Abstract
Randomized branching programs are a probabilistic model of computation defined in analogy to the well-known probabilistic Turing machines. In this paper, we contribute to the complexity theory of randomized read-k-times branching programs.
We first consider the case read-k-times = 1 and present a function which has nondeterministic read-once branching programs of polynomial size, but for which every randomized read-once branching program with two-sided error at most 27/128 is exponentially large. The same function also exhibits an exponential gap between the randomized read-once branching program sizes for different constant worst-case errors, which shows that there is no “probability amplification” technique for read-once branching programs which allows to decrease the error to an arbitrarily small constant by iterating probabilistic computations.
Our second result is a lower bound for randomized read-k-times branching programs with two-sided error, where k > 1 is allowed. The bound is exponential for k < clog n, c an appropriate constant. Randomized read-k-times branching programs are thus one of the most general types of branching programs for which an exponential lower bound result could be established.
This work has been supported by DFG grants We 1066/7-3 and We 1066/8-1.
Preview
Unable to display preview. Download preview PDF.
References
F. Ablayev. Randomization and nondeterminism are incomparable for polynomial ordered binary decision diagrams. In Proc. of ICALP, LNCS 1256, 195–202. Springer, 1997.
F. Ablayev and M. Karpinski. On the power of randomized branching programs. In Proc. of ICALP, LNCS 1099, 348–356. Springer, 1996.
L. Babai, P Frankl, and J. Simon. Complexity classes in communication complexity theory. In Proc. of the 27th IEEE Symp. on Foundations of Computer Science, 337–347, 1986.
A. Borodin, A. A. Razborov, and R. Smolensky.On lower bounds for read-k-timesbranching programs. Computational Complexity, 3:1–18, 1993.
R. E. Bryant. Graph-based algorithms for Boolean function manipulation. IEEE Trans. Computers, C-35(8):677–691, Aug. 1986.
B. Chor and O. Goldreich. Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM J. Comput., 17(2):230–261, Apr. 1988.
J. Gill. Probabilistic Turing Machines and Complexity of Computations. Ph. D. dissertation, U. C. Berkeley, 1972.
S. Jukna, A. Razborov, P Savický, and I. Wegener. On P versus NP ⊂ coNP for decision diagrams and read-once branching programs. In Proc. of the 22th Int. Symp. on Mathematical Foundations of Computer Science (MFCS), LNCS 1295, 319–326. Springer, 1997. Submitted to Computational Complexity.
E. Kushilevitz and N. Nisan. Communication Complexity. Cambridge University Press, 1997.
C. Meinel. The power of polynomial size Ω-branching programs. In Proc. of the 5th Ann. ACM Symp. on Theoretical Aspects of Computer Science, LNCS 294,81–90. Springer, 1988.
E. A. Okolnishnikova. On lower bounds for branching programs. Siberian Advances in Mathematics, 3(1):152–166, 1993.
C. H. Papadimitriou and M. Sipser. Communication complexity. In Proc. of the 14th Ann. ACM Symp. on Theory of Computing, 196–200, 1982.
A. A. Razborov. Lower bounds for deterministic and nondeterministic branching programs. In Proc. of Fundamentals of Computation Theory, LNCS 529, 47–60. Springer, 1991.
M. Sauerhoff. A lower bound for randomized read-k-times branching programs. Technical Report TR97-019, Electronic Colloquium on Computational Complexity, 1997. Available via WWW from http: / /www. eccc. uni-trier. de/.
M. Sauerhoff. On non-determinism versus randomness for read-once branching programs. Technical Report TR97-030, Electronic Colloquium on Computational Complexity, 1997. Available via WWW from http: / /www. eccc. uni-trier. de/.
A. C. Yao. Lower bounds by probabilistic arguments. In Proc. of the 24th IEEE Symp. on Foundations of Computer Science, 420–428, 1983.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag
About this paper
Cite this paper
Sauerhoff, M. (1998). Lower bounds for randomized read-k-times branching programs. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028553
Download citation
DOI: https://doi.org/10.1007/BFb0028553
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64230-5
Online ISBN: 978-3-540-69705-3
eBook Packages: Springer Book Archive