Title: Theory / Unimportant / CS / Fundamental / Automata / Finite / Pin{ / D Advanced tools= / 15 Polynomial closure+30
Tags: récupéré

Name: An \(\mathcal L\)-monomial of degree \(n\)
Definition: A language of the form \(L_0a_1L_1\dots a_nL_n\) with \(a_i\in A\), \(L_i\in\mathcal L\)
Page: 221
Chapter: XII
Section: 1
Variables: \(A\) an alphabet,
\(\mathcal L\) a set of languages

Name: An \(\mathcal L\)-polynomial
Definition: A finite union of \(\mathcal L\)-monomial
Page: 221
Chapter: XII
Section: 1
Variables: \(A\) an alphabet,
\(\mathcal L\) a set of languages

Name: The degree of \(P\)
Definition: The maximal degree of the monomials of \(P\)
Page: 221
Chapter: XII
Section: 1
Variables: \(A\) an alphabet,
\(\mathcal L\) a set of languages
\(P\) an \(\mathcal L\)-polynomial

Name: The polynomial closure of \(\mathcal L\)
Definition: the set of \(\mathcal L\)-polynomials
Page: 221
Chapter: XII
Section: 1
Variables: \(A\) an alphabet,
\(\mathcal L\) a set of languages
Notation: \(\text{Pol}(\mathcal L)\)
Index: , 1
Kind: , Theo
Definition2: the set of languages defined by the set of equations \(\Sigma(\mathcal L)\) (assuming \(\mathcal L\) \(\Sigma(\mathcal L)\)is a lattice of languages)

Definition: the set of equations of the form \(x^\omega\le x^\omega yx^\omega\) where \(x,y\) are profinite words of \(\hat A^*\) such that the equations \(x=x^2\) and \(x\le y\) are satisfied by \(\mathcal R\)
Page: 221
Chapter: XII
Section: 1
Variables: \(A\) an alphabet,
\(\mathcal L\) a set of languages
Notation: \(\Sigma(\mathcal L)\)
Typ: Monotonic with respect to inclusion
Assuming: \(\mathcal L\)'s language are recognizable