Skip to main content
SpringerLink
Log in

Juris Hartmanis: Fundamental Contributions to Isomorphism Problems

  • Chapter
Complexity Theory Retrospective

Abstract

In this paper we survey Juris Hartmanis’ contributions to isomorphism problems. These problems are primarily of two forms. First, isomorphism problems for restricted programming systems, including the Hartmanis-Baker conjecture that all polynomial time programming systems are polynomially isomorphic. Second, the research on isomorphisms, and particularly polynomial time isomorphisms for complete problems for various natural complexity classes, including the Berman-Hartmanis conjecture that all sets complete for NP under Karp reductions are polynomially isomorphic. We discuss not only the work of Hartmanis and his students on these isomorphism problems, but we also include a (necessarily partial and incomplete) discussion of the the impact which this research has had on other topics and other researchers in structural complexity theory.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

Introduction and General Background

  1. Hartmanis, J. and J. Hopcroft, “An overview of the theory of computational complexity,” J Assoc Comp Mach 18 (1971), 444–475.

    Article  MathSciNet  MATH  Google Scholar 

  2. Hartmanis, J., Feasible Computations and Provable Complexity Properties, SI AM CBMS-NSF Regional Conference Series in Applied Math 30 (1978).

    Google Scholar 

  3. Hartmanis, J., “Observations About the Development of Theoretical Computer Science,” Annals History Comput 3 (1981), 42–51.

    Article  MathSciNet  MATH  Google Scholar 

  4. Bertoni, A., D. Bruschi, D. Joseph, M. Sitharam, and P. Young, “Generalized Boolean hierarchies and Boolean hierarchies over RP,” final version available as Univ Wise CS Tech Report; short abstract in Proc 7 th Symp Foundations Computing Theory, (FCT-1989), Springer-Verlag, LNCS 380, 35–46.

    Google Scholar 

  5. Blum, M., “A machine-independent theory of complexity of recursive functions,” J Assoc Comput Mach 14 (1967), 322–336.

    Article  MathSciNet  MATH  Google Scholar 

  6. Blum, M., “On the size of machines,” Inform and Control 11 (1967), 257–265.

    Article  MATH  Google Scholar 

  7. Borodin, A., “Complexity classes of recursive functions and the existence of complexity gaps,” Proc 1 st ACM Symp Theory Comput (1969), 67–78.

    Google Scholar 

  8. Borodin A., R. Constable and J. Hopcroft, “Dense and nondense families of complexity classes,” Proc 10 th IEEE Switching and Automata Theory Conf, (1969), 7–19.

    Google Scholar 

  9. Bruschi, D., D. Joseph, and P. Young, “A structural overview of NP optimization problems,” Proc 2 nd International Conference on Optimal Algorithms; Springer-Verlag, Lecture Notes Comp Sc, (1989), 27 pages, to appear.

    Google Scholar 

  10. Constable, R., “The operator gap,” Proc 10 th IEEE Symp Switching Automata Theory, (1969), 20–26.

    Google Scholar 

  11. Constable, R., “On the size of programs in subrecursive formalisms,” Proc 2 nd ACM Symp Theory Comput (1970), 1–9.

    Google Scholar 

  12. Constable, R. and A. Borodin, “Subrecursive programming languages, Part I: Efficiency and program structure,” J Assoc Comput Mach 19 (1972), 526–568. Some of the results in this paper first appeared in, “On the efficiency of programs in subrecursive formalisms,” presented at the 11 th IEEE Symp Switching and Automata Theory, (1970), 60–67.

    Article  MathSciNet  MATH  Google Scholar 

  13. Crescenzi, P. and Panconesi, A., “Completeness in approximation classes,” Proc 7 th Symp Foundations Computing Theory, (FCT-1989), Springer-Verlag, LNCS 380; final version to appear in Inform and Comput.

    Google Scholar 

  14. Krentel, M. “The complexity of optimization problems,” J Comput System Sci 36 (1988), 490–509; (preliminary version in Proc 18 th ACM Symp Theory Comput, (1986), 69–76.)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ladner, R., “On the structure of polynomial time reducibility,” J Assoc Comput Mach 22 (1975), 155–171.

    Article  MathSciNet  MATH  Google Scholar 

  16. Ladner, R., A. Selman, and N. Lynch, “A comparison of polynomial time reducibilities,” Theor Comput Sci (1975) 103–123.

