Infinitely generated semigroups and polynomial complexity

Infinitely generated semigroups and polynomial complexity

This paper continues the functional approach to the P-versus-NP problem, begun in [1]. Here we focus on the monoid RM 2 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 RM 2 , and evaluation functions. We prove that RM 2 is not finitely generated, and use this to show separation resu...

Infinitely Generated Veech Groups

We give a positive response to a question of W. Veech: Infinitely generated Veech groups do exist.

A note on infinitely distributive inverse semigroups

By an infinitely distributive inverse semigroup will be meant an inverse semigroup S such that for every subset X ⊆ S and every s ∈ S, if ∨ X exists then so does ∨ (sX), and furthermore ∨ (sX) = s ∨ X. One important aspect is that the infinite distributivity of E(S) implies that of S; that is, if the multiplication of E(S) distributes over all the joins that exist in E(S) then S is infinitely d...

Power Semigroups and Polynomial Closure

Infinitely Generated Derksen and Makar-limanov Invariant *

In this paper, we give an example of a finitely generated 3-dimensional C-algebra which has infinitely generated Derksen invariant as well as MakarLimaonv invariant.