# 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} }

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.

## 120 Citations

### 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.

### On the complexity of RAM with various operation sets

- Mathematics, Computer ScienceSTOC '92
- 1992

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

- Mathematics, Computer ScienceTAMC
- 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

- Mathematics, Computer ScienceSTOC '81
- 1981

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

- Computer ScienceJ. Algorithms
- 1999

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.

### The RAM equivalent of P vs. RP

- Computer ScienceArXiv
- 2013

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

- Mathematics, Computer ScienceMFCS
- 1990

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?

- Computer ScienceActa 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.

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