Efficient Computation by Three Counter Machines
Holger Petersen

TL;DR
This paper demonstrates that multiplication and certain functions of two variables can be computed efficiently in polynomial time on a simple three counter machine, extending to functions computable in linear space.
Contribution
It introduces a method for efficient computation of multiplication and linear-space functions on a minimal three counter machine.
Findings
Multiplication is computable in polynomial time on a three counter machine.
Functions of two variables computable in linear space are also efficiently computable.
The technique generalizes to a class of functions beyond basic multiplication.
Abstract
We show that multiplication can be done in polynomial time on a three counter machine that receives its input as the contents of two counters. The technique is generalized to functions of two variables computable by deterministic Turing machines in linear space.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Quantum Computing Algorithms and Architecture · Cellular Automata and Applications