    Google Scholar 

  17. Machtey, M., and P. Young, “An Introduction to the General Theory of Algorithms,” Elsevier North Holland, New York (1978), 1–264.

    MATH  Google Scholar 

  18. Marcoux, Y., “Composition is almost as good as S-l-1,” Proc 4 th IEEE Symp Structure Complexity Theory, (1989), 77–86.

    Google Scholar 

  19. McCreight, E. and A. Meyer, “Classes of computable functions defined by bounds on computation,” Proc 1 st ACM Symp Theory Computing, (1969), 79–81.

    Google Scholar 

  20. Meyer, A., “Program size in restricted programming languages,” Inform and Control 21 (1972), 382–394.

    Article  MATH  Google Scholar 

  21. Ritchie, D., Program Structure and Computational Complexity, Ph.D. Thesis Harvard University (1968).

    Google Scholar 

  22. Royer, J., “A Connotational Theory of Program Structure,” Springer Verlag LNCS 273, (1987).

    Google Scholar 

  23. RC-91] Royer, J. and A. Case, “Intensional Subrecursion and Complexity Theory,” Research Notes in Theoretical Computer Science, to appear.

    Google Scholar 

  24. Stockmeyer, L., “Classifying the computational complexity of problems,” J Symb Logic 52 (1987), 1–43.

    Article  MathSciNet  MATH  Google Scholar 

  25. Young, P., “Toward a theory of enumerations,” J Assoc Comput Mach 16 (1969), 328–348.

    Article  MathSciNet  MATH  Google Scholar 

Isomorphisms of Gödel Numberings

  1. Hartmanis, J., “Computational complexity of formal translations,” Math Systems Theory 8 (1974), 156–166. Work presented in this paper concerning formal models for translation extends some of the work in [CH-71], “Complexity of formal translations and speed-up results,” (with R. Constable) presented at STOC 1971.

    Article  MathSciNet  Google Scholar 

  2. Hartmanis, J. and T. Baker, “On simple Gödel numberings and translations,” SIAM J Comput 4 (1975), 1–11. This paper extends work in “On simple Godel numberings and translations,” presented at ICALP 1974.

    Article  MathSciNet  MATH  Google Scholar 

  3. Hartmanis, J., “A note on natural complete sets and Gödel numberings,” Theor Comput Sci 17 (1982), 75–89.

    Article  MathSciNet  MATH  Google Scholar 

  4. Hartmanis, J., “On the problem of finding natural computational complexity measures,” Proc Symp Math Found Comput Sci, (1973), 95–103.

    Google Scholar 

  5. Hartmanis, J., “Observations about the development of theoretical computer science,” Annals History of Comput 3 (1981), 42–51. The work in this paper was originally presented at FOCS (1979).

    Article  MathSciNet  MATH  Google Scholar 

  6. Alton, D., “Nonexistence of program optimizers in several abstract settings,” J Comput System Sci 12 (1976), 368–393.

    Article  MathSciNet  MATH  Google Scholar 

  7. Alton, D., “Program structure, ‘natural’ complexity measures, and subrecursive programming languages,” Proc 2 nd Hungarian Comput Sci Conf, Akad Kiado, Budapest, (1977).

    Google Scholar 

  8. Alton, D., “‘Natural’ complexity measures and time versus memory: some definitional proposals,” Proc 4 th ICALP, Springer Verlag LNCS 52, (1977).

    Google Scholar 

  9. Alton, D., “‘Natural’ complexity measures and subrecursive complexity,” in Recursion Theory: Its Generalizations and Applications, editors F.R. Drake and S.S. Wainer, Cambridge Univ Press, (1980), 248–285.

    Chapter  Google Scholar 

  10. Helm, J., A. Meyer, and P. Young, “On orders of translations and enumerations,” Pacific J Math 46 (1973), 185–195.

    MathSciNet  MATH  Google Scholar 

  11. Kozen, D., “Indexings of subrecursive classes,” Theor Comput Sci 11 (1980), 277–301.

    Article  MathSciNet  MATH  Google Scholar 

  12. Machtey, M., K. Winklmann, and P. Young, “Simple Gödel numberings, isomorphisms, and programming properties,” SIAM J Comput 7 (1978), 39–60. This paper extends work in, “Simple Gödel numberings, translations and the P-hierarchy,” presented at STOC 1976.

