An Improved Simulation of Space and Reversal Bounded Deterministic Turing Machines by Width and Depth Bounded Uniform Circuits

Abstract We present an improved simulation of space and reversal bounded Turing machines by width and depth bounded uniform circuits. (All resource bounds hold simultaneously.) An S(n) space, R(n) reversal bounded deterministic k-tape Turing machine can be simulated by a uniform circuit of O(R(n)log 2 S(n)) depth and O(S(n) k ) width. Our proof is cleaner, and has slightly better resource bounds than the original proof due to Pippenger (1979). The improvement is resource bounds comes primarily from the use of a shared-memory machine instead of an oblivious Turing machine, and the concept of a ‘special situation’.

[1]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[2]  Sartaj Sahni,et al.  Parallel permutation and sorting algorithms and a new generalized connection network , 1982, JACM.

[3]  E. Szemerédi,et al.  O(n LOG n) SORTING NETWORK. , 1983 .

[4]  Kenneth E. Batcher,et al.  Sorting networks and their applications , 1968, AFIPS Spring Joint Computing Conference.

[5]  Allan Borodin,et al.  On Relating Time and Space to Size and Depth , 1977, SIAM J. Comput..

[6]  Stephen A. Cook,et al.  Deterministic CFL's are accepted simultaneously in polynomial time and log squared space , 1979, STOC.

[7]  Uzi Vishkin,et al.  Implementation of Simultaneous Memory Address Access in Models That Forbid It , 1983, J. Algorithms.

[8]  János Komlós,et al.  Sorting in c log n parallel sets , 1983, Comb..

[9]  Ian Parberry.  A complexity theory of parallel computation , 1984 .

[10]  Stephen A. Cook,et al.  Hardware complexity and parallel computation , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[11]  Nicholas Pippenger,et al.  On simultaneous resource bounds , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[12]  Uzi Vishkin,et al.  A Parallel-Design Distributed-Implementation (PDDI) General-Purpose Computer , 2011, Theor. Comput. Sci..

[13]  Leslie M. Goldschlager,et al.  A universal interconnection pattern for parallel computers , 1982, JACM.

[14]  Steven Fortune,et al.  Parallelism in random access machines , 1978, STOC.

[15]  Eli Upfal,et al.  A probabilistic relation between desirable and feasible, models of parallel computation , 1984, STOC '84.

[16]  János Komlós,et al.  An 0(n log n) sorting network , 1983, STOC.

[17]  Ian Parberry,et al.  Some practical simulations of impractical parallel computers , 1983, Parallel Comput..

[18]  Uzi Vishkin,et al.  Finding the maximum, merging and sorting in a parallel computation model , 1981, CONPAR.