Space-efficient deterministic simulation of probabilistic automata

SIAM Journal on Computing

Volumn 27, Issue 2, 1998, Pages 448-465

  Macarie, Ioan I ^a,b  

^a Millennium Computer Corporation   (United States)

^b University of Rochester   (United States)

Author keywords

Deterministic simulation; Matrix inversion; Probabilistic turing machines; Residue representation; Space bounded complexity classes; Stochastic languages

Indexed keywords

EID: 0000310033     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539793253851     Document Type: Article

References (53)

1. [Bo77] A. BORODIN, On relating time and space to size and depth, SIAM J. Comput., 6 (1977), pp. 733-744.
2. [BCP83] A. BORODIN, S. COOK, AND N. PIPPENGER, Parallel computation for well-endowed rings and space-bounded probabilistic machines, Inform. and Control, 48 (1983), pp. 113-136.
3. [Bu67] R. BUKHARAEV, On the representability of events in probabilistic automata, Prob. Methods and Cybernetics, V, Kazan, 1967, pp. 7-20 (in Russian).
4. [Bu85] R. BUKHARAEV, Fundamentals of the Theory of Probabilistic Automata, Nauka, Moscow, 1985 (in Russian).
5. [CK94] K. CULIK AND J. KARHUMAKI, Finite automata computing real functions, SIAM J. Comput., 23 (1994), pp. 789-814.
6. [Co85] S. A. COOK, A taxonomy of problems with fast parallel algorithms, Inform. and Comput., 64 (1985), pp. 2-22.
7. [Cs76] L. CSANKY, Fast parallel matrix inversions algorithms, SIAM J. Comput., 5 (1976), pp. 618-623.
8. [Di71] P. D. DIEU, On a class of stochastic languages, Z. Math. Logik Grundlagen Math. Bd., 17 (1971), pp. 421-425.
9. [Di72] P. D. DIEU, On a necessary condition for stochastic languages, Electron. Inform. Kybernetik EIK, 8/10 (1972), pp. 575-588.
10. [Di93] P. DIETZ, personal communication, 1993.
11. [DL91] G. I. DAVIDA AND B. LITOW, Fast parallel arithmetic via modular representation, SIAM J. Comput., 20 (1991), pp. 756-765.
12. [DMS94] P. DIETZ, I. I. MACARIE, AND J. I. SEIFERAS, Bits and relative order from residues, space efficiently, Inform. Process. Lett., 50 (1994), pp. 123-128.
13. [DS90] C. DWORK AND L. STOCKMEYER, A time complexity gap for two-way probabilistic finite-state automata. SIAM J. Comput., 19 (1990), pp. 1011-1023.
14. [Eb89] W. EBERLY, Very fast parallel matrix and polynomial arithmetic, SIAM J. Comput., 18 (1989), pp. 955-976.
15. [Eb95] W. EBERLY, Fast parallel band matrix arithmetic, Inform. and Comput., 116 (1995), pp. 117-127.
16. [Fr81] R. FREIVALDS, Probabilistic two-way machines, in Proc. 6th Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Comput. Sci., 118, Springer-Verlag, New York, 1981, pp. 33-45.
17. [Fr91] R. FREIVALDS, Complexity of probabilistic versus deterministic automata, Baltic Computer Science, Selected Papers, Lecture Notes in Comput. Sci. 502, Springer-Verlag, Berlin, 1991, pp. 565-613.
18. [Gi77] J. GILL, Computational complexity of probabilistic Turing machines, SIAM J. Comput., 6 (1977), pp. 675-695.
19. [Go83] G. GOLUB AND C. VAN LOAN, Matrix Computations, The Johns Hopkins University Press, Baltimore, MD, 1983.
20. [HU79] J. E. HOPCROFT AND J. D. ULLMAN, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, MA, 1979.
21. [Im87] N. IMMERMAN, Languages that capture complexity classes, SIAM J. Comput., 16 (1987), pp. 760-778.
22. [Ju81] H. JUNG, Relationships between probabilistic and deterministic tape complexity, in Proc. 10th Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Comput. Sci. 118, Springer-Verlag, New York, 1981, pp. 339-346.
23. [Ju84] H. JUNG, On probabilistic tape complexity and fast circuits for matrix inversion problems, 11th Internat. Coll. on Automata, Languages and Programming, (ICALP 1984), Lecture Notes in Comput. Sci. 172, Springer-Verlag, New York, pp. 281-291.
24. [Ka89] J. KANEPS, Stochasticity of the languages recognizable by 2-way finite probabilistic automata, Diskret. Mat., 1 (1989), pp. 63-77 (in Russian).
25. [Ku73] YU. I. KUKLIN, Two-way probabilistic automata, Avtomat. i Vychisl. Tekhn., 5 (1973), pp. 35-36 (in Russian).
26. [LR86] F. LEIGHTON AND R. RIVEST, Estimating a probability using finite memory, IEEE Trans. Inform. Theory, 6 (1986), pp. 733-742.
