What does it mean for a language L to be recognisable in polynomial time?

27 Views Asked by At

Does it mean there exists a TM which decides L in polynomial time - that is, for any input w, the TM decides in time polynomial in the input whether w belongs to L or not - or is it rather just that, for any input w, if w belongs to L then the TM can verify that in polynomial time, but if w does not belong to L then the TM may loop/not run in polynomial time?