# Parallelism in random access machines

@article{Fortune1978ParallelismIR, title={Parallelism in random access machines}, author={Steven Fortune and Jim Wyllie}, journal={Proceedings of the tenth annual ACM symposium on Theory of computing}, year={1978} }

A model of computation based on random access machines operating in parallel and sharing a common memory is presented. [... ] Key Result Similar results hold for other classes. The effect of limiting the size of the common memory is also considered. Expand

## 1,035 Citations

Parallel random access machines with powerful instruction sets

- MathematicsMathematical systems theory
- 2005

It is shown that NP is equal to the class of sets accepted by this model in nondeterministic timeO(logn), that PSPACE isequal to theclass of setsaccepted byThis model in deterministic polynomial time and that P is equal To that of set accepted by a restricted version of thismodel inO( logn) space.

The power of parallel random access machines with augmented instruction sets

- Computer Science[1989] Proceedings. Structure in Complexity Theory Fourth Annual Conference
- 1989

It is proved that the class of languages accepted in polynomial time by a parallel random access machine (PRAM) with both multiplication and shifts contains NEXPTIME and is contained in EXPSPACE.…

On the Power of Probabilistic Choice in Synchronous Parallel Computations

- Computer ScienceICALP
- 1982

It is shown that parallelism uniformly speeds up time bounded Probabilistic sequential RAM computations by nearly a quadratic factor, and that probabilistic choice can be, eliminated from parallel computation by introducing nonuniformity.

Applied Computation Theory ARE PARALLEL MACHINES ALWAYS FASTER THAN SEQUENTIAL MACHINES ?

- Computer Science
- 2017

This paper presents speedup theorems where both M and M' use the same kind of storage medium, which is not linear tapes, and demonstrates that parallel time is strictly more powerful than deterministic time for Turing machines.

A complexity theory for unbounded fan-in parallelism

- Computer ScienceFOCS 1982
- 1982

New upper bounds on the (unbounded fan-in) circuit complexity of symmetric Boolean functions are proved and several reducibilities and equivalences among problems are given.

Division is good

- Computer Science20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
- 1979

It is shown that in certain situations parallelism and stochastic features ('distributed random choices') are provably more powerful than either parallelism or randomness alone.

Multiplication, Division and Shift Instructions in Parallel Random Access Machines

- MathematicsTheor. Comput. Sci.
- 1992

Simultaneous WRITES of parallel random access machines do not help to compute simple arithmetic functions

- Computer ScienceJACM
- 1987

The ability of the strongest parallel random access machine model WRAM, in which different processors may simultaneously try to write into the same cell of the common memory, is investigated, and a logarithmic lower time bound for WRAMs is proved.

Parallel Time O(log n) Recognition of Unambiguous Context-free Languages

- Computer ScienceInf. Comput.
- 1987

## References

SHOWING 1-10 OF 14 REFERENCES

Time-bounded random access machines

- Computer ScienceSTOC
- 1972

This paper introduces a formal model for random access computers and argues that the model is a good one to use in the theory of computational complexity and shows the existence of a time complexity hierarchy which is finer than any standard abstract computer model.

On the Power of Multiplication in Random Access Machines

- Computer ScienceSWAT
- 1974

It is proved that, counting one operation as a unit of time and considering the machines as acceptors, deterministic and nondeterministic polynomial time acceptable languages are the same, and are exactly the languages recognizable in polynomially tape by Turing machines.

Time Bounded Random Access Machines with Parallel Processing

- Computer ScienceJACM
- 1979

The RAM model of Cook and Reckhow ~s extended to allow parallel recursive calls and the elementary theory of such machines is developed The uniform cost criterion is used The results include proofs…

Parallel and Nondeterministic Time Complexity Classes (Preliminary Report)

- Computer ScienceICALP
- 1978

It is shown that NP is equal to the class of sets accepted by this model in nondeterministic time 0(log n), and this result is generalized to arbitrary time classes.

Relationships Between Nondeterministic and Deterministic Tape Complexities

- Computer ScienceJ. Comput. Syst. Sci.
- 1970

A characterization of the power of vector machines

- Computer ScienceSTOC '74
- 1974

Random access machines (RAMs) are usually defined to have registers that hold integers, but their ability to operate bit by bit on the bit vectors used to represent integers is overlooked, so a vector machine is called.

On parallelism in turing machines

- Computer Science17th Annual Symposium on Foundations of Computer Science (sfcs 1976)
- 1976

A natural characterization of the polynomial time hierarchy of Stockmeyer and Meyer in terms of parallel machines is given, and a generalization of Saviten's result NONDET-L(n)-SPACE ⊆ L(n)2-SPACE is given.

Fast parallel matrix inversion algorithms

- Computer Science, Mathematics16th Annual Symposium on Foundations of Computer Science (sfcs 1975)
- 1975

It will be shown in the sequel that the parallel arithmetic complexity of all these four problems is upper bounded by O(log2n) and the algorithms that establish this bound use a number of processors polynomial in n, disproves I. Munro's conjecture.

Parallel algorithms for the transitive closure and the connected component problems

- Computer ScienceSTOC '76
- 1976

Parallel programs are presented that determine the transitive closure of a matrix using n 3 processors and connected components of an undirected graph using n 2 processors and in both cases the desired results are obtained in time 0(log<supscrpt>2</supsCrpt>n).

Parallel Solution of Recurrence Problems

- Mathematics, Computer ScienceIBM J. Res. Dev.
- 1974

It is shown that if the recurrence function f has associated with it two other functions that satisfy certain composition properties, then it can be constructed elegant and efficient parallel algorithms that can compute all N elements of the series in time proportional to ⌈log2N⌉.