On the Power of Multiplication in Random Access Machines

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Abstract
We consider random access machines with a multiplication operation, having the added capability of computing logical operations on bit vectors in parallel. The contents of a register are considered both as an integer and as a vector of bits and both arithmetic and boolean operations may be used on the same register. We prove 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 polynomial tape by a Turing machine. We observe that the same measure on machines without multiplication is polynomially related to Turing machine time - thus the power of multiplication on this model characterizes the difference between Turing machine tape and time measures. We discuss other instruction sets and their power.
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1974-04
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Cornell University
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computer science; technical report
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http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR74-205
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technical report
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