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Properties of complexity classes a short survey

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Mathematical Foundations of Computer Science 1977 (MFCS 1977)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 53))

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Abstract

This short survey of properties of complexity classes (CC's for short) does not pretend to be complete. We rather confine ourselves to the illustration of important features by typical examples. Simultaneously an attempt is made to find a reasonable systematization of the vast variety of papers contributing to our topic. Among the chosen examples there are four so far unpublished statements (numbered (5), (6), (19) and (35)) about the return complexity [70] and a new measure A for nondeterministic Turing machines (NDTM) which is similar to the return complexity.

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References

  1. Aho, A. V., Hopcroft, J. E., Ullman, J. D., The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Mass., 1974.

    Google Scholar 

  2. Barashko, A. S., Roizen, S. I., Kernels of partial recursive functions naming complexity classes. Kibernetika (Kiev) 5 (1976) 10–15.

    Google Scholar 

  3. Book, R. V., On languages accepted in polynomial time. SIAM J. Comp. 1,4 (1972) 281–287.

    Article  Google Scholar 

  4. Book, R. V., Tally languages and complexity classes. Inf. and Contr. 26 (1974) 186–193.

    Article  Google Scholar 

  5. Book, R. V., Translational lemmas, polynomial time and (logn)j-space. TCS 1 (1976) 215–226.

    Article  Google Scholar 

  6. Book, R. V., Greibach, S. A., Ibarra, O. H., Wegbreit, B., Tape bounded Turing acceptors and principal AFL. JCSS 4 (1970) 622–625.

    Google Scholar 

  7. Book, R. V., Greibach, S. A., Wegbreit, B., Time and tape bounded Turing acceptors and AFLs. JCSS 4 (1970) 606–621.

    Google Scholar 

  8. Chytil, M. P., Crossing-bounded computations and their relation to LBA-problem. Kybernetika 12 (1976) 76–85.

    Google Scholar 

  9. Chytil, M. P., Analysis of the non-context-free component of formal languages. LNCS 45 (1976) 230–236.

    Google Scholar 

  10. Cobham, A., The intrinsic computational difficulty of functions. Proc. Int. Congr. Logic, Methodology a. Philosophie of Science 1964, North Holland, Amsterdam 1965, 24–30.

    Google Scholar 

  11. Constable, R. L., Type two computational complexity. Proc. 5th Ann. ACM Symp. Theory of Comput. (1973) 108–121.

    Google Scholar 

  12. Cook, S. A., Characterizations of pushdown machines in terms of time bounded computers. JACM 18,1 (1971) 4–18.

    Article  Google Scholar 

  13. Cook, S. A., Linear time simulation of deterministic two-way pushdown automata. In: Information processing 71 (Proc. IFIP Congress Ljubljana 1971), Vol. 1, pp. 75–80. Amsterdam 1972.

    Google Scholar 

  14. Enderton, H., Degrees of computational complexity. JCSS 6 (1972) 389–396.

    Google Scholar 

  15. Fischer, P. C., Meyer, A. R., Rosenberg, A. L., Counter machines and counter languages. MST 2,3 (1968) 265–283.

    Google Scholar 

  16. Galil, Z., Hierarchies of complete problems. Acta Inf. 6 (1976) 77–88.

    Google Scholar 

  17. Ginsburg, S., Algebraic and Automata-Theoretic Properties of Formal Languages. North-Holland Amsterdam, 1975.

    Google Scholar 

  18. Ginsburg, S., Rose, G., On the existence of generators for certain AFL. Inform. Sci. 2(1970) 431–446.

    Article  Google Scholar 

  19. Giuliano, J. A., Writing stack acceptors. JCSS 6 (1972) 168–204.

    Google Scholar 

  20. Glebski, Ju. V., Kogan, D. I., Additive control systems and languages some algorithmic problems. Kibernetika (Kiev) 4 (1971) 25–29.

    Google Scholar 

  21. Graham, S. L., Harrison, M. A., Ruzzo, W. L., On line context-free language recognition in less than cubic time. Proc. 8th Ann. ACM Symp. Theory of Comput., Hershey 1976, 112–120.

    Google Scholar 

  22. Greibach, S. A., The hardest context-free language. SIAM J. Comp. 2 (1973) 304–310.

    Article  Google Scholar 

  23. Hartmanis, J., Computational complexity of one-tape Turing machine computations. JACM 15,2 (1968) 325–339.

    Article  Google Scholar 

  24. Hartmanis, J., On non-determinacy in simple computing devices. Acta Inf. 1(1972) 336–344.

    Article  Google Scholar 

  25. Hartmanis, J., Hopcroft, J. E., An overview of the theory of computational complexity. JACM 18 (1971) 444–475.

    Article  Google Scholar 

  26. Hartmanis, J., Hunt III, H. B., The LBA problem and its importance in the theory of computing. SIAM-AMS proceedings, vol. 7 (1974) 1–26.

    Google Scholar 

  27. Hartmanis, J., Simon, J., On the structure of feasible computations. In: Advances in Computers, vol. 14, pp. 1–43. Academic Press, New York, 1976.

    Google Scholar 

  28. Hennie, F. C., One-tape off-line Turing machine computations. Information and Control 8,6 (1965) 553–578.

    Article  Google Scholar 

  29. Hopcroft, J., Paul, W., Valiant, L., On time versus space and related problems. 16th Ann. Symp. on Found. of Comp. Sc. 1975, 57–64.

    Google Scholar 

  30. Hopcroft, J. E., Ullman, J. D., Nonerasing stack automata. JCSS 1,2 (1967) 166–186.

    Google Scholar 

  31. Hořejš, J., Recursive functions computable within Cflogf. Kibernetika 5,5 (1969) 384–398.

    Google Scholar 

  32. Hunt III, H. B., On the time and tape complexity of languages I. Proc. 5th Ann. A CM Symp. Theory of Comput. 1973, 10–19.

    Google Scholar 

  33. Ibarra, O. H., Characterizations of some tape and time complexity classes of Turing machines in terms of multihead and auxiliary stack automata. JCSS 5 (1971) 88–117.

    Google Scholar 

  34. Jones, N. D., Reducibility among combinatorial problems in log n space. Proc. 7th Ann. Princeton Conf. on Information Sciences and Systems 1973, 547–551.

    Google Scholar 

  35. Jones, N.D., Selman, A. L., Turing machines and the spectra of first-order formulas. JSL 39, 1 (1974) 139–150.

    Google Scholar 

  36. Kameda, T., Constant-tape-reversal bounded Turing machine computations. Proc. Intern. Computing Symposium 1970, Bonn, 649–654.

    Google Scholar 

  37. Karp, R. M., On the computational complexity of combinatorial problems. Networks 5 (1975) 45–68.

    Google Scholar 

  38. Ladner, R. E., Polynomial time reducibility. Proc. 5th Ann. ACM Symp. Theory of Comput. 1973, 122–129.

    Google Scholar 

  39. Ladner, R. E., Lynch, N. A., Selman, A. L., A comparison of polynomial time reducibilities. TCS 1 (1975) 103–123.

    Google Scholar 

  40. Lewis, F. D., On computational reducibility. JCSS 12,1 (1976) 122–131.

    Google Scholar 

  41. Lewis, II, P. M., Stearns, R. E., Hartmanis, J., Memory bounds for recognition of context-free and contextsensitive languages. IEEE Conf. Rec. Switch. Circuit Theory and Logig Design pp. 191–202, New York, 1965.

    Google Scholar 

  42. Lind, J. C., Computing in logarithmic space. MAC MEM 52, MIT, 1974.

    Google Scholar 

  43. Mager, G., Writing pushdown acceptors, JCSS 3 (1969) 276–318.

    Google Scholar 

  44. Mc Creight, E. M., Classes of computable functions defined by bounds on computation. Diss., Carnegie-Mellon University, Pittsburgh, Pennsylvania, 1969.

    Google Scholar 

  45. Mehlhorn, K., Polynomial and abstract subrecursive classes. JCSS 12,2 (1976) 147–178.

    Google Scholar 

  46. Meyer, A. R., Stockmeyer, L. J., Word problems requiring exponential time. Proc. 5th Ann. ACM Symp. Theory of Computing 1973) 1–9.

