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Function Inverse Question.

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dorion

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I've been reading up on Reversible Logic and encountered a problem that I can't figure out.

If I have the function f(x, y) = (y, x) which I'm pretty sure is bijective, what is it's inverse? From what I see f(f(RxR)) is equal to f-1(f(RxR)) so that means f = f-1? If it does what is the name for this class of functions, cause I'm pretty sure that a function within this class that performs an operation similar to And or Or would be very useful for me to know about.
 
A function which is its own inverse is called involution, and yes, that's one example. It's a fairly general concept defined only by f=f-1, can't see how knowing the name would help with and/or...
 
dorion said:
I've been reading up on Reversible Logic and encountered a problem that I can't figure out.

If I have the function f(x, y) = (y, x) which I'm pretty sure is bijective, what is it's inverse? From what I see f(f(RxR)) is equal to f-1(f(RxR)) so that means f = f-1? If it does what is the name for this class of functions, cause I'm pretty sure that a function within this class that performs an operation similar to And or Or would be very useful for me to know about.
Click to expand...

AND and OR are binary operators. Functions in this space are pretty basic, either mapping to T or F, 0 or 1, etc. I don't see how involutions or bijections are interesting in space with 2 elements.
 
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