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18 votes
2 answers
1k views

Is there a name for sets for which it is easier to test membership than to find members---and vice versa?

This is a question my son Bob asked me. For some sets it is relatively easy to test for membership but a lot more difficult to find members, and for others the reverse is true. Here is an elementary ...
Dick Palais's user avatar
  • 15.3k
17 votes
1 answer
960 views

Polynomial-time algorithm to compare numbers in Conway chained arrow notation

I am looking for a polynomial-time algorithm which, given a character string containing two numbers in Conway's chained arrow notation for large numbers, indicates whether the first number is less ...
khaaan's user avatar
  • 171
6 votes
2 answers
276 views

Extending polynomial hierarchy above $\omega$

The arithmetic hierarchy is naturally extended to all ordinals via ordinal notations creating a hierarchy for all hyperarithmetic sets. The polynomial time hierarchy is defined analogously to the ...
Peter Gerdes's user avatar
  • 3,029
1 vote
0 answers
127 views

Does relationship between c.e.set, productive set, immune set, ML-random set exist between sets of class of other level

Is relationship between c.e.set, productive set, immune set, ML-random set similar to relationship between polynomial complexity set, polynomial complexity-productive set, P-immune set, P-random set?
XL _At_Here_There's user avatar