How is an arithmetic model defined?
What relations are between it and Turing machine? Are they equivalent in some sense?
Is it true that
in the arithmetic model of computation, the basic arithmetic operations (addition, subtraction, multiplication, division, and comparison) take a constant unit time step to perform, regardless of the sizes of the operands.
in the Turing machine, the time each operation takes will depends on the storage size of the operands?
What is the point of having these two different computational models?
Are there other models of computation distinct from the Turing machine and the arithmetic model?
There are algorithms which run in polynomial time in the Turing machine model, but not in the arithmetic model. The Euclidean algorithm for computing the greatest common divisor of two integers is one example.
If an algorithm runs in polynomial time in the Turing machine, will it run in polynomial time in the arithmetic model?
Is an algorithm running in polynomial storage space defined the same under the Turing machine and the arithmetic model?
Thanks and regards!