Nondeterministic stack register machines

Theoretical Computer Science

Volumn 178, Issue 1-2, 1997, Pages 37-76

  Clote, P ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTABILITY AND DECIDABILITY; POLYNOMIALS; RECURSIVE FUNCTIONS;

STACK REGISTER MACHINES;

COMPUTATIONAL COMPLEXITY;

EID: 0031146527     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(96)00051-5     Document Type: Article

References (43)

1. G. Asser, Das Repräsentantenproblem im Prädikatenkalkül der ersten Stufe mit Identität, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 1 (1955) 252-263.
2. 1, J. Comput. System Sci. 38 (1989) 150-164. Preliminary version in Proc. 18th Ann. ACM Symp. Theory of Computing (1986) 1-5.
3. 1, J. Comput. System Sci. 38 (1989) 150-164. Preliminary version in Proc. 18th Ann. ACM Symp. Theory of Computing (1986) 1-5.
4. 1, J. Comp. Syst. Sci. 41(3) (1990) 274-306. Preliminary version appeared in: Structure in Complexity Theory: 3rd Ann. Conf. (IEEE Computer Society Press, 1988) 47-59.
5. 1, J. Comp. Syst. Sci. 41(3) (1990) 274-306. Preliminary version appeared in: Structure in Complexity Theory: 3rd Ann. Conf. (IEEE Computer Society Press, 1988) 47-59.
6. A. Bel'tyukov, A computer description and a hierarchy of initial Grzegorczyk classes, J. Sov. Math. 20 (1982) 2280-2289. Translation from Zap. Nauk. Sem. Lening. Otd. Mat. Inst., V. A. Steklova AN SSSR 88 (1979) 30-46.
7. A. Bel'tyukov, A computer description and a hierarchy of initial Grzegorczyk classes, J. Sov. Math. 20 (1982) 2280-2289. Translation from Zap. Nauk. Sem. Lening. Otd. Mat. Inst., V. A. Steklova AN SSSR 88 (1979) 30-46.
8. J.H. Bennett, On Spectra, Ph.D. Thesis, Department of Mathematics, Princeton University, 1962.
9. J.-Y. Cai and M.L. Furst, PSPACE survives three-bit bottlenecks, Proc. 3rd Ann. IEEE Conf. Structure in Complexity Theory (1988) 94-102. Journal version in Internat. J. Found. Comput. Sci. 2 (1991) 67-76.
10. J.-Y. Cai and M.L. Furst, PSPACE survives three-bit bottlenecks, Proc. 3rd Ann. IEEE Conf. Structure in Complexity Theory (1988) 94-102. Journal version in Internat. J. Found. Comput. Sci. 2 (1991) 67-76.
11. P. Cegielski, Thèse de Doctorat de 3-ième Cycle, Université Paris VII, 1980.
12. A. Chandra, D. Kozen, and L.J. Stockmeyer, Alternation, J. Assoc. Comput. Mach. 28 (1981) 114-133.
13. k and NC. in: P.J. Scott and S.R. Buss, eds., Feasible Mathematics (Birkhäuser, 1990) 49-70.
14. P. Clote, Stack register machines: nondeterminism, the linear time hierarchy, and boolean circuits. Contributed talk, Spring meeting of the Association for Symbolic Logic, 19-22 March 1992, Durham NC.
15. P. Clote, B. Kapron and A. Ignjatovic, Parallel computable higher type functionals, in: Proc. IEEE 34th Ann. Symp. on Foundations of Computer Science (Palo Alto CA, 3-5 November 1993) 72-83.
16. P. Clote and J. Krajíček, Arithmetic, Proof Theory and Computational Complexity (Oxford University Press, 1993).
17. P. Clote and G. Takeuti, First order bounded arithmetic and small boolean circuit complexity classes, P. Clote and J. Remmel, eds., Feasible Mathematics II (Birkhäuser, 1995).
18. A. Cobham, The intrinsic computational difficulty of functions, in: Y. Bar-Hillel, ed., Logic, Methodology and Philosophy of Science II (North-Holland, Amsterdam, 1965) 24-30.
