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
Upper and lower time bounds for parallel random access machines without simultaneous writes
SIAM Journal on Computing
On the time required to sum n semigroup elements on a parallel machine with simultaneous writes
Proc. of the Aegean workshop on computing on VLSI algorithms and architectures
One, two, three . . . infinity: lower bounds for parallel computation
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Parallel machines and their communication theoretical limits
3rd annual symposium on theoretical aspects of computer science on STACS 86
Optimal bounds for decision problems on the CRCW PRAM
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Separation and lower bounds for ROM and nondeterministic models of parallel computation
Information and Computation
Tape versus queue and stacks: the lower bounds
Information and Computation
An O(n2 log n) parallel max-flow algorithm
Journal of Algorithms
Computing connected components on parallel computers
Communications of the ACM
Bounds on the time for parallel RAM's to compute simple functions
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Relations between concurrent-write models of parallel computation
PODC '84 Proceedings of the third annual ACM symposium on Principles of distributed computing
Optimal parallel algorithms for string matching
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Lower bounds in parallel machine computation
Lower bounds in parallel machine computation
IEEE Transactions on Computers
Optimal bounds for decision problems on the CRCW PRAM
Journal of the ACM (JACM)
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Lower bounds are proven on the parallel-time complexity of several basic functions on the most powerful concurrent-read concurrent-write PRAM with unlimited shared memory and unlimited power of individual processors (denoted by PRIORITY(∞)):It is proved that with a number of processors polynomial in n, &OHgr; (log n) time is needed for addition, multiplication or bitwise OR of n numbers, when each number has n' bits. Hence even the bit complexity (i.e., the time complexity as a function of the total number of bits in the input) is logarithmic in this case. This improves a beautiful result of Meyer auf der Heide and Wigderson [22]. They proved a log n lower bound using Ramsey-type techniques. Using Ramsey theory, it is possible to get an upper bound on the number of bits in the inputs used. However, for the case of polynomially many processors, this upper bound is more than a polynomial in n.An &OHgr; (log n) lower bound is given for PRIORITY(∞) with no(1) processors on a function with inputs from {0, 1}, namely for the function ƒ(x1, … , xn,) = &Sgr; nl- 1 xlai where a is fixed and xi &egr; {0, 1}.Finally, by a new efficient simulation of PRIORITY(∞) by unbounded fan-in circuits, that with less than exponential number of processors, it is proven a PRIORITY(∞) cannot compute PARITY in constant time, and with nO(1) processors &OHgr;(@@@@log n) time is needed. The simulation technique is of independent interest since it can serve as a general tool to translate circuit lower bounds into PRAM lower bounds.Further, the lower bounds in (1) and (2) remain valid for probabilistic or nondeterministic concurrent-read concurrent-write PRAMS.