    Article  MathSciNet  MATH  Google Scholar 

  13. Pager, D., “On finding programs of minimal length,” Infor and Control 15 (1969), 550–554.

    Article  Google Scholar 

  14. Riccardi, G., “The independence of control structures in abstract programming systems,” J Comput System Sci 22 (1981), 107–143.

    Article  MathSciNet  MATH  Google Scholar 

  15. Rogers, H., “Gödel numberings of partial recursive functions,” J Symbolic Logic 23 (1958), 331–341.

    Article  Google Scholar 

  16. Schnorr, C. P., “Optimal enumerations and optimal Gödel numberings,” Math Systems Theory, 8 (1975), 182–191.

    Article  MathSciNet  Google Scholar 

  17. Shay, M. and P. Young, “Characterizing the orders changed by program translators,” Pacific J Math 76 (1978), 485–490.

    MathSciNet  MATH  Google Scholar 

  18. Young, P., “Toward a theory of enumerations,” J Assoc Comput Mach 16 (1969), 328–348.

    Article  MathSciNet  MATH  Google Scholar 

  19. Young, P., “A note on ‘axioms’ for computational complexity and computation of finite functions,” Inform and Control 19 (1971), 377–386.

    Article  Google Scholar 

  20. Young, P., “A note on dense and nondense families of complexity classes,” Math Systems Theory 5 (1971), 66–70.

    Article  MathSciNet  MATH  Google Scholar 

The Berman-Hartmanis Conjecture

  1. Berman, L. and J. Hartmanis, “On isomorphism and density of NP and other complete sets,” SIAM J Comput 6 (1977), 305–322. The results in this paper were first presented in [HB-76], “On isomorphism and density of NP and other complete sets,” at STOC (1976).

    Article  MathSciNet  MATH  Google Scholar 

  2. Berman, L. and J. Hartmanis, “On polynomial time isomorphisms of complete sets,” Proc 3 rd Theor Comput Sci GI Conf Springer Verlag LNCS 48 (1977), 1–15.

    Google Scholar 

  3. Hartmanis, J. and L. Berman, “On polynomial time isomorphisms of some new complete sets,” J Comput System Sci 16 (1978), 418–422.

    Article  MathSciNet  MATH  Google Scholar 

  4. Hartmanis, J., Feasible computations and provable complexity properties, SIAM CBMS-NSF Regional Conf Series in Applied Math 30, (1978).

    Google Scholar 

  5. Hartmanis, J., N. Immerman and S. Mahaney, “One-way, log-tape reductions,” Proc 19 th IEEE FOCS, (1978), 65–72.

    Google Scholar 

  6. Hartmanis, J., “On log-tape isomorphisms of complete sets,” Theor Comput Sci 7 (1978), 273–286.

    Article  MathSciNet  MATH  Google Scholar 

  7. Hartmanis, J. and S. Mahaney, “Languages simultaneously complete for one-way and two-way log-tape automata,” SIAM J Comput 10 (1981), 383–390.

    Article  MathSciNet  MATH  Google Scholar 

  8. Hartmanis, J., “A note on natural complete sets and Gödel numberings,” Theor Comput Sci 17 (1982), 75–89.

    Article  MathSciNet  MATH  Google Scholar 

  9. Hartmanis, J., “Sparse sets in NP — P,” Infor Processing Letters, 16 (1983), 55–60.

    Article  MathSciNet  MATH  Google Scholar 

  10. Hartmanis, J. and L. Hemachandra, “One-way functions, robust-ness, and the non-isomorphism of NP-complete sets,” Proc 2 nd IEEE Symp Structure Complexity Theory, (1987), 160–173. (Also to appear in Theor Comput Sci.)

    Google Scholar 

  11. Allender, E., “Isomorphisms and 1-L reductions,” J Comput System Sci 36 (1988), 336–350. (Some of the results of this paper were first reported in Proc 1 st Symp Structure Complexity Theory, Springer Verlag LNCS, 223 (1986), 12–22.

    Article  MathSciNet  MATH  Google Scholar 

  12. Berman, L., Polynomial Reducibilities and Complete Sets, PhD Thesis, Cornell Univ, (1977).

    Google Scholar 

  13. Dowd, M., “On isomorphism,” Unpublished manuscript (1978).

    Google Scholar 

  14. Dowd, M., “Isomorphism of complete sets,” Rutgers U. (Busch Campus) Lab for CS Research Tech Report, 34, (1982).

    Google Scholar 

  15. Fenner, S., S. Kurtz, and J. Royer, “Every polynomial-time 1-degree collapses iff P = PSPACE,” Proc 30 t h IEEE Symp Found Comput Sci, (1989), 624–629.