19. S.A. Cook, A taxonomy of problems with fast parallel algorithms, Inform. and Control 64 (1985) 2-22.
20. A. Grzegorczyk, Some clases of recursive functions, Rozprawy Matematyczne 4 (1953).
21. n, the semigroup of binary relations on {0, 1, . . ., n - 1}. Theoret. Comput. Sci., accepted.
22. 3, the semigroup of functions on {0, 1, 2}; submitted.
23. W.G. Handley, Nondeterministic summation mod the semigroup of pregraphs over {0, 1, 2} yields ALINTIME, typescript, December 1994.
24. 4, the semigroup of functions on {0, 1, 2, 3}, typescript, September 1994.
25. I.N. Herstein, Topics in Algebra (Ginn, 1964).
26. J. Hicks, A machine characterization of quantification and primitive recursion with applications to low level complexity classes, Ph.D. Thesis, Department of Mathematics, Oxford University, 1983.
27. N. Immerman, Expressibility and parallel complexity, SIAM J. Comput. 18(3) (1989) 625-638.
28. N.D. Jones and A.L. Selman, Turing machines and the spectra of first-order formulas, J. Symbolic Logic 39 (1974) 139-150.
29. J.C. Lind, Computing in logarithmic space, Tech. Report Project MAC Technical Memorandum 52, Massachusetts Institute of Technology, September 1974.
30. V.A. Nepomnjascii, Rudimentary interpretation of two-tape turing computation, Kibernetika 2 (1970) 29-35. Translated in Cybernetica (1972) 43-50.
31. V.A. Nepomnjascii, Rudimentary interpretation of two-tape turing computation, Kibernetika 2 (1970) 29-35. Translated in Cybernetica (1972) 43-50.
32. J.B. Paris, Private correspondence.
33. J.B. Paris, W.G. Handley and A.J. Wilkie, Characterizing some low arithmetic classes, in: Theory of Algorithms (Akademie Kyado, Budapest, 1984) 353-364. Colloquia Societatis Janos Bolyai.
34. J.B. Paris and A.J. Wilkie, Counting problems in bounded arithmetic, in: C.A. di Prisco, ed., Methods in Mathematical Logic, Springer Lecture Notes in Mathematics, (Springer, Berlin, 1983). Proc. Logic Conf. (Caracas, 1983).
35. J.B. Paris and A.J. Wilkie, Counting problems in bounded arithmetic, in: C.A. di Prisco, ed., Methods in Mathematical Logic, Springer Lecture Notes in Mathematics, (Springer, Berlin, 1983). Proc. Logic Conf. (Caracas, 1983).
36. A.A. Razborov, Lower bounds for the size of circuits of bounded depth in basis {∧, ⊕}, preprint in English (translated from the Russian), 1986.
37. R.W. Ritchie, Classes of predictably computable functions, Trans. Amer. Math. Soc. 106 (1963) 139-173.
38. R. Smolensky, Algebraic methods in the theory of lower bounds for boolean circuit complexity, in: Proc. 19th Ann. ACM Symp. on Theory of Computing (1987) 77-82.
39. C. Smorynski, Logical Number Theory I (Springer, Berlin, 1991).
40. H. Straubing, Finite Automata, Formal Languages, and Circuit Complexity, Series Progress in Theoretical Computer Science (Birkhäuser. Basel, 1994).
41. D.B. Thompson, Subrecursiveness: machine independent notions of computability in restricted time and storage, Math. Systems Theory 6 (1972) 3-15.
42. A.R. Woods, Some problems in logic and number theory and their connections, Ph.D. Dissertation, Department of Mathematics, University of Manchester, 1981.
43. C. Wrathall, Complete sets and the polynomial time hierarchy, Theoret. Comput. Sci. 3 (1976) 23-33.