On the Power of Random Access Machines

@inproceedings{Schnhage1979OnTP,
  title={On the Power of Random Access Machines},
  author={Arnold Sch{\"o}nhage},
  booktitle={International Colloquium on Automata, Languages and Programming},
  year={1979}
}
  • A. Schönhage
  • Published in
    International Colloquium on…
    16 July 1979
  • Mathematics, Computer Science
We study the power of deterministic successor RAM's with extra instructions like +,*,⋎ and the associated classes of problems decidable in polynomial time. Our main results are NP ... PTIME (+,*,⋎) and PTIME(+,*) ... RP, where RP denotes the class of problems randomly decidable (by probabilistic TM's) in polynomial time. 

Division is good

  • Janos Simon
  • Computer Science
    20th 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.

Division in Idealized Unit Cost RAMS

On the complexity of RAM with various operation sets

We prove that polynomial time bounded RAMs with the instruction set [shift, +, X, boolean ] accept exactly the languages in PSPACE. This generalizes previous results: [5] showed the same for the

Computing with and without Arbitrary Large Numbers

  • M. Brand
  • Mathematics, Computer Science
    TAMC
  • 2013
A characterization of the power of an extra input integer, having no special properties other than being sufficiently large, for general problems.

A characterization of the class of functions computable in polynomial time on Random Access Machines

This work has shown that the solution of enumeration problems by means of solving formulas, generally based on the usual arithmetic operations, can be formally represented as programs for a Random Access Machine with arithmetical primitives.

Lower Bounds for the Complexity of Functions in a Realistic RAM Model

No nontrivial lower bound is known when the RAM model also uses bitwise boolean operations or bit shift operations, so lower bounds for the complexity of computing functions in random access machines (RAMs) are not known.

P-RAM vs. RP-RAM

  • M. Brand
  • Computer Science
    Theor. Comput. Sci.
  • 2017

The RAM equivalent of P vs. RP

This paper fully characterising the class of languages recognisable in polynomial time by each of the RAMs regarding which the question was posed shows that for some of these, stochasticity entails no advantage, but, more interestingly, it is shown that for others it does.

On the Complexity of Genuinely Polynomial Computation

We present separation results on genuinely (or strongly) time bounded sequential, parallel and nondeterministic complexity classes defined by RAMs with fixed set of arithmetic operations. In

Does indirect addressing matter?

  • M. Brand
  • Computer Science
    Acta Informatica
  • 2012
It is shown that for RAMs equipped with a sufficiently rich set of basic operations, indirect addressing does not increase computational power, and can be simulated either in linear time or on-line in real time.
...

References

SHOWING 1-5 OF 5 REFERENCES

On time versus space and related problems

The main result of this paper is to settle in the affirmative the fundamental question as to whether space is strictly more powerful than time as a resource for multi-tape Turing machines. As a

On the Power of Multiplication in Random Access Machines

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.

A characterization of the power of vector machines

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.

Storage Modification Machines

This paper gives a complete description of the SMM model and its real time equivalence to the so-called successor RAMS and shows the existence of an SMM that performs integer-multiplication in linear time.

A Fast Monte-Carlo Test for Primality

A uniform distribution a from a uniform distribution on the set 1, 2, 3, 4, 5 is a random number and if a and n are relatively prime, compute the residue varepsilon.