Introduction to the theory of complexity

1. Mathematical Preliminaries. 2. Elements of Computability Theory. 4. The Class P. 5. The Glass NP. 6. The Complexity of Optiimzation Problems. 7. Beyond NP. 8. Space-Complexity Classes. 9. Probabiillistic. 10. Algorithms and Complexity Classes. 11. Interactivite Proof. 12. Systems. 13. Models of Parallel Computer. 14. Parallel Algorithms.

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

[2]  Juris Hartmanis,et al.  An Overview of the Theory of Computational Complexity , 1971, JACM.

[3]  Michael J. Fischer,et al.  Relations Among Complexity Measures , 1979, JACM.

[4]  Juris Hartmanis,et al.  On Isomorphisms and Density of NP and Other Complete Sets , 1977, SIAM J. Comput..

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

[6]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[7]  Abraham Robinson,et al.  Random-Access Stored-Program Machines, an Approach to Programming Languages , 1964, JACM.

[8]  Bolyai János Matematikai Társulat,et al.  Theory of algorithms , 1985 .

[9]  Carsten Lund,et al.  On the hardness of approximating minimization problems , 1994, JACM.

[10]  Vijay V. Vazirani,et al.  Matching is as easy as matrix inversion , 1987, STOC.

[11]  Paul Young,et al.  An introduction to the general theory of algorithms , 1978 .

[12]  Christos H. Papadimitriou,et al.  Games against nature , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[13]  P. Boas Machine models and simulations , 1991 .

[14]  Aaron D. Wyner,et al.  Computability by Probabilistic Machines , 1993 .

[15]  Michael Sipser,et al.  On Relativization and the Existence of Complete Sets , 1982, ICALP.

[16]  Uwe Schöning Graph Isomorphism is in the Low Hierarchy , 1988, J. Comput. Syst. Sci..

[17]  Giorgio Ausiello,et al.  Structure Preserving Reductions among Convex Optimization Problems , 1980, J. Comput. Syst. Sci..

[18]  Stephen R. Mahaney Sparse Complete Sets of NP: Solution of a Conjecture of Berman and Hartmanis , 1982, J. Comput. Syst. Sci..

[19]  Michael R. Fellows,et al.  Nonconstructive tools for proving polynomial-time decidability , 1988, JACM.

[20]  M. Furst A Subexponential Algorithm for Trivalent Graph Isomorphism , 1980 .

[21]  Paul Seymour,et al.  The metamathematics of the graph minor theorem , 1985 .

[22]  R. Carmichael On Composite Numbers P Which Satisfy the Fermat Congruence a P-1 ≡1 mod P , 1912 .

[23]  Juris Hartmanis,et al.  The Boolean Hierarchy II: Applications , 1989, SIAM J. Comput..

[24]  Christos H. Papadimitriou,et al.  The complexity of facets resolved , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[25]  Michael A. Harrison,et al.  Introduction to switching and automata theory , 1965 .

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

[27]  John Michael Robson,et al.  N by N Checkers is Exptime Complete , 1984, SIAM J. Comput..

[28]  L. Khachiyan Polynomial algorithms in linear programming , 1980 .

[29]  David S. Johnson,et al.  Approximation algorithms for combinatorial problems , 1973, STOC.

[30]  Richard J. Lipton,et al.  Some connections between nonuniform and uniform complexity classes , 1980, STOC '80.

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

[32]  Brenda S. Baker,et al.  Approximation algorithms for NP-complete problems on planar graphs , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[33]  E. F. Moore,et al.  On the Possibilities of Designing Circuits out of Various Elements.On the Synthesis of Contact Circuits.On the Synthesis of Contact Networks , 1959 .

[34]  Stuart J. Berkowitz,et al.  On Computing the Determinant in Small Parallel Time Using a Small Number of Processors , 1984, Inf. Process. Lett..

[35]  Richard M. Karp,et al.  Parallel Algorithms for Shared-Memory Machines , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[36]  Ming Li,et al.  Kolmogorov Complexity and its Applications , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[37]  Larry J. Stockmeyer,et al.  A characterization of the power of vector machines , 1974, STOC '74.

[38]  Vaughan R. Pratt,et al.  Every Prime has a Succinct Certificate , 1975, SIAM J. Comput..

[39]  R. Z. Norman,et al.  An algorithm for a minimum cover of a graph , 1959 .

