TY - JOUR

T1 - On the theory of average case complexity

AU - Ben-David, Shai

AU - Chor, Benny

AU - Goldreich, Oded

AU - Luby, Michel

N1 - Funding Information:
* An extended abstract has appeared in the “Proceedings, 21st ACM Symp. on Theory of Computing.” An abstract has appeared in the “Proceedings 4th Conf. on Structure in Complexity Theory.” ** Partially funded by the Fund for Promotion of Research in the Technion. ’ Supported by Technion VPR Fund-ENJ Bishop Research Fund. * Partially supported by Grant 86-00301 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. 5 Research partially done while still at University of Toronto. Partially supported by a Natural Sciences and Engineering Research Council of Canada operating Grant A8092, by a University of Toronto Grant, by NSF Grant CCR-9016468 and by Grant No. 89-00312 from the US-Israel Binational Science Foundation.

PY - 1992/4

Y1 - 1992/4

N2 - This paper takes the next step in developing the theory of average case complexity initiated by Leonid A. Levin. Previous works have focused on the existence of complete problems. We widen the scope to other basic questions in computational complexity. Our results include: 1. {multiset union}|the equivalence of search and decision problems in the context of average case complexity; 2. {multiset union}|an initial analysis of the structure of distributional-NP (i.e., NP problems coupled with "simple distributions") under reductions which preserve average polynomial-time; 3. {multiset union}|a proof that if all of distributional-NP is in average polynomial-time then non-deterministic exponential-time equals deterministic exponential time (i.e., a collapse in the worst case hierarchy); 4. {multiset union}|definitions and basic theorems regarding other complexity classes such as average log-space. An exposition of the basic definitions suggested by Levin and suggestions for some alternative definitions are provided as well.

AB - This paper takes the next step in developing the theory of average case complexity initiated by Leonid A. Levin. Previous works have focused on the existence of complete problems. We widen the scope to other basic questions in computational complexity. Our results include: 1. {multiset union}|the equivalence of search and decision problems in the context of average case complexity; 2. {multiset union}|an initial analysis of the structure of distributional-NP (i.e., NP problems coupled with "simple distributions") under reductions which preserve average polynomial-time; 3. {multiset union}|a proof that if all of distributional-NP is in average polynomial-time then non-deterministic exponential-time equals deterministic exponential time (i.e., a collapse in the worst case hierarchy); 4. {multiset union}|definitions and basic theorems regarding other complexity classes such as average log-space. An exposition of the basic definitions suggested by Levin and suggestions for some alternative definitions are provided as well.

UR - http://www.scopus.com/inward/record.url?scp=0026853668&partnerID=8YFLogxK

U2 - 10.1016/0022-0000(92)90019-F

DO - 10.1016/0022-0000(92)90019-F

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AN - SCOPUS:0026853668

SN - 0022-0000

VL - 44

SP - 193

EP - 219

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

IS - 2

ER -