17,500 research outputs found
Classes of representable disjoint NP-pairs
For a propositional proof system P we introduce the complexity class of all disjoint -pairs for which the disjointness of the pair is efficiently provable in the proof system P. We exhibit structural properties of proof systems which make canonical -pairs associated with these proof systems hard or complete for . Moreover, we demonstrate that non-equivalent proof systems can have equivalent canonical pairs and that depending on the properties of the proof systems different scenarios for and the reductions between the canonical pairs exist
Disjoint NP-pairs from propositional proof systems
For a proof system P we introduce the complexity class DNPP(P) of all disjoint NP-pairs for which the disjointness of the pair is efficiently provable in the proof system P. We exhibit structural properties of proof systems which make the previously defined canonical NP-pairs of these proof systems hard or complete for DNPP(P). Moreover we demonstrate that non-equivalent proof systems can have equivalent canonical pairs and that depending on the properties of the proof systems different scenarios for DNPP(P) and the reductions between the canonical pairs exist
On the existence of complete disjoint NP-pairs
Disjoint NP-pairs are an interesting model of computation with important applications in cryptography and proof complexity. The question whether there exists a complete disjoint NP-pair was posed by Razborov in 1994 and is one of the most important problems in the field. In this paper we prove that there exists a many-one hard disjoint NP-pair which is computed with access to a very weak oracle (a tally NP-oracle). In addition, we exhibit candidates for complete NP-pairs and apply our results to a recent line of research on the construction of hard tautologies from pseudorandom generators
An Atypical Survey of Typical-Case Heuristic Algorithms
Heuristic approaches often do so well that they seem to pretty much always
give the right answer. How close can heuristic algorithms get to always giving
the right answer, without inducing seismic complexity-theoretic consequences?
This article first discusses how a series of results by Berman, Buhrman,
Hartmanis, Homer, Longpr\'{e}, Ogiwara, Sch\"{o}ening, and Watanabe, from the
early 1970s through the early 1990s, explicitly or implicitly limited how well
heuristic algorithms can do on NP-hard problems. In particular, many desirable
levels of heuristic success cannot be obtained unless severe, highly unlikely
complexity class collapses occur. Second, we survey work initiated by Goldreich
and Wigderson, who showed how under plausible assumptions deterministic
heuristics for randomized computation can achieve a very high frequency of
correctness. Finally, we consider formal ways in which theory can help explain
the effectiveness of heuristics that solve NP-hard problems in practice.Comment: This article is currently scheduled to appear in the December 2012
issue of SIGACT New
Resource Bounded Immunity and Simplicity
Revisiting the thirty years-old notions of resource-bounded immunity and
simplicity, we investigate the structural characteristics of various immunity
notions: strong immunity, almost immunity, and hyperimmunity as well as their
corresponding simplicity notions. We also study limited immunity and
simplicity, called k-immunity and feasible k-immunity, and their simplicity
notions. Finally, we propose the k-immune hypothesis as a working hypothesis
that guarantees the existence of simple sets in NP.Comment: This is a complete version of the conference paper that appeared in
the Proceedings of the 3rd IFIP International Conference on Theoretical
Computer Science, Kluwer Academic Publishers, pp.81-95, Toulouse, France,
August 23-26, 200
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