[40]  Uzi Vishkin,et al.  Simulation of Parallel Random Access Machines by Circuits , 1984, SIAM J. Comput..

[41]  Maciej Liskiewicz,et al.  Two Applications of Fürer's Counter to One-Tape Nondeterministic TMs , 1988, MFCS.

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

[43]  Faith Ellen,et al.  Relations Between Concurrent-Write Models of Parallel Computation , 1988, SIAM J. Comput..

[44]  Peter van Emde Boas,et al.  Machine Models and Simulation , 1990, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[45]  Manuel Blum,et al.  A Machine-Independent Theory of the Complexity of Recursive Functions , 1967, JACM.

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

[47]  Michael R. Fellows,et al.  Constructive complexity , 1991, Discret. Appl. Math..

[48]  Joseph Y.-T. Leung,et al.  An Optimal Solution for the Channel-Assignment Problem , 1979, IEEE Transactions on Computers.

[49]  Richard Edwin Stearns,et al.  Hierarchies of memory limited computations , 1965, SWCT.

[50]  László Lovász,et al.  On determinants, matchings, and random algorithms , 1979, FCT.

[51]  Allan Borodin,et al.  Fast parallel matrix and GCD computations , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[52]  Albert R. Meyer,et al.  The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space , 1972, SWAT.

[53]  Leslie M. Goldschlager,et al.  A universal interconnection pattern for parallel computers , 1982, JACM.

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

[55]  Paul Young,et al.  Juris Hartmanis: fundamental contributions to isomorphism problems , 1988, [1988] Proceedings. Structure in Complexity Theory Third Annual Conference.

[56]  David Eppstein,et al.  Parallel Algorithmic Techniques for Combinatorial Computation , 1988, ICALP.

[57]  Neil D. Jones,et al.  Space-Bounded Reducibility among Combinatorial Problems , 1975, J. Comput. Syst. Sci..

[58]  Timothy J. Long,et al.  Relativizing complexity classes with sparse oracles , 1986, JACM.

[59]  Jacob T. Schwartz,et al.  Fast Probabilistic Algorithms for Verification of Polynomial Identities , 1980, J. ACM.

[60]  S.-Y. Kuroda,et al.  Classes of Languages and Linear-Bounded Automata , 1964, Inf. Control..

[61]  Gary L. Miller,et al.  Riemann's Hypothesis and tests for primality , 1975, STOC.

[62]  Leslie G. Valiant,et al.  On Time Versus Space , 1977, JACM.

[63]  Fanica Gavril,et al.  Algorithms for Minimum Coloring, Maximum Clique, Minimum Covering by Cliques, and Maximum Independent Set of a Chordal Graph , 1972, SIAM J. Comput..

[64]  Robert E. Tarjan,et al.  A Combinatorial Problem Which Is Complete in Polynomial Space , 1976, JACM.

[65]  Stephen A. Cook,et al.  A Taxonomy of Problems with Fast Parallel Algorithms , 1985, Inf. Control..

[66]  Emil L. Post Formal Reductions of the General Combinatorial Decision Problem , 1943 .

[67]  Diana Schmidt The Recursion-Theoretic Structure of Complexity Classes , 1985, Theor. Comput. Sci..

[68]  Gary L. Miller,et al.  On the nlog n isomorphism technique (A Preliminary Report) , 1978, STOC.

[69]  Edith Hemaspaandra,et al.  Nondeterminism fairness and a fundamental analogy , 1989, Bull. EATCS.

[70]  P. Young,et al.  Easy constructions in complexity theory: Gap and speed-up theorems , 1973 .

[71]  M. Rabin Degree of difficulty of computing a function and a partial ordering of recursive sets , 1960 .

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

[73]  L. Csanky,et al.  Fast Parallel Matrix Inversion Algorithms , 1976, SIAM J. Comput..

[74]  Alexander Shen IP = SPACE: simplified proof , 1992, JACM.

[75]  Seinosuke Toda On the computational power of PP and (+)P , 1989, 30th Annual Symposium on Foundations of Computer Science.

[76]  Juris Hartmanis,et al.  The Boolean Hierarchy I: Structural Properties , 1988, SIAM J. Comput..

[77]  Shafi Goldwasser,et al.  Private coins versus public coins in interactive proof systems , 1986, STOC '86.

[78]  Jan van Leeuwen,et al.  Graph Algorithms , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[79]  Alan M. Turing,et al.  Systems of Logic Based on Ordinals , 2012, Alan Turing's Systems of Logic.