    Google Scholar 

  16. Ganesan, K., “Complete problems, creative sets and isomorphism conjectures,” Ph.D. Dissertation, Comput Sci Dept, Boston University, (1990), 1–76.

    Google Scholar 

  17. Ganesan, K. and S. Homer, “Complete problems and strong polynomial reducibilities,” Boston Univ Tech Report, 88–001, (1988).

    Google Scholar 

  18. Goldsmith, J. and D. Joseph, “Three results on the polynomial isomorphism of complete sets,” Proc 27 th IEEE FOCS, (1986), 390–397.

    Google Scholar 

  19. Goldsmith, J., “Polynomial isomorphisms and near-testable sets,” PhD Thesis, Univ Wisconsin, (1988); paper on collapsing degrees in preparation.

    Google Scholar 

  20. Grollmann, J. and A. Selman, “Complexity measures for public key cryptosystems,” Proc 25 th IEEE FOCS, (1984), 495–503.

    Google Scholar 

  21. Homer, S., “On simple and creative sets in NP,” Theor Comput Sci 47 (1986), 169–180.

    Article  MathSciNet  MATH  Google Scholar 

  22. Homer, S. and A. Selman, “Oracles for structural properties: the isomorphism problem and public-key cryptography,” Proc 4 th IEEE Symp Structure Complexity Theory, (1989), 3–14.

    Google Scholar 

  23. Joseph, D. and P. Young, “Some remarks on witness functions for nonpolynomial and noncomplete sets in NP,” Theor Comp Sci 39 (1985), 225–237. The results in this paper were first reported in the survey [Yo-83].

    Article  MathSciNet  MATH  Google Scholar 

  24. Ko, K., T. Long and D. Du, “A note on one-way functions and polynomial-time isomorphisms,” Theor Comput Sci 47 (1986), 263–276. The results of this paper were first reported in Proc 18 th STOC, 1986, 295–303.

    Article  MathSciNet  MATH  Google Scholar 

  25. Ko, K. and D. Moore, “Completeness, approximation and density,” SIAM J Comput 10 (1981), 787–796.

    Article  MathSciNet  MATH  Google Scholar 

  26. Kurtz, S., S. Mahaney and J. Royer, “Collapsing degrees,” Extended abstract in Proc 27 th FOCS (1986), 380–389. To appear in J Comput Sys Sci.

    Google Scholar 

  27. Kurtz, S., S. Mahaney and J. Royer, “Non-collapsing degrees,” Univ Chicago Tech Report 87-001.

    Google Scholar 

  28. Kurtz, S., S. Mahaney and J. Royer, “Progress on collapsing degrees,” Proc 2 nd IEEE Symp Structure in Complexity Theory, (1987), 126–131.

    Google Scholar 

  29. Kurtz, S., S. Mahaney and J. Royer, “The isomorphism conjecture fails relative to a random oracle,” Proc 21 st ACM Symp Theory Comput 1989, 157–166.

    Google Scholar 

  30. Kurtz, S., S. Mahaney and J. Royer, “The structure of complete degrees,” In A. Selman, editor, Complexity Theory Retrospective, pages 108–146, Springer Verlag, 1990.

    Google Scholar 

  31. Long, T., “One-way functions, isomorphisms, and complete sets,” invited presentation at Winter, 1988, AMS meetings (Atlanta), Abstracts AMS, Issue 55, vol 9, number I, January 1988, 125.

    Google Scholar 

  32. Long, T. and A. Selman, “Relativizing complexity classes with sparse oracles,” JACM 33 (1986), 618–627.

    Article  MathSciNet  Google Scholar 

  33. Mahaney, S., “On the number of P-isomorphism classes of NP-complete sets,” Proc 22 nd IEEE Symp Found Comput Sci, (1981), 271–278.

    Google Scholar 

  34. Mahaney, S. and P. Young, “Reductions among polynomial isomorphism types,” Theor Comp Sci 39 (1985), 207–224.

    Article  MathSciNet  MATH  Google Scholar 

  35. Myhill, J., “Creative sets,” Z Math Logik Grundlagen Math (1955), 97–108.

    Google Scholar 

  36. Wang, J. “P-creative sets us. P-completely creative sets,” Proc 4 th IEEE Symp Structure in Complexity Theory, (1989), 24–35.

