Separating the polynomial-time hierarchy by oracles
Proc. 26th annual symposium on Foundations of computer science
Almost optimal lower bounds for small depth circuits
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Limits on the power of concurrent-write parallel machines
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
New lower bounds for parallel computation
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Borel sets and circuit complexity
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Lower bounds in parallel machine computation
Lower bounds in parallel machine computation
Parallel symmetry-breaking in sparse graphs
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Optimal bounds for decision problems on the CRCW PRAM
Journal of the ACM (JACM)
New lower bounds for parallel computation
Journal of the ACM (JACM)
Parallel RAMs with bounded memory wordsize
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Highly parallelizable problems
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Optimal separations between concurrent-write parallel machines
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Converting high probability into nearly-constant time—with applications to parallel hashing
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Fast hashing on a PRAM—designing by expectation
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
A parallel algorithm for linear programming in fixed dimension
Proceedings of the eleventh annual symposium on Computational geometry
Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
Optimal parallel approximation for prefix sums and integer sorting
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Parallel integer sorting is more efficient than parallel comparison sorting on exclusive write PRAMs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
An O(log log n) time algorithm to compute the kernel of a polygon
Nordic Journal of Computing
Incomparability in parallel computation
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
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We prove optimal &OHgr;(log n/log log n) lower bounds on the time for CRCW PRAM's with polynomially bounded numbers of processors or memory cells to compute parity and a number of related problems. We also exhibit a strict time hierarchy of explicit Boolean functions of n bits on such machines which holds up to &Ogr;(log n/log log n) time. Furthermore, we show that almost all Boolean functions of n bits require log n - log log n + &OHgr;(1) time when the number of processors is at most polynomial in n. Our bounds do not place restrictions on the uniformity of the algorithms nor on the instruction sets of the machines.