[80]  Lance Fortnow,et al.  Are There Interactive Protocols for CO-NP Languages? , 1988, Inf. Process. Lett..

[81]  Pierluigi Crescenzi,et al.  A Uniform Approach to Define Complexity Classes , 1992, Theor. Comput. Sci..

[82]  W. T. Tutte The Factors of Graphs , 1952, Canadian Journal of Mathematics.

[83]  Henryk Wozniakowski,et al.  Complexity of linear programming , 1982, Oper. Res. Lett..

[84]  Maciej Liskiewicz,et al.  Some Time-Space Bounds for One-Tape Deterministic Turing Machines , 1989, FCT.

[85]  Deborah Joseph,et al.  Some Remarks on Witness Functions for Nonpolynomial and Noncomplete Sets in NP , 1985, Theor. Comput. Sci..

[86]  Yehoshua Bar-Hillel,et al.  The Intrinsic Computational Difficulty of Functions , 1969 .

[87]  J. Edmonds Paths, Trees, and Flowers , 1965, Canadian Journal of Mathematics.

[88]  Stephen A. Cook,et al.  Deterministic CFL's are accepted simultaneously in polynomial time and log squared space , 1979, STOC.

[89]  R. Ladner The circuit value problem is log space complete for P , 1975, SIGA.

[90]  Juris Hartmanis,et al.  Gödel, von Neumann and the P =? NP Problem , 1989, Current Trends in Theoretical Computer Science.

[91]  David S. Johnson,et al.  `` Strong '' NP-Completeness Results: Motivation, Examples, and Implications , 1978, JACM.

[92]  Giorgio Ausiello,et al.  Abstract Computational Complexity and Cycling Computations , 1971, J. Comput. Syst. Sci..

[93]  Larry J. Stockmeyer,et al.  On Approximation Algorithms for #P , 1985, SIAM J. Comput..

[94]  Walter J. Savitch,et al.  Relationships Between Nondeterministic and Deterministic Tape Complexities , 1970, J. Comput. Syst. Sci..

[95]  Eugene S. Santos,et al.  Probabilistic Turing machines and computability , 1969 .

[96]  Wolfgang Maass,et al.  Oracle-Dependent Properties of the Lattice of NP Sets , 1983, Theor. Comput. Sci..

[97]  S. C. Kleene,et al.  Introduction to Metamathematics , 1952 .

[98]  Phokion G. Kolaitis,et al.  Approximation properties of NP minimization classes , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

[99]  Jeffrey D. Ullman,et al.  Relations Between Time and Tape Complexities , 1968, JACM.

[100]  Sartaj Sahni,et al.  Parallel Scheduling Algorithms , 1983, Oper. Res..

[101]  Allan Borodin,et al.  Computational Complexity and the Existence of Complexity Gaps , 1972, JACM.

[102]  Christoph M. Hoffmann,et al.  Group-Theoretic Algorithms and Graph Isomorphism , 1982, Lecture Notes in Computer Science.

[103]  Prabhakar Ragde,et al.  Incomparability in parallel computation , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[104]  Steven Fortune,et al.  Parallelism in random access machines , 1978, STOC.

[105]  Carsten Lund,et al.  Algebraic methods for interactive proof systems , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[106]  Allan Borodin,et al.  On Relating Time and Space to Size and Depth , 1977, SIAM J. Comput..

[107]  Stephen A. Cook,et al.  Upper and Lower Time Bounds for Parallel Random Access Machines without Simultaneous Writes , 1986, SIAM J. Comput..

[108]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[109]  Leonard M. Adleman,et al.  Recognizing primes in random polynomial time , 1987, STOC.

[110]  C Berge,et al.  TWO THEOREMS IN GRAPH THEORY. , 1957, Proceedings of the National Academy of Sciences of the United States of America.

[111]  Paul Young,et al.  A Structural Overview of NP Optimization Problems , 1989, Optimal Algorithms.

[112]  Gerd Wechsung,et al.  On the Boolean closure of NP , 1985, FCT.

[113]  Uwe Schöning,et al.  Complexity and Structure , 1986, Lecture Notes in Computer Science.

[114]  Marc Snir,et al.  On Parallel Searching , 2011, SIAM J. Comput..

[115]  Juris Hartmanis,et al.  An Eassay about Research on Sparse NP Complete Sets , 1980, MFCS.