    Google Scholar 

  37. Watanabe, O., “On one-one polynomial time equivalence relations,” Theor Comput Sci 38 (1985), 157–165.

    Article  MATH  Google Scholar 

  38. Watanabe, O., “On the structure of intractable complexity classes,” PhD Dissertation, Tokyo Institute of Technology, 1987.

    Google Scholar 

  39. Watanabe, O., “Some observations of k-creative sets,” Unpublished manuscript (1987).

    Google Scholar 

  40. Young, P., “Linear orderings under one-one reducibility,” J Symbolic Logic 31 (1966), 70–85.

    Article  MathSciNet  MATH  Google Scholar 

  41. Young, P., “Some structural properties of polynomial reducibilities and sets in NP,” Proc 15 th ACM Symp Theory Computing, (1983) 392–401. This is an overview of research which appears in journal form in [JY-85], [MY-85], and [LY-88].

    Google Scholar 

Results on Sparse Sets and Kolmogorov Complexity Related to the Berman-Hartmanis Conjecture

  1. Hartmanis, J. and S. Mahaney, “An essay about research on sparse NP-complete sets,” Proc 9 th Symp Math Found Computer Sci, Springer Verlag Lecture Notes Comput Sci 88, (1980), 40–57.

    Google Scholar 

  2. Hartmanis, J., “Generalized Kolmogorov complexity and the structure of feasible computations,” Proc 24 th FOCS, (1983), 439-445. Similar and related results also appear in, “On non-isomorphic NP-complete sets,” Bull EATCS 24 (1984), 73–78.

    Google Scholar 

  3. Hartmanis, J., “The equivalence of sequential machine models,” IEEE Trans Elect Comput EC-12, (1963), 18–19.

    Article  Google Scholar 

  4. Hartmanis, J., “Further results on the structure of sequential machines,” J Assoc Comput Mach 10 (1963), 78–88.

    Article  MathSciNet  Google Scholar 

  5. Baker, T. and J. Hartmanis, “Succinctness, verifiability and determinism in representations of polynomial-time languages,” Proc 20 th IEEE Symp Found Comput Sci, (1979), 392–396.

    Google Scholar 

  6. Hartmanis, J., “On the succinctness of different representations of languages,” SIAM J Comput 9 (1980), 114–120. This paper extends work in a paper by the same title presented at ICALP in 1979.

    Article  MathSciNet  MATH  Google Scholar 

  7. Hartmanis, J., “Observations about the development of theoretical computer science,” Annals History Comput 3 (1981), 42–51. The work in this paper was originally presented at the 20th FOCS, (1979), in a paper with the same title.

    Article  MathSciNet  MATH  Google Scholar 

  8. Hartmanis, J., “On Gödel speed-up and succinctness of language representations,” Theor Comput Sci 26 (1983), 335–342.

    Article  MathSciNet  MATH  Google Scholar 

  9. Hartmanis, J., N. Immerman and V. Sewelson, “Sparse sets in NP-P: EXPTIME versus NEXPTIME,” Infor and Control 65 (1985), 159–181. The work in this paper was first presented under the same title at the 15 th ACM Symp Theory Comput in 1983.

    Google Scholar 

  10. Hartmanis, J., “Sparse complete sets for NP and the optimal collapses of the polynomial time hierarchy,” Bull EATCS 32 - Structural Complexity Theory Column, (June 1987), 73–81.

    Google Scholar 

  11. Hartmanis, J., “The collapsing hierarchies,” Bull EATCS 33 - Structural Complexity Theory Column, (October 1987), 26–39.

    Google Scholar 

  12. Berman, P., “Relationship between density and deterministic complexity of NP-complete languages,” Proc 5 th ICALP, Springer Verlag LNCS, 62 (1978), 63–71.

    Google Scholar 

  13. Book, R., “Sparse sets, tally sets, and polynomial reducibilities,” invited talk, MFCS summer 1988, to appear.

    Google Scholar 

  14. Book, R., C. Wrathall, A. Selman and D. Dobkin, “Inclusion complete tally languages and the Berman-Hartmanis conjecture,” Math Systems Theory 11 (1977), 1–8.

