On uniform circuit complexity

We consider uniform circuit complexity, introduced by Borodin as a model of parallel complexity. Three main results are presented. First, we show that simultaneous size/depth of uniform circuits is the same as space/time of alternating Turing machines, with depth and time within a constant factor and likewise log(size) and space. Second, we apply this to characterize the class of polynomial size and polynomial-in-log depth circuits in terms of tree-size bounded alternating TM's, in particular showing that context-free recognition is in this class of circuits. Third, we investigate various definitions of uniform circuit complexity, showing that it is fairly insensitive to the choice of definition.

[1]  Leslie Michael Goldschlager,et al.  Synchronous parallel computation. , 1978 .

[2]  Larry J. Stockmeyer,et al.  A characterization of the power of vector machines , 1974, STOC '74.

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

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

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

[6]  L. Csanky,et al.  Fast parallel matrix inversion algorithms , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).

[7]  Larry J. Stockmeyer,et al.  The Polynomial-Time Hierarchy , 1976, Theor. Comput. Sci..

[8]  Larry J. Stockmeyer,et al.  A Characterization of the Power of Vector Machines , 1976, J. Comput. Syst. Sci..

[9]  Walter L. Ruzzo,et al.  Tree-size bounded alternation(Extended Abstract) , 1979, J. Comput. Syst. Sci..

[10]  R. Ladner.  The circuit value problem is log space complete for P , 1975, SIGA.

[11]  Walter J. Savitch,et al.  Time Bounded Random Access Machines with Parallel Processing , 1979, JACM.

[12]  Juris Hartmanis,et al.  On the Power of Multiplication in Random Access Machines , 1974, SWAT.

[13]  Dexter Kozen,et al.  On parallelism in turing machines , 1976, 17th Annual Symposium on Foundations of Computer Science (sfcs 1976).

[14]  I. H. Sudborough.  The complexity of the membership problem for some extensions of context-free languagest† , 1977 .

[15]  Walter J. Savitch,et al.  Parallel and Nondeterministic Time Complexity Classes (Preliminary Report) , 1978, ICALP.

[16]  Michael J. Fischer,et al.  Relations Among Complexity Measures , 1979, JACM.

[17]  Ivan Hal Sudborough.  Time and Tape Bounded Auxiliary Pushdown Automata , 1977, MFCS.

[18]  Leslie M. Goldschlager,et al.  A unified approach to models of synchronous parallel machines , 1978, STOC.

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

[20]  Stephen A. Cook,et al.  Characterizations of Pushdown Machines in Terms of Time-Bounded Computers , 1971, J. ACM.

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