Concatenation Definition/Meaning:
Concatenation
of the strings u = a1 . .
. am and v = b1. . . bn.
The siring
a1 . . . amb1. . . bn
It is variously denoted by
uv, u + v, u || v, u & v
Concatenation is an associative operation.
In formal language theory, if u and
v are two
∑-words, their concatenation, uv, given as above, will also be
a
∑-word. If L is the empty
word then for a word w
Lw = w = wL
Since concatenation is associative, the set of all
∑-words,
∑, forms a
monoid
under concatenation, with identity L;
this is the free monoid over ∑.
The concatenation of two sets of strings, say two languages, L1
and L2 is the set of strings L1L2
(a language) formed by the pairwise concatenation of elements of L1
with L2.
L1L2 = {w1w2 | w1
Î L1, w2
Î L2}
This also gives monoid structure - the
identity is {L}.
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