Infinitely generated semigroups and polynomial complexity
Abstract
This paper continues the functional approach to the P-versus-NP problem, begun in [1]. Here we focus on the monoid RM2P of right-ideal morphisms of the free monoid, that have polynomial input balance and polynomial time-complexity. We construct a machine model for the functions in RM2P, and evaluation functions. We prove that RM2P is not finitely generated, and use this to show separation results for time-complexity.
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