The existence and density of generalized complexity cores
Journal of the ACM (JACM)
Structural complexity 1
SIAM Journal on Computing
Structural complexity 2
Complete problems and strong polynomial reducibilities
SIAM Journal on Computing
Almost every set in exponential time is P-bi-immune
Theoretical Computer Science
On P-immunity of exponential time complete sets
Journal of Computer and System Sciences - special issue on complexity theory
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Note: on universally easy classes for NP-complete problems
Theoretical Computer Science
ACM SIGACT News
On the structure of complete sets: Almost everywhere complexity and infinitely often speedup
SFCS '76 Proceedings of the 17th Annual Symposium on Foundations of Computer Science
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This paper introduces and studies two notions of easy sets without hard subsets: i) 𝒞-hollow sets are defined to be sets in P that have no 𝒞 - P subsets for (presumably) superclasses 𝒞 of P such as NP, PSPACE, E, NE, RE, etc.; and ii) 𝒞-scant sets are defined to be sets in P that have no many-one 𝒞-complete subsets. These sets complement well-studied objects in complexity such as P-printable sets, immune sets and complexity cores. First, characterizations of 𝒞-hollow sets and 𝒞-scant sets are obtained in terms of universally easy sets, introduced and studied in [7] as an automatic method for generating easy instances of intractable problems. Second, the following results regarding existence of 𝒞-hollow sets are obtained: infinite NP-hollow tally (equivalently, P-printable) sets exist iff some nondeterministic time complexity class equals its deterministic counterpart; in contrast, infinite E/NE/RE-hollow sets do not exist. Finally, it is shown that P-printable-immune sets in P are 𝒞-scant for E and NE.