Talk:Reduction (complexity)

message: Seems like we should merge in Reduction (recursion theory), since the method is basically the same between recursion theory and complexity theory. Thoughts? Bihzad (talk) 03:11, 5 April 2012 (UTC)
thread_title: Untitled

message: first of all, shouldn't this be the other way around?  by the definition at the top, what's being described is a reduction from multiplication to squaring, i.e. reducing any multiplication problem to a squaring problem (also given addition and subtraction), not the other way around.  also, the reduction described requires that you be able to divide by 2, which isn't mentioned as one of the requirements, and is non-trivial (at best) to express using only addition and subtraction.
Benwing 21:41, 7 September 2006 (UTC)
replies: text: Yes, the reduction is from multiplication to squaring. I'm not sure what the best way is to address the division by 2 thing - in many cases it doesn't matter, as having double the product is good enough - but for argument's sake I just added "division by 2" to the list of permitted operations. Deco 00:07, 8 September 2006 (UTC)
thread_title:  problem: "reducing squaring to multiplication" 

message: What? Was this written by a third grader? Something being "hard" to solve is a wholly subjective phenomenon. Aside from that, the application of a new technology or idea to an old phenomenon or problem which simplifies it, does not imply that utilization of the new idea on a formerly complex problem creates a paradox, or that the new, simpler idea or technology is "hard." It simply means that the previous methodology rendering the previous action "hard" has been rendered invalid, as a sufficient new methodology has been created as to simplify the previous problem, and it becomes, an "easy" problem to solve via reduction.
:wow. youre right. brilliant!!! ----88.64.153.44 17:23, 30 March 2007 (UTC)
replies: text: The use of the word "hard" is pretty standard in the field and is used in a formal sense to describe problems such that every problem in a class reduces to them. Maybe you're not clear on the concept that "B is hard and there exists a reduction from A to B implies A is hard". Reductions are used both to show easiness and hardness of problems -  there is no contradiction. If you think the discussion is too informal or verbose it could be made more formal. Dcoetzee 10:52, 2 April 2007 (UTC)
replies: text: I agree, the use of ``hard" is appropriate here. If you do not agree then add a definition to explain what hard means in this context. Bah23 15:51, 27 April 2007 (UTC)

text: Dcoetzee, shouldn't your statement read "...a reduction from B to A..."?  --Doradus (talk) 01:24, 10 October 2009 (UTC)
thread_title:  contradiction - usage of the term `hard' 

message: Sorry if this is a dumb question, but the introductory diagram on the current version of the page contains an edge between two white vertices both labeled "B".  This edge is not incident to a blue vertex, so I don't understand how the blue vertices form a vertex cover.  --Doradus (talk) 01:20, 10 October 2009 (UTC)
thread_title:  Image doesn't look like a vertex cover 

message: "reduction is an algorithm for transforming one problem into another problem." - this is a many-one reduction. The Turing reduction is using the solution of one problem to solve another one. The latter can hardly be formally described as "transforming the problem". 22:29, 2 December 2015 (UTC)
thread_title:  Sloppy lede