27. [LSH65] P. M. LEWIS II, R. STEARN, AND J. HARTMANIS, Memory bounds for recognition of context-free and context-sensitive languages, in IEEE Conference Record on Switching Circuit Theory and Logical Design, 1965, IEEE Computer Science Press, Los Alamitos, CA, pp. 191-202.
28. [Ma93] I. MACARIE, Closure Properties of Stochastic Languages, Technical Report TR441, Dept. of Comp. Science, University of Rochester, Rochester, NY, 1993.
29. [Ma95] I. I. MACARIE, Decreasing the bandwidth of a configuration transition matrix, Inform. Process. Lett., 53 (1995), pp. 315-320.
30. [MS82] B. MONIEN AND I. H. SUDBOROUGH, On eliminating nondeterminism from Turing machines which use less than logarithm worktape space, Theoret. Comput. Sci., 21 (1982), pp. 237-253.
31. [Ni90] N. NISAN, Pseudorandom generators for space-bounded computation, Proc. 22nd Annual ACM Symposium on the Theory of Computing, ACM, New York, 1990, pp. 204-212.
32. [Ni92] N. NISAN, RL ⊆ SC, in Proc. 24th Annual ACM Symposium on the Theory of Computing, ACM, New York, 1992, pp. 619-623.
33. [NZ93] N. NISAN AND D. ZUCKERMAN, More deterministic simulation in logspace, in Proc. 25th Annual ACM Symposium on the Theory of Computing, ACM, New York, 1993, pp. 235-244.
34. [Pa71] A. PAZ, Introduction to probabilistic automata, in Computer Science and Applied Mathematics, Academic Press, New York, 1971.
35. [Ra63] M. O. RABIN, Probabilistic automata, Inform. and Control, 6 (1963), pp. 230-244.
36. [Re86] J. REIF, Logarithmic depth circuits for algebraic functions, SIAM J. Comput., 15 (1986), pp. 231-242.
37. [Ra92] B. RAVIKUMAR, Some Observations on 2-way Probabilistic Finite Automata, Technical Report TR92-208, Dept. of Comp. Science and Statistics, Univ. of Rhode Island, Kingston, RI, 1992.
38. [RST82] W. RUZZO, J. SIMON, AND M. TOMPA, Space-bounded hierarchies and probabilistic computation, in Proc. 14th Annual ACM Symposium on Theory of Computing, ACM, New York, 1982, pp. 215-223; also in J. Comput. System Sci., 28 (1984), pp. 216-230.
39. [RST82] W. RUZZO, J. SIMON, AND M. TOMPA, Space-bounded hierarchies and probabilistic computation, in Proc. 14th Annual ACM Symposium on Theory of Computing, ACM, New York, 1982, pp. 215-223; also in J. Comput. System Sci., 28 (1984), pp. 216-230.
40. [Sa70] W. J. SAVITCH, Relationships between nondeterministic and deterministic tape complexity, J. Comput. System Sci., 4 (1970), pp. 177-192.
41. [SHL65] R. E. STEARNS, J. HARTMANIS, AND P. M. LEWIS II, Hierarchies of memory limited computations, in IEEE Conf. Record on Switching Circuit Theory and Logical Design, IEEE Computer Society Press, Los Alamitos, CA, 1965, pp. 179-190.
42. [Si77] J. SIMON, On the difference between one and many, in Proc. 4th Internat. Coll. on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 52, Springer-Verlag, New York, 1977, pp. 480-491.
43. [Si81] J. SIMON, Space-bounded probabilistic Turing machine complexity classes are closed under complement, in Proc. 13th Annual ACM Symposium on Theory of Computing, ACM, New York, 1981, pp. 158-167.
44. [SiSO] M. SIPSER, Halting space-bounded computation, Theoret. Comput. Sci. 10 (1980), pp. 335-338.
45. [SS78] A. SALOMAA AND M. SOITTOLA, Automata-theoretic Aspects of Formal Power Series, Springer-Verlag, Berlin, 1978.
46. [St66] P. STARKE, Stochastische Ereignisse und Wortmengen, Z. Math. Logik Grundlagen Math. Bd., 12 (1966), pp. 61-68.
47. [St73] H. STONE, An efficient parallel algorithm for the solution of a tridiagonal linear system of equations, J. ACM, 20 (1973), pp. 27-38.
48. 3/2), in Proc. 36th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1995, pp. 344-353.
49. [Tu68] P. TURAKAINEN, On stochastic languages, Inform. and Control, 12 (1968), pp. 304-313.
50. [Tu69a] P. TURAKAINEN, On languages representable in rational probabilistic automata, Ann. Acad. Sci. Fenn. Ser. A I, 439 (1969).
51. [Tu69b] P. TURAKAINEN, Generalized automata and stochastic languages, Proc. Amer. Math. Soc., 21 (1969), pp. 303-309.
52. [Tu71] P. TURAKAINEN, Some closure properties of the family of stochastic languages, Inform. and Control, 18 (1971), pp. 253-256.
53. [Wa92] J. WANG, A note on two-way probabilistic automata, Inform. Process Lett., 43 (1992), pp. 321-326.