl0826.68048MR1047862
  4. [4] S. Even, A.L. Selman and Y. Yacobi, The Complexity of Promise Problems with Applications to Public-Key Cryptography. Information and Control61 (1984) 159–173. Zbl0592.94012MR772678
  5. [5] O. Goldreich, On Promise-Problems, A Survey in Memory of Shimon Even. Dep. Comp. Science, Weizmann Institute of Science (2005). MR2248667
  6. [6] M.A. Harrison, Introduction to Formal Language Theory. Addison-Wesley Publishing Company (1978). Zbl0411.68058MR526397
  7. [7] G. Rozenberg and A. Salomaa, Word, Language, Grammar, in vol. 1 of Handbook of Formal Languages. Springer Verlag (1997). MR1469992
  8. [8] H.R. Jun, Theory of Recursive Functions and Effective Computability. MacGraw-Hill Book Company (1967). Zbl0183.01401MR224462
  9. [9] R.I. Soare, Recursively enumerable Sets and Degrees. Springer Verlag (1987). Zbl0667.03030MR882921

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