Morphology Question

Morphology Question

by Alexander Khalil Arwadi -
Number of replies: 2

Hello,

I understand what A + ⊗ B+ means but what does (A ⊗ B)+ mean?

In reply to Alexander Khalil Arwadi

Re: Morphology Question

by Huan-Cheng Chang -

I guess it's like concatenating multiple (a x b) so you end up getting a's x b's but the strings must have the same length?

In reply to Huan-Cheng Chang

Re: Morphology Question

by Jean-Cédric Chappelier -

indeed:
X+ is X | XX | XXX | XXXX | \cdots
thus
(a \otimes b)+ is (a \otimes b) | (a \otimes b)(a \otimes b) | (a \otimes b)(a \otimes b)(a \otimes b)| \cdots
that is
 (a,b) | (aa,bb) | (aaa,bbb) | (aaaa,bbbb) | \cdots

(since, by concatenation, (a,b)(a,b) is (aa,bb))

Summary:

  • a+\otimes b+ = (a^n, b^m), n\geq1, m\geq1
  • (a\otimes b)+ = (a^n, b^n), n\geq1