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Views: 45895
Kernel: Python 3

automaton.difference(aut)

automaton % aut

Restricting an automaton to the words not accepted by the second. In other words:

$$ (\mathcal{A} \% \mathcal{B})(u) = \begin{cases} \mathcal{A}(u) & \text{if $\mathcal{B}(u) \ne 0$} \ 0 & \text{otherwise} \end{cases} $$

Preconditions:

  • None

Caveat:

  • The name difference is wrong, and will certainly be changed in the future.

  • If the second argument is not Boolean, because we determinize it, the process might loop for ever.

See also:

Examples

In the following example, we map every non empty word on {a,b}\{a, b\} to 22 with the exception of words that are repetitions of abab or of baba.

import vcsn
ctx = vcsn.context('lal, q')
aut = lambda e: ctx.expression(e).automaton()
a = aut('<2>[ab]{+}')
b = aut('(ab+ba)*')
vcsn.ipython.table([["a", "b"], [a, b]])
a b 
a % b
Image in a Jupyter notebook
(a%b).shortest(len = 4)

⟨2⟩a⊕⟨2⟩b⊕⟨2⟩aa⊕⟨2⟩bb⊕⟨2⟩aaa⊕⟨2⟩aab⊕⟨2⟩aba⊕⟨2⟩abb⊕⟨2⟩baa⊕⟨2⟩bab⊕⟨2⟩bba⊕⟨2⟩bbb⊕⟨2⟩aaaa⊕⟨2⟩aaab⊕⟨2⟩aaba⊕⟨2⟩aabb⊕⟨2⟩abaa⊕⟨2⟩abbb⊕⟨2⟩baaa⊕⟨2⟩babb⊕⟨2⟩bbaa⊕⟨2⟩bbab⊕⟨2⟩bbba⊕⟨2⟩bbbb\left\langle 2\right\rangle \mathit{a} \oplus \left\langle 2\right\rangle \mathit{b} \oplus \left\langle 2\right\rangle \mathit{aa} \oplus \left\langle 2\right\rangle \mathit{bb} \oplus \left\langle 2\right\rangle \mathit{aaa} \oplus \left\langle 2\right\rangle \mathit{aab} \oplus \left\langle 2\right\rangle \mathit{aba} \oplus \left\langle 2\right\rangle \mathit{abb} \oplus \left\langle 2\right\rangle \mathit{baa} \oplus \left\langle 2\right\rangle \mathit{bab} \oplus \left\langle 2\right\rangle \mathit{bba} \oplus \left\langle 2\right\rangle \mathit{bbb} \oplus \left\langle 2\right\rangle \mathit{aaaa} \oplus \left\langle 2\right\rangle \mathit{aaab} \oplus \left\langle 2\right\rangle \mathit{aaba} \oplus \left\langle 2\right\rangle \mathit{aabb} \oplus \left\langle 2\right\rangle \mathit{abaa} \oplus \left\langle 2\right\rangle \mathit{abbb} \oplus \left\langle 2\right\rangle \mathit{baaa} \oplus \left\langle 2\right\rangle \mathit{babb} \oplus \left\langle 2\right\rangle \mathit{bbaa} \oplus \left\langle 2\right\rangle \mathit{bbab} \oplus \left\langle 2\right\rangle \mathit{bbba} \oplus \left\langle 2\right\rangle \mathit{bbbb}