Abstract
Although randomization is now a standard tool for the design of efficient algorithms or for building simpler systems, we are far from fully understanding the power of randomized computing. Hence it is advisable to study randomization for restricted models of computation.We followthis approach by investigating the power of randomization for pushdown automata.
Our main results are as follows. First we show that deterministic pushdown automata are weaker than Las Vegas pushdown automata, which in turn are weaker than one-sided-error pushdown automata. Finally one-sided-error pushdown automata are weaker than (nondeterministic) pushdown automata.
In contrast to many other fundamental models of computing there are no known methods of decreasing error probabilities.We show that such methods do not exist by constructing languages which are recognizable by one-sided-error pushdown automata with error probability 1/2, but not by one-sided-error pushdown automata with error probability p < 1/2. On the other hand we construct languages which are not deterministic context-free (resp. not context-free) but are recognizable with arbitrarily small error by one-sided-error (resp. bounded-error) pushdown automata.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Kaneps, D. Geidmanis, R. Freivalds: Tally languages accepted by Monte Carlo pushdown automata. In: RANDOM’ 97, Lexture Notes in Computer Science 1269, pp. 187–195.
A.V. Aho, J.E. Hopcroft, and M. Yannakakis, “On notions of information transfer in VLSI circuits”, Proc. 15th Annual ACM STOCS, ACM 1983, pp. 133–139.
L. Babai, “Monte Carlo algorithms in graph isomorphism techniques”, Research Report no. 79-10, Département de mathématiques et statistique, Université de Montréal, 1979.
Duriš, P., Hromkovič, J., Inone, K.: A separation of determinism, Las Vegas and nondeterminism for picture recognition. In: Proc. IEEE Conference on Computational Complexity, IEEE 2000, pp. 214–228. Full Version: Electronic Colloqium on Computational Complexity, Report No. 27 (2000).
P. Ďuriš, J. Hromkovič, J.D.P. Rolim, and G. Schnitger, “Las Vegas versus determinism for one-way communication complexity, finite automata and polynomialtime computations”, Proc. STACS’97, Lecture Notes in Computer Science 1200, Springer, 1997, pp. 117–128.
M. Dietzfelbinger, M. Kutylowski, and R. Reischuk, “Exact lower bounds for computing Boolean functions on CREW PRAMs”, J. Computer System Sciences 48, 1994, pp. 231–254.
R. Freivalds: Projections of languages recognizable by probabilistic and alternating multitape automata. Information Processing Letters 13 (1981), 195–198.
J. Gill, “Computational complexity of probabilistic Turing machines”, SIAM J. Computing 6, 1977, pp. 675–695.
J. Hromkovič, Communication Complexity and Parallel Computing, Springer 1997.
J. Hromkovič, “Communication Protocols-An Exemplary Study of the Power of Randomness”, Handbook on Randomized Computing, (P. Pardalos, S. Kajasekaran, J. Reif, J. Rolim, Eds.), Kluwer Publisher 2001, to appear.
J. Hromkovič, and M. Sauerhoff, “Tradeoffs between nondeterminism and complexity for communication protocols and branching programs”, Proc. STACS 2000, Lecture Notes in Computer Science 1770, Springer 2000, pp. 145–156.
J. Hromkovič, G. Schnitger, “On the power of LasVegas for one-way communication complexity, OBDD’s and finite automata”. Information and Computation, to appear.
J. Hromkovič, and G. Schnitger, “On the power of Las Vegas II, Two-way finite automata”, Proc. ICALP’99, Lecture Notes in Computer Science 1644, Springer 1999, pp. 433–443. (extended version: to appear in Theoretical Computer Science)
E. Kushilevitz, and N. Nisan, Communication Complexity, Cambridge University Press 1997.
Macarie, I, “On the structure of log-space probabilistic complexity classes.” Technical Report TR-506, Dept. of Computer Science, University of Rochester 1994.
Macarie, I., Ogihara, M., “Properties of probabilistic pushdown automata.” Technical Report TR-554, Dept. of Computer Science, University of Rochester 1994.
K. Mehlhorn, and E. Schmidt, “Las Vegas is better than determinism in VLSI and distributed computing”, Proc. 14th ACM STOC’82, ACM 1982, pp. 330–337.
I.I. Macarie, and J.I. Seiferas, “Amplification of slight probabilistic advantage at absolutely no cost in space”, Information Processing Letters 72, 1999, pp. 113–118.
Ch. Papadimitrou, and M. Sipser, “Communication complexity”, Proc. 14th ACM STOC, ACM 1982, pp. 196–200, also in J. Computer System Sciences 28, 1984, pp. 260–269.
M. Sauerhoff, “On nondeterminism versus randomness for read-once branching programs”, Electronic Colloquium on Computational Complexity, TR 97-030, 1997.
M. Sauerhoff, “On the size of randomized OBDDs and read-once branching programs for k-stable functions”, Proc. STACS’ 99, Lecture Notes in Computer Science 1563, Springer 1999, pp. 488–499.
A.C. Yao, “Some complexity questions related to distributed computing”, Proc. 11th ACM STOC, ACM 1979, pp. 209–213.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hromkovič, J., Schnitger, G. (2002). On the Power of Randomized Pushdown Automata. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds) Developments in Language Theory. DLT 2001. Lecture Notes in Computer Science, vol 2295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46011-X_22
Download citation
DOI: https://doi.org/10.1007/3-540-46011-X_22
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43453-5
Online ISBN: 978-3-540-46011-4
eBook Packages: Springer Book Archive