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

[117]  Mihalis Yannakakis,et al.  The complexity of facets (and some facets of complexity) , 1982, STOC '82.

[118]  Noam Chomsky,et al.  On Certain Formal Properties of Grammars , 1959, Inf. Control..

[119]  John E. Savage,et al.  Computational Work and Time on Finite Machines , 1972, JACM.

[120]  Richard J. Lipton,et al.  On the Structure of Sets in NP and Other Complexity Classes , 1981, Theor. Comput. Sci..

[121]  Andreas Blass,et al.  On the Unique Satisfiability Problem , 1982, Inf. Control..

[122]  Selim G. Akl,et al.  Design and analysis of parallel algorithms , 1985 .

[123]  Leonid A. Levin,et al.  Checking computations in polylogarithmic time , 1991, STOC '91.

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

[125]  Larry J. Stockmeyer,et al.  The Polynomial-Time Hierarchy , 1976, Theor. Comput. Sci..

[126]  Mark W. Krentel The complexity of optimization problems , 1986, STOC '86.

[127]  Janos Simon On some central problems in computational complexity , 1975 .

[128]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, Comb..

[129]  László Lovász,et al.  Approximating clique is almost NP-complete , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[130]  Volker Strassen,et al.  A Fast Monte-Carlo Test for Primality , 1977, SIAM J. Comput..

[131]  Carl A. Gunter,et al.  In handbook of theoretical computer science , 1990 .

[132]  L. Goldschlager The monotone and planar circuit value problems are log space complete for P , 1977, SIGA.

[133]  Ker-I Ko,et al.  Some Observations on the Probabilistic Algorithms and NP-hard Problems , 1982, Inf. Process. Lett..

[134]  Celia Wrathall,et al.  Complete Sets and the Polynomial-Time Hierarchy , 1976, Theor. Comput. Sci..

[135]  R. Solovay,et al.  Relativizations of the $\mathcal{P} = ?\mathcal{NP}$ Question , 1975 .

[136]  Faith Ellen,et al.  Relations between concurrent-write models of parallel computation , 1984, PODC '84.

[137]  Michael Sipser,et al.  Parity, circuits, and the polynomial-time hierarchy , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[138]  Shlomo Moran,et al.  Non Deterministic Polynomial Optimization Problems and their Approximations , 1977, Theoretical Computer Science.

[139]  Kojiro Kobayashi On Proving Time Constructibility of Functions , 1985, Theor. Comput. Sci..

[140]  Wojciech Rytter,et al.  Efficient parallel algorithms , 1988 .

[141]  David S. Johnson,et al.  A Catalog of Complexity Classes , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[142]  Giorgio Ausiello,et al.  Toward a Unified Approach for the Classification of NP-Complete Optimization Problems , 1979, Theor. Comput. Sci..

[143]  Sartaj Sahni,et al.  Parallel Matrix and Graph Algorithms , 1981, SIAM J. Comput..

[144]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[145]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[146]  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).

[147]  A. Yao Separating the polynomial-time hierarchy by oracles , 1985 .

[148]  Uwe Schöning A Uniform Approach to Obtain Diagonal Sets in Complexity Classes , 1982, Theor. Comput. Sci..

[149]  Joel I. Seiferas Machine-Independent Complexity Theory , 1990, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[150]  Stuart A. Kurtz,et al.  The Structure of Complete Degrees , 1990 .

[151]  ZVI GALIL,et al.  Efficient algorithms for finding maximum matching in graphs , 1986, CSUR.

[152]  Jeffrey D. Smith,et al.  Design and Analysis of Algorithms , 2009, Lecture Notes in Computer Science.

[153]  Rossella Petreschi,et al.  Experimental comparison of 2-satisfiability algorithms , 1991 .

[154]  Silvio Micali,et al.  Proofs that yield nothing but their validity and a methodology of cryptographic protocol design , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[155]  László Babai,et al.  Trading group theory for randomness , 1985, STOC '85.

[156]  John H. Conway,et al.  Knots and links in spatial graphs , 1983, J. Graph Theory.

[157]  Juris Hartmanis On Sparse Sets in NP - P , 1983, Inf. Process. Lett..

[158]  Claude E. Shannon,et al.  The synthesis of two-terminal switching circuits , 1949, Bell Syst. Tech. J..

[159]  Stephen A. Cook,et al.  An observation on time-storage trade off , 1973, J. Comput. Syst. Sci..

