Resource bounded reductions

Acknowledgments First I would like to thank my promotores and Steven Homer and Peter van Emde Boas. Steve invited me in a very early stage of my research to come to Boston. My visits to Boston were very inspiring and invaluable. A substantial part of my research consists of joint work with him. We had many inspiring conversations, sometimes on a daily basis. I thank Steve for his support during my visits to Boston and via e-mail when I was in Amsterdam. Peter provided in the beginning a pleasant atmosphere that gave me above all the freedom to do things my way. Whenever I got stuck I could ask him for advice, that he either could give me immediately or, after consulting his oracle, the next day. In the end stages of writing this thesis he was of great value by reading my rapidly changing versions of the manuscript, debugging the proofs and being patient with me. I thank my co-promotor Leen Torenvliet. Leen is the person who started it all and made it possible for me to do this research in the rst place. I remember vividly his inspiring lectures when I was still a masters student. I thank him also for supporting me through the early stages and the numerous exciting`brain storm sessions' we had. It would not have been possible to write this thesis without him. This thesis is by no means the work of a single person. It consists of papers written with others. But also discussions and ideas of other people have contributed to this work. I would like to thank Edith Spaan, for many long and inspiring discussions, Luc Longpr e for his insights in many things and his hospitality during my visits to Boston. Special thanks are due to Albrecht Hoene, who was my ooce mate for a very short period in Boston and inspired a lot of the work done back in Amsterdam. I thank Jim Kadin for working with me in very exciting v surroundings. I thank Michiel Smid for the conversations we had in the beginning of my research and the frequent e-mail messages later. I would like to thank Alan Selman for sharing results and suggestions related to the last chapter of this thesis. His insights are invaluable. I would like to thank Jos e I thank Paul van Ulsen for reading my manuscript thoroughly. Special thanks go to …

[1]  Antoni Lozano i Bojados Computational complexity versus structural simplicity , 1992 .

[2]  Edith Hemaspaandra,et al.  SPARSE reduces conjunctively to TALLY , 1993, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference.

[3]  Paul H. Morris,et al.  On Subcreative Sets and S-Reducibility , 1974, J. Symb. Log..

[4]  C. Jockusch Semirecursive sets and positive reducibility , 1968 .

[5]  Juris Hartmanis,et al.  On isomorphisms and density of NP and other complete sets , 1976, STOC '76.

[6]  Steven Homer,et al.  Complete Problems and Strong Polynomial Reducibilities , 1992, SIAM J. Comput..

[7]  Ker-I Ko,et al.  On Sets Truth-Table Reducible to Sparse Sets , 1988, SIAM J. Comput..

[8]  José L. Balcázar,et al.  Functional Oracle Queries as a Measure of Parallel Time , 1991, STACS.

[9]  Osamu Watanabe,et al.  On polynomial time bounded truth-table reducibility of NP sets to sparse sets , 1990, STOC '90.

[10]  Nicholas Pippenger,et al.  On simultaneous resource bounds , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[11]  Osamu Watanabe,et al.  On the Computational Complexity of Small Descriptions , 1993, SIAM J. Comput..

[12]  Noam Nisan,et al.  Hardness vs Randomness , 1994, J. Comput. Syst. Sci..

[13]  Jim Kadin,et al.  P^(NP[O(log n)]) and Sparse Turing-Complete Sets for NP , 1989, J. Comput. Syst. Sci..

[14]  Nancy A. Lynch,et al.  Comparison of polynomial-time reducibilities , 1974, STOC '74.

[15]  Mitsunori Ogihara,et al.  On Using Oracles That Compute Values , 1993, STACS.

[16]  Sanjeev Saluja Relativized limitations of left set technique and closure classes of sparse sets , 1993, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference.

[17]  Tchébichef,et al.  Mémoire sur les nombres premiers. , 1852 .

[18]  Alan L. Selman,et al.  Analogues of Semicursive Sets and Effective Reducibilities to the Study of NP Complexity , 1982, Inf. Control..

[19]  R. Friedberg,et al.  TWO RECURSIVELY ENUMERABLE SETS OF INCOMPARABLE DEGREES OF UNSOLVABILITY (SOLUTION OF POST'S PROBLEM, 1944). , 1957, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Osamu Watanabe,et al.  How hard are sparse sets? , 1992, [1992] Proceedings of the Seventh Annual Structure in Complexity Theory Conference.

