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Tau Meta Language and the notion of Fixed Point by dana-edwards

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· @dana-edwards ·
$69.00
Tau Meta Language and the notion of Fixed Point
Tau Meta Language and the notion of Fixed Point
---------

Tau Meta Language is very unique in how it works. Each TML program is described as a loop without an arbitrary stopping condition. This is the case because the states of computation are finite. So a TML program merely defines what happens within a single iteration or "instance". 

The loop continues until

S  ∨  F

A) Two consequetive iterations return the same result (this means success)
i+(1).. i++(1).. S

B) Two non-consequetive iterations return the same result (this means fail)
i+(1).. i++(x).. i+++(1).. F

There can only ever be two possibilities so in essence this is boolean, an either or situation. A represents a Fixed Point which indicates the result is final because the state of the computation has not changed after two consequentive iterations.

To put it more precisely, if a loop ever has a length greater than 1 then it is a fail.

Partial fixed point requires ORDERED structures such as an ordered set. This allows for P-SPACE complexity to be recovered.
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@frank1in ·
this is an excellent mini manual that will be useful to those who decided to deal with the concept of a fixed point. On the principle of nothing complicated here, but I took some of the nuances for myself from your post.
Thank you
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@fth ·
Thank your for this article.
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@mervesaglam ·
Thank you very much :)
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@munawar1235 ·
$2.76
nice post reminding me of my university days. will you please check  my post?
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@nainaztengra ·
Informative post Dana. Regards Nainaz.
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@vm2904 ·
$0.10
@dana-edwards - Wow.  I remember the tightly bound structures of the C and C++ language programs I wrote during my Master's degree.   Though object oriented, the if..then kind of structures were so restrictive and required us to list of every eventuality.   This is so simple and logical.
I must read up more.  Thanks for the heads up.
Upvoted full through Steemfollower.

Regards,
![](https://steemitimages.com/DQmaJ2HfMDXuvpZTno49rP8v8wu4YfC82iWMULLUjZJKv3b/image.png)
@vm2904
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@yanis01 ·
thanks gan, post very useful and helpful, do not forget vote my post also yes.
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