XPost: comp.theory, sci.logic, sci.math

On 12/17/2021 6:46 PM, Ben Bacarisse wrote:

olcott <NoOne@NoWhere.com> writes:

On 12/17/2021 3:25 PM, Ben Bacarisse wrote:

olcott <NoOne@NoWhere.com> writes:

A function f with domain D is said to be Turing-computable
or just computable if there exists some Turing machine
M = (Q, Σ, Γ, δ, q0, □, F) such that q0 w ⊢* Mqff(w), qf ∈ F
for all w ∈ D (Linz:1990:243)

We all know your cut and paste skills are top notch.

Olcott paraphrase of above machine definition: Machine M begins at
start state q0 on input w and transitions to qf as a function of input >>>> w.

But that's not a correct paraphrase.

A Turing machine computes a function by starting with the input to the
function on the tape and halting with the output of the function on
the tape (Sipser:1997:190).

Within the context of the Sipser and Kozen quotes that you erased
exactly how is my paraphrase of Linz incorrect?

Your paraphrase was of the Linz definition. If not, its reference to
q0, qf and w are all wrong. As a paraphrase of Linz, it's wrong because
it substitutes ambiguity for clarity.

To say that M "transitions to qf
as a function of w" is pure waffle.

On 12/17/2021 9:21 AM, olcott wrote:

A function f with domain D is said to be Turing-computable
or just computable if there exists some Turing machine
M = (Q, Σ, Γ, δ, q0, □, F) such that q0 w ⊢* M qf f(w), qf ∈ F
for all w ∈ D (Linz:1990:243)

Olcott paraphrase of above machine definition:
Machine M begins at start state q0 on input w and
transitions to qf as a function of input w.

M = (Q, Σ, Γ, δ, q0, □, F) such that
q0 w ⊢* M qf f(w), qf ∈ F

Machine M
begins a start state q0
on input w
transitions to qf
as a function of w
...

Not really any ambiguity or waffle at all.
Not really any ambiguity or waffle at all.
Not really any ambiguity or waffle at all.
Not really any ambiguity or waffle at all.


--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

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