Abstract
We show the existence of an explicit pseudorandom generator G of linear stretch such that for every constant k, the output of G is pseudorandom against:
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Oblivious branching programs over alphabet {0,1} of length kn and size 2O(n/logn) on inputs of size n.
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Non-oblivious branching programs over alphabet Σ of length kn, provided the size of Σ is a power of 2 and sufficiently large in terms of k.
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The model of logarithmic space randomized Turing Machines (over alphabet {0,1}) extended with an unbounded stack that make k passes over their randomness.
The construction of the pseudorandom generator G is the same as in our previous work (FOCS 2011). The results here rely on a stronger analysis of the construction. For the last result we give a length-efficient simulation of stack machines by non-deterministic branching programs. (over a large alphabet) whose accepting computations have a unique witness.
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References
Ajtai, M., Ben-Or, M.: A theorem on probabilistic constant depth computations. In: Proceedings of the Sixteenth Annual ACM Symposium on Theory of Computing, STOC 1984, pp. 471–474. ACM, New York (1984)
Alon, N., Goldreich, O., Håstad, J., Peralta, R.: Simple constructions of almost k-wise independent random variables. In: Proceedings of the 31st Annual Symposium on Foundations of Computer Science, pp. 544–553 (1990)
Ajtai, M.: A non-linear time lower bound for boolean branching programs. In: 40th Annual Symposium on Foundations of Computer Science, pp. 60–70. IEEE (1999)
Allender, E.W.: P-uniform circuit complexity. Journal of the ACM 36(4), 912–928 (1989)
Ajtai, M., Wigderson, A.: Deterministic simulation of probabilistic constant depth circuits. In: 26th Annual Symposium on Foundations of Computer Science, pp. 11–19. IEEE (1985)
Borodin, A., Cook, S.A., Dymond, P.W., Ruzzo, W.L., Tompa, M.: Two applications of inductive counting for complementation problems. SIAM J. Comput 18(3), 559–578 (1989)
Beame, P., Jayram, T.S., Saks, M.: Time-space tradeoffs for branching programs. Journal of Computer and System Sciences 63(4), 542–572 (2001)
Bogdanov, A., Papakonstantinou, P.A., Wan, A.: Pseudorandomness for read-once formulas. In: Proceedings of the 52nd IEEE Symposium on Foundations of Computer Science, FOCS 2011 (2011)
Braverman, M.: Polylogarithmic independence fools AC 0 circuits. Journal of the ACM (JACM) 57(5), 1–10 (2010)
Beame, P., Saks, M., Sun, X., Vee, E.: Time-space trade-off lower bounds for randomized computation of decision problems. Journal of the ACM (JACM) 50(2), 154–195 (2003)
Cook, S.A.: Characterizations of pushdown machines in terms of time-bounded computers. Journal of ACM (JACM) 18(1), 4–18 (1971)
David, M., Nguyen, P., Papakonstantinou, P.A., Sidiropoulos, A.: Computationally limited randomness. In: Chazelle, B. (ed.) Proceedings of Innovations in Computer Science - ICS 2010, January 7-9, pp. 522–536. Tsinghua University Press, Beijing (2011)
David, M., Papakonstantinou, P.A.: Trade-off lower bounds for stack machines. In: IEEE Conference on Computational Complexity (CCC), Boston, USA, pp. 163–171 (2010)
Guruswami, V.: Algorithmic results in list decoding. Foundations and Trends® in Theoretical Computer Science 2(2), 107–195 (2007)
Impagliazzo, R., Nisan, N., Wigderson, A.: Pseudorandomness for network algorithms. In: Proceedings of the 26th Annual ACM Symposium on Theory of Computing, STOC 1994, Montréal, Québec, Canada, May 23-25, pp. 356–364. ACM Press, New York (1994)
Kabanets, V., Impagliazzo, R.: Derandomizing polynomial identity tests means proving circuit lower bounds. Computational Complexity 13(1-2), 1–46 (2004)
Nisan, N.: Pseudorandom bits for constant depth circuits. Combinatorica 11(1), 63–70 (1991)
Nisan, N.: Pseudorandom generators for space-bounded computation. Combinatorica 12(4), 449–461 (1992)
Niedermeier, R., Rossmanith, P.: Unambiguous auxiliary pushdown automata and semi-unbounded fan-in circuits. Information and Computation 118(2), 227–245 (1995)
Ruzzo, W.L.: Tree-size bounded alternation. Journal of Computer Systems and Sciences (JCSS) 21(2), 218–235 (1980)
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Bogdanov, A., Papakonstantinou, P.A., Wan, A. (2012). Pseudorandomness for Linear Length Branching Programs and Stack Machines. In: Gupta, A., Jansen, K., Rolim, J., Servedio, R. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2012 2012. Lecture Notes in Computer Science, vol 7408. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32512-0_38
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DOI: https://doi.org/10.1007/978-3-642-32512-0_38
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