XPost: comp.theory, sci.logic, sci.math
On 9/19/2021 1:00 AM, André G. Isaak wrote:
On 2021-09-18 23:12, olcott wrote:
On 9/18/2021 11:19 PM, André G. Isaak wrote:
On 2021-09-18 22:10, André G. Isaak wrote:
And note that Rice is talking about properties of Turing Machines
(or, more properly, of the language accepted by a TM), not
computations.
I realized immediately after hitting 'send' that the above will no
doubt confuse you since people have been telling you that Turing
Machines can only express computations whereas C/x86 aren't thus
constrained.
A computation is a Turing Machine description PLUS an input string.
Rice's theorem is concerned with the Turing Machine's themselves.
The Linz proof shows that you cannot construct a halting decider,
i.e. a decider which correctly determines for any given TM + input
string pair, whether that pair represents a halting computation.
Rice's theorem, on the other hand, would rule out the construction of
something like a Decider Decider, i.e. a TM which takes as its input
a TM description and determines whether that TM qualifies as a
decider, i.e. is guaranteed to halt on *any* possible input.
André
Bingo! I have said it this same way recently.
No, you have not.
On 9/9/2021 10:25 AM, olcott wrote:
It is the case that H(P,P)==0 is correct
It is the case that H1((P,P)==1 is correct
It is the case the this is inconsistent.
It is the case that this inconsistency defines a
decidability decider that correctly rejects P on
the basis that P has the
pathological self-reference(Olcott 2004) error.
decidability decider that correctly rejects P on
the basis that P has the
pathological self-reference(Olcott 2004) error.
decidability decider that correctly rejects P on
the basis that P has the
pathological self-reference(Olcott 2004) error.
// Decidability Decider
u32 PSR_Olcott_2004(u32 P)
{
return H1(P,P) == H(P,P);
}
And how is the above related to anything I wrote in my original post or
in the post clarifying that post to which you are responding? You don't answer the actual question which was asked (i.e. which semantic property
do you claim to be able to decide using the above?) nor do you show even
the remotest evidence of having even read my post.
André
--
Copyright 2021 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
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