Efficient parallel evaluation of straight-line code and arithmetic circuits
A new parallel algorithm is given to evaluate a straight line program. The algorithm evaluates a program over a commutative semi-ring R of degree d and size n in time O(log n(log nd)) using M(n) processors, where M(n) is the number of processors required for multiplying n×n matrices over the semi-ring R in O (log n) time.
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- 1.A. Aho, J. Hopcroft, and J. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, 1974.Google Scholar
- 2.R.P. Brent. "The Parallel Evaluation of General Arithmetic Expressions". JACM 21, 2 (April 1974), 201–208.Google Scholar
- 3.S. A. Cook. Towards a Complexity Theory of Synchronous Parallel Computation. Internationales Symposium uber Logik und Algorithmik zu Enren von Professor Hort Specker,, February, 1980, pp.Google Scholar
- 4.D. Coppersmith, and S. Winograd. "On The Asymptotic Complexity of Matrix Multipication". SIAM J. Comput. 11, 3 (August 1982), 472–492.Google Scholar
- 5.R. E. Ladner. "The Circuit Value Problem Is Log Space Complete for P". SIGACT News 7, 1 (1975), 18–20.Google Scholar
- 6.G.L. Miller and J.H. Reif. Parallel Tree Contraction and Its Applications. 26th Symposium on Foundations of Computer Science, IEEE, Portland, Oregon, 1985, pp. 478–489.Google Scholar
- 7.L. G. Valiant, S. Skyum, S. Berkowitz, and C. Rackoff. "Fast Parallel Computation of Polynomials Using Few Processors". SIAM J. Comput. 12, 4 (November 1983), 641–644.Google Scholar
- 8.L. G. Valiant, and S. Skyum. Lecture Notes in Computer Science. Volume 118: Fast Parallel Computation of Polynomials Using Few Processors. In, Springer-Verlag, New York, 1981, pp. 132–139.Google Scholar