expansion.complement.ipynb

Kernel: Python 3

expansion.complement

An expansion which denotes the complement of this expansion.

See also:

• automaton.complement

• expression.complement

References:

• demaille.2016.ictac introduces expansions and their support for conjunction and complement

Examples

import vcsn
e = vcsn.B.expression('a*b')
e.expansion()

$a \odot \left[{a}^{*} \, b\right] \oplus b \odot \left[\varepsilon\right]$

e.expansion().complement()

$\left\langle \top\right\rangle \oplus a \odot \left[\left({a}^{*} \, b\right)^{c}\right] \oplus b \odot \left[{\varepsilon}^{c}\right]$

e.complement().expansion()

$\left\langle \top\right\rangle \oplus a \odot \left[\left({a}^{*} \, b\right)^{c}\right] \oplus b \odot \left[{\varepsilon}^{c}\right]$

e.complement().derived_term()

Note that complementing an expansion "determinizes" it: each first is mapped to a monomial. Note in the following example that the label $a$ maps to a two-term polynomial ($a$ and $b$), but in the complement, it has a single-term polynomial ($a+b$, observe $\oplus$ vs. $+$).

e = vcsn.B.expression('aa+ab')
x = e.expansion()
x

$a \odot \left[a \oplus b\right]$

x.complement()

$\left\langle \top\right\rangle \oplus a \odot \left[\left(a + b\right)^{c}\right] \oplus b \odot \left[{\emptyset}^{c}\right]$

e.derived_term()

e.complement().derived_term()