[21]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[22]  Alan L. Selman,et al.  P-Selective Sets, Tally Languages, and the Behavior of Polynomial Time Reducibilities on NP , 1979, ICALP.

[23]  P. Vitányi,et al.  Applications of Kolmogorov Complexity in the Theory of Computation , 1990 .

[24]  Richard E. Ladner,et al.  Mitotic recursively enumerable sets , 1973, Journal of Symbolic Logic.

[25]  Osamu Watanabe,et al.  A Comparison of Polynomial Time Completeness Notions , 1987, Theor. Comput. Sci..

[26]  Neil Immerman,et al.  Languages that Capture Complexity Classes , 1987, SIAM J. Comput..

[27]  Christopher B. Wilson Relativized circuit complexity , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[28]  Mitsunori Ogihara,et al.  P-selective sets, and reducing search to decision vs. self-reducibility , 1993, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference.

[29]  Alan J. Demers,et al.  Some Comments on Functional Self-Reducibility and the NP Hierarchy , 1976 .

[30]  José L. Balcázar,et al.  Structural Complexity II , 2012, EATCS.

[31]  Stephen R. Mahaney Sparse complete sets for NP: Solution of a conjecture of Berman and Hartmanis , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[32]  渡邉 治 On the structure of intractable complexity classes , 1987 .

[33]  Ravi Kannan,et al.  Circuit-Size Lower Bounds and Non-Reducibility to Sparse Sets , 1982, Inf. Control..

[34]  L. Berman Polynomial reducibilities and complete sets. , 1977 .

[35]  Neil Immerman,et al.  Expressibility as a complexity measure: results and directions , 1987, SCT.

[36]  Ronald V. Book,et al.  Tally Languages and Complexity Classes , 1974, Inf. Control..

[37]  Ker-I Ko On Self-Reducibility and Weak P-Selectivity , 1983, J. Comput. Syst. Sci..

[38]  Luc Longpré,et al.  On Reductions of NP Sets to Sparse Sets , 1994, J. Comput. Syst. Sci..

[39]  D. Garling,et al.  Algebra, Volume 1 , 1969, Mathematical Gazette.

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

[41]  Edith Hemaspaandra,et al.  Bounded Reductions , 1991, Complexity Theory: Current Research.

[42]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[43]  Steven Fortune,et al.  A Note on Sparse Complete Sets , 1978, SIAM J. Comput..

[44]  José L. Balcázar,et al.  Structural Complexity I , 1995, Texts in Theoretical Computer Science An EATCS Series.

[45]  Leonard Berman,et al.  On the structure of complete sets: Almost everywhere complexity and infinitely often speedup , 1976, 17th Annual Symposium on Foundations of Computer Science (sfcs 1976).

[46]  Zoltán Füredi,et al.  Families of Finite Sets in Which No Set Is Covered by the Union of Two Others , 1982, J. Comb. Theory, Ser. A.

[47]  Vikraman Arvind,et al.  On Bounded Truth-Table, Conjunctive, and Randomized Reductions to Sparse Sets , 1992, FSTTCS.

[48]  Richard Chang,et al.  Connections between the complexity of unique satisfiability and the threshold behavior of randomized reductions , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

[49]  S. S. Marchenkov One class of partial sets , 1976 .

[50]  José L. Balcázar Self-Reducibility , 1990, J. Comput. Syst. Sci..

[51]  Richard E. Ladner,et al.  On the Structure of Polynomial Time Reducibility , 1975, JACM.

[52]  Alan L. Selman,et al.  Promise Problems Complete for Complexity Classes , 1988, Inf. Comput..

[53]  Peter van Emde Boas,et al.  Twenty Questions to a P-Selector , 1993, Inf. Process. Lett..

[54]  L. Hemachandra,et al.  Counting in structural complexity theory , 1987 .

[55]  Neil Immerman,et al.  Sparse sets in NP-P: Exptime versus nexptime , 1983, STOC.

[56]  Carsten Lund,et al.  Non-deterministic exponential time has two-prover interactive protocols , 2005, computational complexity.

[57]  Bin Fu,et al.  Exponential-Time and Subexponential-Time Sets , 1993, Theor. Comput. Sci..

[58]  Yu. L. Ershov Positive equivalences , 1971 .