Jump to content

Is permutation the essence of computation?


Hrvoje1

Recommended Posts

Can computation always be reduced to permutation of certain states of a certain subtrate, or be performed by permutation of these, in every possible model of computation, classical or quantum? Or is it too general statement?

Link to comment
Share on other sites

5 hours ago, Hrvoje1 said:

Can computation always be reduced to permutation of certain states of a certain subtrate, or be performed by permutation of these, in every possible model of computation, classical or quantum? Or is it too general statement?

Would you like to explain further, ?

Link to comment
Share on other sites

14 hours ago, Hrvoje1 said:

Can computation always be reduced to permutation of certain states of a certain subtrate, or be performed by permutation of these, in every possible model of computation, classical or quantum? Or is it too general statement?

No. Consider the computation that maps every input to zero. That's not reversible and is not a permutation.

Link to comment
Share on other sites

OK, thanks wtf. I have probably misrepresented the theory from that paper a bit, so let me please rephrase my question. Is permutation the essence of reversible computation? Can reversible computation always be reduced to a permutation, ie be performed by it?

Link to comment
Share on other sites

8 hours ago, Hrvoje1 said:

OK, thanks wtf. I have probably misrepresented the theory from that paper a bit, so let me please rephrase my question. Is permutation the essence of reversible computation? Can reversible computation always be reduced to a permutation, ie be performed by it?

Not sure what the paper is about. But any reversible process may be represented as a group; and every group may be represented as a group of permutations. That's the famous Cayley's theorem. https://en.wikipedia.org/wiki/Cayley's_theorem

Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.