    Article  MathSciNet  MATH  Google Scholar 

  15. Fortune, S., “A note on sparse complete sets,” SIAM J Comput (1979), 431–433.

    Google Scholar 

  16. Hromkovič, J., “Two independent solutions of the 23 years old open problem in one year, or NSpace is closed under complementation by two authors,” Bulletin EATCS 34 (1988), 310–312.

    Google Scholar 

  17. Immerman, N., “Nondeterministic space is closed under complementation,” Proc 3 rd IEEE Symp Structure Complexity Theory, (1988), 112–115

    Google Scholar 

  18. Kadin, J., “The polynomial hierarchy collapses if the boolean hierarchy collapses,” Proc 3 rd IEEE Structure Complexity Theory, (1988), 278–292.

    Google Scholar 

  19. Karp, R. and R. Lipton, “Some connections between uniform and nonuniform complexity classes,” Proc. of the 12 th ACM STOC, 1980, 302–309. (Also appears as “Turing machines that take advice,” L’Enseignement Mathématique 82 (1982), 191–210.)

    MathSciNet  Google Scholar 

  20. Ko, K., “On the notion of infinite pseudorandom sequences,” Theor Comput Sci 48 (1986), 9–33. The work presented in this paper first appeared in 1983 in an unpublished manuscript entitled, “Resource-bounded program-size complexity and pseudo-random sequences,” and is often referenced in that form.

    Article  MATH  Google Scholar 

  21. Levin, L., “Universal sequential search problems,” Prob Info Transmission 9 (1973), 265–266.

    Google Scholar 

  22. Levin, L., “Randomness conservation inequalities; information and independence mathematical theories,” Inform and Control 61 (1984), 15–37.

    Article  MathSciNet  MATH  Google Scholar 

  23. Li M. and P. Vitányi, “Applications of Kolmogorov Complexity in the Theory of Computation,” A. Selman, editor, “Complexity Theory Retrospective,” Springer Verlag, 1990, this volume. This paper expands on the article “Two decades of applied Kolmogorov complexity,” in Proc 3 rd IEEE Symp Struct Complexity Theory, (1988), 80–101.

    Google Scholar 

  24. Long, T., “A note on sparse oracles for NP,” J Comput Systems Sci 24 (1982), 224–232.

    Article  MATH  Google Scholar 

  25. Longpré, L., “Resource bounded Kolmogorov complexity, a link between computational complexity and information theory,” Cornell University Ph.D. Thesis, Tech Report TR-86-776, (1986).

    Google Scholar 

  26. Longpré, L., and P. Young, “Cook is faster than Karp: A study of reducibilities in NP,” Proc 3 rd IEEE Symp Structure Complexity Theory, (1988), 293–302. Also, JCSS, to appear.

    Google Scholar 

  27. Mahaney, S., “Sparse complete sets for NP: solution of a conjecture of Berman and Hartmanis,” J Comput Systems Sci 25 (1982), 130–143. The work in this paper first appeared in a paper of the same title presented at FOCS in 1980.

    Article  MathSciNet  MATH  Google Scholar 

  28. Mahaney, S., “The isomorphism conjecture and sparse sets,” in Computational Complexity Theory, edited by J. Hartmanis, AMS Proc Symp Applied Math Series, (1989). (This paper is an update and revision of “Sparse sets and reducibilities,” in Studies in Complexity Theory, edited by R. Book, (1986), 63–118.)

    Google Scholar 

  29. Schöning, U. and K. Wagner, “Collapsing oracle hierarchies, census functions and logarithmically many queries,” Proc STACS, (1988), Springer Verlag LNCS, 294, 91–97.

    Google Scholar 

  30. Sipser, M., “A complexity theoretic approach to randomness” Proc 15 th ACM Symp Theory of Comput (1983), 330–335.

    Google Scholar 

  31. Szelepcsényi, R., “The method of forced enumeration for nondeter-ministic automata,” ACTA Informatica 26 (1988), 279–284.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, University of Washington, Seattle, WA, 98195, USA

    Paul Young

Authors
  1. Paul Young
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. College of Computer Science, Northeastern University, Boston, MA, 02115, USA

    Alan L. Selman

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Young, P. (1990). Juris Hartmanis: Fundamental Contributions to Isomorphism Problems. In: Selman, A.L. (eds) Complexity Theory Retrospective. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4478-3_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4478-3_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8793-3

  • Online ISBN: 978-1-4612-4478-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation