On the LBA problem

  • Burkhard Monien
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 117)


Turing Machine Finite State Automaton Pushdown Automaton Deterministic Turing Machine Counter Automaton 


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  1. (1).
    Aho, A.V., J.E. Hopcroft and J.D. Ullman, (1968). Time and tape complexity of pushdown automaton languages, Info. and Control 13, pp. 186–206.Google Scholar
  2. (2).
    Aho, A.V., J.E. Hopcroft and J.D. Ullman, (1974) The design and analysis of computer algorithms, Addison-Wesley Publ. Comp., Reading, Massachussetts.Google Scholar
  3. (3).
    Alelinuas, R., R.M. Karp, R.J. Lipton, L. Lovasz and C. Rackhoff, (1979). Random walks, universal sequences and the complexity of maze problems, Proc. 20th IEEE Symp. on Foundations of Computer Science.Google Scholar
  4. (4).
    Book, R.V. (1972). On languages accepted in polynomial time, SIAM J. Computing 4, 281–287.Google Scholar
  5. (5).
    Book, R.V., (1976). Translational lemmas, polynomial time, and (log n)j-space, Theor. Comput. Sci. 1, pp 215–226.Google Scholar
  6. (6).
    Book, R.V., (1978). Simple representations of certain classes of languages, J.Ass. Comp. Mach. 25, 23–31.Google Scholar
  7. (7).
    von Braunmühl, B. and R. Verbeek, (1980). A recognition algorithm for deterministic CFLs optimal in time and space, Proc. 21st Annual Symp. Foundations of Computer Science pp. 411–420.Google Scholar
  8. (8).
    Chomsky, N., (1959). On certain formal properties of grammars, Inform. and Control 2, 133–167.Google Scholar
  9. (9).
    Chomsky, N., (1962). Context-free grammars and pushdown storage, Quart. Progr. Rept. No. 65, MIT, pp. 187–194.Google Scholar
  10. (10).
    Cook, S.A., (1970). Path Systems and language recognition, Proc. 2nd ACM Symp. Theory of Computing, 70–72.Google Scholar
  11. (11).
    Cook, S.A., (1971). Characterizations of pushdown machines in terms of time-bounded computers, J. Assoc. Comput. Mach. 18, pp. 4–18.Google Scholar
  12. (12).
    Cook, S.A., (1971). The complexity of theorem proving procedures, Proc. 3rd Annual ACM Symp. on Theory of Computing, 151–158.Google Scholar
  13. (13).
    Cook, S.A., (1979) Deterministic CFLs are accepted simultaneously in polynomial time and log squared space, Proc. 11th Annual ACM Symp. on Theory of Computing, 338–345.Google Scholar
  14. (14).
    Duris, P. and Z. Galil, (1980). Fooling a two-way automaton or One pushdown store is better than one counter for two-way machines, submitted for publication.Google Scholar
  15. (15).
    Galil, Z., (1977) Some open problems in the theory of computation as questions about two-way deterministic pushdown automata languages, Math. Systems Theory 10, pp. 211–218.Google Scholar
  16. (16).
    Garey, M.R. and D.S. Johnson, (1979). Computers and Intractability: A guide to the Theory of NP-Completeness, W.H. Freeman and Co., San Francisco.Google Scholar
  17. (17).
    Greibach, S.A., (1973). The hardest context-free language, SIAM J. Computing 2, pp. 304–310.Google Scholar
  18. (18).
    Greibach, S.A., (1977) A note on NSPACE(log n) and substitution, RAIRO Informatique théorique 11, 127–132.Google Scholar
  19. (19).
    Greibach, S.A., (1978) Remarks on blind and partially blind one-way multicounter machines, Theoretical Comp. Sci. 7, 311–324.Google Scholar
  20. (20).
    Hartmanis, J., (1972) On non-determinacy in simple computing devices, Acta Informatica, 334–336.Google Scholar
  21. (21).
    Hartmanis, J., (1978). On log-tape isomorphisms of complete sets, Theoretical computer Science 7, 273–286.Google Scholar
  22. (22).
    Hartmanis, J. and H.B. Hunt, (1973). The LBA problem and its importance in the theory of computing, Cornell University, Technical Report.Google Scholar
  23. (23).
    Hartmanis, J. and R.E. Stearns, (1965). On the computational complexity of algorithms, Transactions of American Math. Society 117, 285–306.Google Scholar
  24. (24).
    Hopcroft, J.E. and J.D. Ullman, (1969; new edition = 1979), Formal Languages and their Relation to Automata, Addison-Wesley, Reading. Mass., USA.Google Scholar
  25. (25).
    Jones, N.D. (1975). Space bounded reducibility among combinatorial problems, J. Comput. System Sci. 11, 62–85.Google Scholar
  26. (26).
    Jones, N.D., Y.E. Lien and W.T. Laaser. (1976). New problems complete for non-deterministic Log space, Math. Systems Theory 10, 1–17.Google Scholar
  27. (27).
    Jung, H., (1981), Relationships between probabilistic and deterministic tape complexity, submitted for publication.Google Scholar
  28. (28).
    Karp, R.M., (1972). Reducibility among combinatorial problems, in Complexity of Computer Computation, (R. Miller and J. Thatcher, eds.) Plenum Publishing Co., New York, pp. 85–103.Google Scholar
  29. (29).
    Kuroda, S.Y., (1964). Classes of languages and linear-bounded automata, Inform. and Control 7, 207–223.Google Scholar
  30. (30).
