In the field of computation theory, concatenation is one of the regular operations. If A and B are languages (not necessarily regular languages) then the concatenation of A and B (usually written AB) is defined as follows.

{xy | x A and y B}

In plain English: AB is the set of all strings which can be created by concatenating (read: putting together) a string from A with a string from B.

For example, if A = {yes,no}, and B = {maybe,probably}
AB = {yesmaybe,yesprobably,nomaybe,noprobably}

Some interesting things to note about the concatenation operation:

  • Concatenation of strings and concatenation of languages are very different. Many fallacious proofs are based on this fact.
  • Unlike the union operation, concatenation is not commutative. Unless A and B are equivalent, AB and BA are different languages.
  • Regular languages are closed under the concatenation operation. This means that if A and B are regular languages, then so is AB.

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