[160]  John C. Shepherdson,et al.  Computability of Recursive Functions , 1963, JACM.

[161]  S. Kleene General recursive functions of natural numbers , 1936 .

[162]  Donald E. Knuth,et al.  The art of computer programming: V.1.: Fundamental algorithms , 1997 .

[163]  Jin-Yi Cai,et al.  The Boolean Hierarchy: Hardware over NP , 1986, SCT.

[164]  John Gill,et al.  Relative to a Random Oracle A, PA != NPA != co-NPA with Probability 1 , 1981, SIAM J. Comput..

[165]  Robert E. Tarjan,et al.  A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean Formulas , 1979, Inf. Process. Lett..

[166]  José L. Balcázar,et al.  Immunity and Simplicity in Relativizations of Probabilistic Complexity Classes , 1988, RAIRO Theor. Informatics Appl..

[167]  Uwe Schöning,et al.  Immunity, Relativizations, and Nondeterminism , 1984, SIAM J. Comput..

[168]  Oded Goldreich Randomness, interactive proofs, and zero-knowledge—A survey , 1988 .

[169]  P. Orponen,et al.  On Approximation Preserving Reductions: Complete Problems and Robust Measures (Revised Version) , 1987 .

[170]  Jr. Hartley Rogers Theory of Recursive Functions and Effective Computability , 1969 .

[171]  Daniel A. Spielman,et al.  PP is closed under intersection , 1991, STOC '91.

[172]  Leslie G. Valiant,et al.  Relative Complexity of Checking and Evaluating , 1976, Inf. Process. Lett..

[173]  Martin D. Davis,et al.  Computability and Unsolvability , 1959, McGraw-Hill Series in Information Processing and Computers.

[174]  John Gill,et al.  Computational Complexity of Probabilistic Turing Machines , 1977, SIAM J. Comput..

[175]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[176]  David E. Muller,et al.  Bounds to Complexities of Networks for Sorting and for Switching , 1975, JACM.

[177]  H. James Hoover,et al.  A Compendium of Problems Complete for P , 1991 .

[178]  Norbert Blum A Boolean Function Requiring 3n Network Size , 1984, Theor. Comput. Sci..

[179]  Silvio Micali,et al.  The knowledge complexity of interactive proof-systems , 1985, STOC '85.

[180]  Alan L. Selman,et al.  Qualitative Relativizations of Complexity Classes , 1985, J. Comput. Syst. Sci..

[181]  Shlomo Moran,et al.  Non Deterministic Polynomial Optimization Problems and their Approximations , 1977, Theor. Comput. Sci..

[182]  Robert L. Constable,et al.  The Operator Gap , 1969, JACM.

[183]  Mihalis Yannakakis,et al.  Optimization, approximation, and complexity classes , 1991, STOC '88.

[184]  M. Rabin Probabilistic algorithm for testing primality , 1980 .

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

[186]  Alessandro Panconesi,et al.  Completeness in Approximation Classes , 1989, Inf. Comput..

[187]  Evangelos Kranakis Primality and cryptography , 1986, Wiley-Teubner series in computer science.

[188]  Claude E. Shannon,et al.  The Number of Two‐Terminal Series‐Parallel Networks , 1942 .

[189]  Sartaj Sahni,et al.  Data broadcasting in SIMD computers , 1981, IEEE Transactions on Computers.

[190]  John Gill,et al.  Relativizations of the P =? NP Question , 1975, SIAM J. Comput..

[191]  Robert W. Deming,et al.  Independence numbers of graphs-an extension of the Koenig-Egervary theorem , 1979, Discret. Math..

[192]  L. G. H. Cijan A polynomial algorithm in linear programming , 1979 .

[193]  Satoru Miyano,et al.  A List of P-Complete Problems , 1989 .

[194]  Ludek Kucera,et al.  Parallel Computation and Conflicts in Memory Access , 1982, Information Processing Letters.

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

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

[197]  Manuel Blum On the Size of Machines , 1967, Inf. Control..

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

[199]  Walter L. Ruzzo,et al.  Tree-size bounded alternation(Extended Abstract) , 1979, J. Comput. Syst. Sci..

[200]  Richard M. Karp,et al.  An introduction to randomized algorithms , 1991, Discret. Appl. Math..

[201]  Pierluigi Crescenzi,et al.  Complexity classes and sparse oracles , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

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