Time Hierarchies: A Survey

We survey time hierarchies, with an emphasis on recent work on hierarchies for semantic classes.

[1]  Michael J. Fischer,et al.  Separating Nondeterministic Time Complexity Classes , 1978, JACM.

[2]  Oscar H. Ibarra.  A Hierarchy Theorem for Polynomial-Space Recognition , 1974, SIAM J. Comput..

[3]  Carsten Lund,et al.  Algebraic methods for interactive proof systems , 1992, JACM.

[4]  J. Hartmanis,et al.  On the Computational Complexity of Algorithms , 1965 .

[5]  Avi Wigderson,et al.  On Pseudorandomness with respect to Deterministic Observes , 2000, ICALP Satellite Workshops.

[6]  Adi Shamir,et al.  IP = PSPACE , 1992, JACM.

[7]  Luca Trevisan,et al.  From logarithmic advice to single-bit advice , 2004, Electron. Colloquium Comput. Complex..

[8]  Dieter van Melkebeek,et al.  A generic time hierarchy for semantic models with one bit of advice , 2006, 21st Annual IEEE Conference on Computational Complexity (CCC'06).

[9]  Carsten Lund,et al.  Nondeterministic exponential time has two-prover interactive protocols , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[10]  Stephen A. Cook,et al.  A hierarchy for nondeterministic time complexity , 1972, J. Comput. Syst. Sci..

[11]  Joel I. Seiferas,et al.  Limitations on Separating Nondeterministic Complexity Classes , 1981, SIAM J. Comput..

[12]  Sanjeev Arora,et al.  Probabilistic checking of proofs; a new characterization of NP , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[13]  Neil Immerman.  Nondeterministic Space is Closed Under Complementation , 1988, SIAM J. Comput..

[14]  Dima Grigoriev,et al.  Time hierarchies for cryptographic function inversion with advice , 2009, Electron. Colloquium Comput. Complex..

[15]  Sheila A. Greibach,et al.  Time- and Tape-Bounded Turing Acceptors and AFLs , 1970, J. Comput. Syst. Sci..

[16]  M. Karpinski,et al.  On the Monte Carlo Space Constructible Functions and Separation Results for Probabilistic Complexity Classes (Revised Version) , 1986 .

[17]  Konstantin Pervyshev.  On Heuristic Time Hierarchies , 2007, Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07).

[18]  Patrick C. Fischer,et al.  Translational methods and computational complexity , 1965, SWCT.

[19]  Eric Allender,et al.  Almost-Everywhere Complexity Hierarchies for Nondeterministic Time , 1993, Theor. Comput. Sci..

[20]  Stanislav Zák,et al.  A Turing Machine Time Hierarchy , 1983, Theor. Comput. Sci..

[21]  Robert E. Wilber.  Randomness and the density of hard problems , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[22]  Journal of the Association for Computing Machinery , 1961, Nature.

[23]  Boaz Barak,et al.  A Probabilistic-Time Hierarchy Theorem for "Slightly Non-uniform" Algorithms , 2002, RANDOM.

[24]  Luca Trevisan,et al.  Hierarchies for semantic classes , 2005, STOC '05.

[25]  Carsten Lund,et al.  Non-deterministic exponential time has two-prover interactive protocols , 1992, computational complexity.

[26]  C. J. Keyser.  Contributions to the Founding of the Theory of Transfinite Numbers , 1916 .

[27]  Róbert Szelepcsényi,et al.  The method of forced enumeration for nondeterministic automata , 1988, Acta Informatica.

[28]  A. Turing.  On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[29]  John T. Gill,et al.  Computational complexity of probabilistic Turing machines , 1974, STOC '74.

[30]  Lance Fortnow,et al.  Hierarchy theorems for probabilistic polynomial time , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[31]  Joel I. Seiferas,et al.  A Note on Almost-Everywhere-Complex Sets and Separating Deterministic-Time-Complexity Classes , 1991, Inf. Comput..

[32]  Richard Edwin Stearns,et al.  Two-Tape Simulation of Multitape Turing Machines , 1966, JACM.