    Landweber, P.S. (1963). Three theorems on phrase structure grammars of type 1, Inform. and Control 6, 131–136.Google Scholar
  31. (31).
    Lewis, P.M., R.E. Stearns, and J. Hartmanis, (1965). Memory bounds for the recognition of context-free and context-sensitive languages, Proc. 6th Annual IEEE Cinf. on Switching Circuit Theory and Logical Design, pp. 191–202.Google Scholar
  32. (32).
    Monien, B., (1972). Relationships between pushdown automata and tape-bounded Turing machines, Proc. First Symp. on Automata Languages and Programming, North-Holland Publ. Comp. Amsterdam, pp. 575–583.Google Scholar
  33. (33).
    Monien, B. (1975). About the deterministic simulation of nondeterministic (logn)-tape bounded Turing machines, Lecture Notes in Comp. Sci. 33, Springer Verlag, pp. 118–126.Google Scholar
  34. (34).
    Monien, B., (1977). Transformational methods and their application to complexity problems, Acta Informatica 6, pp. 95–108, Corrigenda, Acta Informatica 8, pp. 383–384.Google Scholar
  35. (35).
    Monien, B., (1977). The LBA-problem and the deterministic tape complexity of two-way one-counter languages over a one-letter alphabet, Acta Informatica 8, 371–382.Google Scholar
  36. (36).
    Monien, B., (1977). About the derivation languages of grammars and machines, Lecture Notes in Comp. Sci. 52, Springer Verlag, pp. 337–351.Google Scholar
  37. (37).
    Monien, B. (1979) Connections between the LBA problem and the knapsack problem, Proceedings Frege-Konferenz, University Jena, pp. 262–280.Google Scholar
  38. (38).
    Monien, B., (1980). On a subclass of pseudonomial problems, Lecture Notes in Comp. Sci. 88, Springer Verlag, pp. 414–425.Google Scholar
  39. (39).
    Monien, B. and I.H. Sudborough, (1979). On eliminating nondeterminism from Turing machines which use less than logarithm worktape space, Lecture Notes in Comp. Sci. 71, Springer Verlag, pp. 431–445.Google Scholar
  40. (40).
    Monien, B. and I.H. Sudborough, (1980). Bounding the bandwidth of NP-complete problems, Lecture Notes in Comp. Sci. 100, Springer Verlag, pp. 279–292.Google Scholar
  41. (41).
    Monien, B. and I.H. Sudborough, (1981). Bandwidth constrained NP-complete problems, Proc. 13th ACM Symp. Theory of Computing.Google Scholar
  42. (42).
    Myhill, J., (1960). Linear bounded automata, Wright Air Development Division, Tech. Note No. 60–165, Cincinnati, USA.Google Scholar
  43. (43).
    Rabin, M.O. and D. Scott, (1959). Finite automata and their decision problems, IBM.J.Res. 3:2, 115–125.Google Scholar
  44. (44).
    Ruby, S. and P.C. Fischer, (1965). Translational methods and computational comlexity, Proc. 6th Annual IEEE Conf. on Switching Circuit Theory and Logical Design, pp. 173–178.Google Scholar
  45. (45).
    Savitch, W.J., (1970). Relationships between nondeterministic and deterministic tape complexities, J. Comput. System Sci. 4, 177–192.Google Scholar
  46. (46).
    Savitch, W.J., (1973). A Note on multihead Automata and context-sensitive languages, Acta Informatica 2 (1973), pp. 249–252.Google Scholar
  47. (47).
    Schützenberger, M., (1963). Context-free languages and pushdown automata, Inform. and Control 6, 246–264.Google Scholar
  48. (48).
    Seiferas, J. I., (1977). Techniques for separating space complexity classes, J. Comput. System Sci. 14, pp. 73–99.Google Scholar
  49. (49).
    Seiferas, J.I., (1977). Relating refined space complexity classes, J. Comput. System Sci. 14, pp. 100–129.Google Scholar
  50. (50).
    Stearns R.E., J. Hartmanis, and P.M. Lewis II, (1965). Hierarchies of memory limited computations, Proc. 6th Annual IEEE Conf. on Switching Circuit Theory and Logical Design, 179–190.Google Scholar
  51. (51).
    Stockmeyer, L.J. and A.R. Meyer, (1973). Word problems requiring exponential time, Proc. 5th Annual ACM Symp. Theory of Comput. pp. 1–9.Google Scholar
  52. (52).
    Sudborough, I.H., (1975). A note on tape bounded complexity classes and linear context-free languages, J. Assoc. Comput. Mach. 22, pp. 500–501.Google Scholar
  53. (53).
    Sudborough, I.H., (1975). On tape bounded complexity classes and multihead finite automata, J. Comput. System Sci. 10, pp. 62–76.Google Scholar
  54. (54).
    Sudborough, I.H., (1977). Some remarks on multihead automata, R.A.I.R.O. Informatique théorique/Theoretical Computer Science II, pp. 181–195.Google Scholar
  55. (55).
    Sudborough, I.H., (1978). Relating open problems on the tape complexity of context-free languages and path system problems, Proc. Conf. on Info. Sciences and Systems, The John Hopkins University, Baltimore (USA).Google Scholar
  56. (56).
    Voelkel, L., (1979). Language recognition by linear bounded and copy programs, Proc. Fundamentals of Computation Theory, Akademie-Verlag Berlin, pp. 491–495.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Burkhard Monien
    • 1
  1. 1.Universität PaderbornPaderbornWest - Germany

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