Regular Languages

It is said that human intelligence is mainly the capability to represent a problem, its solution, or related facts in many seemingly different ways. You must have encountered it in several problem-solving situations. You first represent the problem in a known language, where you might like to eliminate or omit the irrelevant aspects and consider only the appropriate ones. The methodology is followed throughout mathematics starting from solving first arithmetic problems such as “if you already had five candies and your friend offers you one more, then how many candies do you have now?”.

To give another example, the memory in a computer is only an assembly of switches which, at any moment, may be off or on. If there is a trillion of them, then it may be represented as a trillion digited binary number, when, say, off corresponds to 0 and on to 1. In some situations, we may not be interested in all possible binary numbers, but only those having a few number of digits out of the trillion, or only those having a particular pattern, such as “there is at least one 0 following every occurrence of a 1.” There might arise a situation where we would like to have a representational scheme having more than two symbols. We will, however, consider only a finite number of symbols at a time, and in parallel with the existing natural languages, we will develop formal languages out of these symbols.