On Probabilistic Space-Bounded Machines with Multiple Access to Random Tape

We investigate probabilistic space-bounded Turing machines that are allowed to make multiple passes over the random tape. As our main contribution, we establish a connection between derandomization of such probabilistic space-bounded classes to the derandomization of probabilistic time-bounded classes. Our main result is the following.

[1]  Emanuele Viola,et al.  Fooling Parity Tests with Parity Gates , 2004, APPROX-RANDOM.

[2]  Noam Nisan,et al.  Pseudorandom generators for space-bounded computation , 1992, Comb..

[3]  Leslie G. Valiant,et al.  On Time Versus Space , 1977, JACM.

[4]  Noam Nisan,et al.  On read-once vs. multiple access to randomness in logspace , 1990, Proceedings Fifth Annual Structure in Complexity Theory Conference.

[5]  Periklis A. Papakonstantinou,et al.  Computationally Limited Randomness , 2011, ICS.

[6]  Rahul Santhanam,et al.  Holographic Proofs and Derandomization , 2003, Computational Complexity Conference.

[7]  Michael E. Saks.  Randomization and derandomization in space-bounded computation , 1996, Proceedings of Computational Complexity (Formerly Structure in Complexity Theory).

[8]  M. Panella.  Associate Editor of the Journal of Computer and System Sciences , 2014 .

[9]  Richard J. Lipton,et al.  On the complexity of intersecting finite state automata and N L versus N P , 2003, Theor. Comput. Sci..

[10]  Lance Fortnow,et al.  Linear Advice for Randomized Logarithmic Space , 2006, STACS.

[11]  Omer Reingold,et al.  S-T Connectivity on Digraphs with a Known Stationary Distribution , 2007, Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07).

[12]  Periklis A. Papakonstantinou,et al.  How strong is Nisanʼs pseudo-random generator? , 2011, Inf. Process. Lett..

[13]  Michael Saks,et al.  BP H SPACE(S)⊆DSPACE(S 3/2 ) , 1999, FOCS 1999.

[14]  Allan Borodin,et al.  Parallel Computation for Well-Endowed Rings and Space-Bounded Probabilistic Machines , 1984, Inf. Control..

[15]  Richard J. Lipton,et al.  Non-uniform Depth of Polynomial Time and Space Simulations , 2003, FCT.

[16]  Luca Trevisan,et al.  Pseudorandom walks on regular digraphs and the RL vs. L problem , 2006, STOC '06.

[17]  Sanjeev Arora,et al.  Computational Complexity: A Modern Approach , 2009 .

[18]  Leonard M. Adleman,et al.  Two theorems on random polynomial time , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[19]  Ran Raz,et al.  On recycling the randomness of states in space bounded computation , 1999, STOC '99.

[20]  Noam Nisan,et al.  Pseudorandom generators for space-bounded computations , 1990, STOC '90.

[21]  Sergey Yekhanin,et al.  Towards 3-query locally decodable codes of subexponential length , 2008, JACM.

[22]  Rahul Santhanam,et al.  Holographic Proofs and Derandmization , 2005, SIAM J. Comput..

[23]  John T. Gill,et al.  Computational complexity of probabilistic Turing machines , 1974, STOC '74.

[24]  Omer Reingold,et al.  Undirected connectivity in log-space , 2008, JACM.

[25]  Noam Nisan,et al.  Pseudorandomness for network algorithms , 1994, STOC '94.

[26]  Marek Karpinski,et al.  There Is No Polynomial Deterministic Space Simulation of Probabilistic Space with a Two-Way Random-Tape Generator , 1986, Inf. Control..