Date: Nov 5, 2013 10:38 PM
Author: Ben Bacarisse
Subject: Re: AN ERROR IN PEANO ARITHMETIC! x X [ s Y ] [ + X Z ] <- x X Y Z
grahamcooper7@gmail.com writes:

<snip>

>> > But all of them require unlimited memory to perform unlimited size

>> > number multiplication.

>>

>> It would be nice to see a proof. I don't have one.

>

> There is a proof but I don't recall it.

>

> The number of states of the machine is less than the

> intermediate sums to perform multiplication.

>

> Starting with Least Significant Bit

>

> 010101010101

> X

> 010101

> ____________

>

>

> Now you have X carry states, LEN(TERM2)

> and only Y internal states.

That's an argument that one representation (I'm guessing -- you don't

actually give the input representation) and method fails. Whilst I am

sure they all do, any argument for that must be more general.

To all intents a purposes, it probably suffices to say that neither

{ "x*y=z" | v(x) * v(y) = v(z) }

{ interleave(x, y, z) | v(x) * v(y) = v(z) }

is regular.

<snip>

--

Ben.