Talk:Least fixed point

Should there be a link to least weasel? I'm glad to know that even if there isn't a least fixed point of some function, there's always a least weasel. &mdash;Ashley Y 10:28, 2005 May 2 (UTC)
 * And it's always carnivorous. Life is so much more predictable than math, isn't it? Deco 21:26, 2 May 2005 (UTC)

"Definable in LFP" is undefined
The article says:


 * Immerman and Vardi independently showed the descriptive complexity result that the polynomial-time computable properties of linearly ordered structures are deﬁnable in LFP. However, LFP is too weak to express all polynomial-time properties of unordered structures (for instance that a structure has even size).

The meaning of the acronym "LFP" is not explained. Supposing that it stands for "least fixed point", then it cannot be understood in terms of what else is in the article, because the phrases "definable in least fixed point" and "least fixed point is too weak" does not make sense. "LFP" here seems to refer to some sort of logical or axiomatic system, but the article never explains what this system might be. Perhaps it refers here to first-order logic augmented with some sort of least fixed point operator? —Mark Dominus (talk) 17:26, 9 March 2011 (UTC)


 * Yes, LFP stands for least fixpoint logic. Tijfo098 (talk) 20:03, 7 November 2012 (UTC)

Colossal non-sequitur
"Unfortunately computing the optimal fixed point is undecidable in general so it is primarily of theoretical interest."

Math is undecidable in general, so math is primarily of theoretical interest.

Proving the correctness of algorithms is undecidable in general, so proving the correctness of algorithms is primarily of theoretical interest.

Computing is undecidable in general, so computing is primarily of theoretical interest.

Checking logical validity is undecidable in general, so checking logical validity is primarily of theoretical interest.

Classes of things that are 'undecidable' in the general case are a ubiquitous reality. Undecidability in the general case can not be shown to impact the practicality of anything. Even CSS is undecidabile. If you found out that the network protocols that you use everyday were undecidable it would probably be an occasion for a shrug. Your car stereo might be undecidable, and you wouldn't even notice it. In fact, the engine of your car might well be undecidable. Your microwave is probably undecidable. 'Undecidable' without qualification doesn't imply anything about practicality. So the referenced statement should be given some qualification, modified, or removed. Comiscuous (talk) 21:40, 16 January 2022 (UTC)