    Google Scholar 

  47. Moll, R., An operator imbedding theorem for complexity classes of recursive functions. TCS 1 (1976) 193–198.

    Article  Google Scholar 

  48. Monien, B., Characterization of time bounded computations by limited primitive recursion. LNCS 14 (1974) 280–293.

    Google Scholar 

  49. Monien, B., Relationships between pushdown automata with counters and complexity classes. MST 9 (1975) 248–264.

    Google Scholar 

  50. Monien, B., About the simulation of nondeterministic log n-tape bounded Turing machines. LNCS 33 (1975) 118–126.

    Google Scholar 

  51. Monien, B., A recursive and grammatical characterization of the exponential time languages. TCS 3 (1977) 61–74.

    Article  Google Scholar 

  52. Nepomnyashchi, V. A., A rudimentary interpretation of two-tape Turing computations. Kibernetika (Kiev) 2 (1970) 29–35.

    Google Scholar 

  53. Nepomnyashchi, V. A., On tape complexity for recognition of context-free languages. Kibernetika (Kiev) 5 (1975) 64–68.

    Google Scholar 

  54. Paterson, M. S., Tape bounds for time bounded Turing machines. JCSS 6 (1972) 116–124.

    Google Scholar 

  55. Peckel, J., On a deterministic subclass of context-free languages. This volume.

    Google Scholar 

  56. Ritchie, R., Springsteel, F. N., Language recognition by marking automata. Inf. and Contr. 20 (1972) 313–330.

    Article  Google Scholar 

  57. Robertson, E. L., Complexity classes of partial recursive functions. JCSS 9 (1974) 69–87.

    Google Scholar 

  58. Rosenberg, A. L., Real-time definable languages. JACM 14, 4 (1967) 645–662.

    Article  Google Scholar 

  59. Rounds, W. C., A grammatical characterization of exponential time languages. 16th Ann. Symp. on Found. of Computer Sc. (1975) 135–143.

    Google Scholar 

  60. Savitch, W. J., Relationship between nondeterministic and deterministic tape complexities. JCSS 4 (1970) 177–192.

    Google Scholar 

  61. Schaefer, T. J., Complexity of decision problems based on finite two-person perfect-information games. 8th. Ann. ACM Symp. Theory of Computing (1976) 41–49.

    Google Scholar 

  62. Shamir, E., Beeri, C., Checking stacks and context-free programmed grammars accept p-complete languages. LNCS 14 (1974) 27–33.

    Google Scholar 

  63. Smith III, A.R., Cellular automata complexity trade-offs. Inf. and Control 18 (1971) 466–482.

    Article  Google Scholar 

  64. Specker, E., Strassen, V., Komplexität von Entscheidungsproblemen. LNCS 43, Springer Verlag 1976.

    Google Scholar 

  65. Springsteel, F. N., On the pre-AFL of logn space and related families of languages. TCS 2 (1976) 295–304.

    Article  Google Scholar 

  66. Stearns, R. E., Hartmanis, J., Lewis II, P. M., Hierarchies of memory limited computations. IEEE Conf. Rec. Switch. Circuit Theory and Logic. Design, New York 1965, 179–190.

    Google Scholar 

  67. Stockmeyer, L. J., The polynomial-time hierarchy. TCS 3 (1977) 1–22.

    Article  Google Scholar 

  68. Sudborough, I. H., On tape-bounded complexity classes and multihead finite automata. JCSS 10 (1975) 62–76.

    Google Scholar 

  69. Trachtenbrot, B. A., Turing computations with logarithmic delay. Algebra i Logika 3, 4 (1964) 33–48.

    Google Scholar 

  70. Wechsung, G., Kompliziertheitstheoretische Charakterisierung der kontextfreien und linearen Sprachen. EIK 12 (1976) 289–300.

    Google Scholar 

  71. Weihrauch, K., Teilklassen primitiv-rekursiver Wortfunktionen. Ges. f. Mathematik und Datenverarbeitung, Bonn 1974, Nr. 91.

    Google Scholar 

  72. Wrathall, C., Complete sets and the polynomial-time hierarchy. TCS 3 (1977) 23–33.

    Article  Google Scholar 

  73. Younger, D. H., Recognition and parsing of context-free languages in time n3. Inf. and Contr. 10, 2 (1967) 189–208.

    Article  Google Scholar 

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Jozef Gruska

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Wechsung, G. (1977). Properties of complexity classes a short survey. In: Gruska, J. (eds) Mathematical Foundations of Computer Science 1977. MFCS 1977. Lecture Notes in Computer Science, vol 53. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08353-7_136

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  • DOI: https://doi.org/10.1007/3-540-08353-7_136

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