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Complexity Measures for Public-Key Cryptosystems
A general theory of public-key cryptography is developed that is based on the mathematical framework of complexity theory. Two related approaches are taken to the development of this theory, and th...
A Comparison of Polynomial Time Reducibilities
Abstract Various forms of polynomial time reducibility are compared. Among the forms examined are many-one, bounded truth table, truth table and Turing reducibility. The effect of introducingExpand
A Taxonomy of Complexity Classes of Functions
  • A. Selman
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1 April 1994
A systematic comparison of several complexity classes of functions that are computed nondeterministically in polynomial time or with an oracle in NP shows that there exists a disjoint pair of NP-complete sets such that every separator is NP-hard. Expand
The Complexity of Promise Problems with Applications to Public-Key Cryptography
This paper disproves a conjecture made by Even and Yacobi (1980) that would imply nonexistence of public-key cryptosystems with NP-hard cracking problems and raises a new conjecture that implies that NP-complete sets cannot be accepted by Turing machines that have at most one accepting computation for each input word. Expand
Computability and Complexity Theory
Conise, focused materials cover the most fundamental concepts and results in the field of modern complexity theory, including the theory of NP-completeness, NP-hardness, the polynomial hierarchy, and complete problems for other complexity classes. Expand
Arithmetical Reducibilities I
A 3D reductibility relation is defined to be a transitive and reflexive relation & on sets of natural numbers, so that for every two sets A and B, A&B implies AeZ^. Two hierarchies of suchExpand
Quantitative Relativizations of Complexity Classes
This paper studies restrictions R on both the deterministic and also the nondeterministic polynomial time-bounded oracle machines such that the size of the set of strings queried by the oracle in computations of a machine on an input is bounded by aPolynomial in the length of the input. Expand
Comparison of polynomial-time reducibilities
Comparison of the polynomial-time-bounded reducibilities introduced by Cook [1] and Karp] leads naturally to the definition of several intermediate truth-tableredcibilities, and it is noted that all redu cibilities of this type which do not have obvious implication relationships are in fact distinct in a strong sense. Expand
P-Selective Sets, Tally Languages, and the Behavior of Polynomial Time Reducibilities on NP
  • A. Selman
  • Mathematics, Computer Science
  • 16 July 1979
It is proved that for m every tally language set in NP there exists a polynomial time equivalent set inNP that is p-selective, and from this result it follows that if NEXT ~ DEXT, then polynometric time Turing and many-one reducibilities differ on NP. Expand
Reductions on NP and P-Selective Sets
  • A. Selman
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 1 September 1982
It is shown that the class of all sets which are both P-selective and have positive reductions to their complements is P, and it follows that various naturally defined apparently intractible problems are not p- selective unless P = NP. Expand