Monday, April 18, 2016

Define Alphabets and power of an alphabet

Alphabets : An alphabet is a finite nonempty set of symbols. Conventionally we use the symbol summession symbol for an alphabet, common alphabets include :

1. summession symbol = {0,1}, the binary alphabet
2. summession symbol = {a,b...z}, the set of the lower case letters.
3. The set of all ASCII characters or the set of all printable ASCII characters.


Powers of an Alphabet : If summession symbol is an alphabet, we can express the set of all strings of a certain length from that alphabet by using an exponential notation. We  define summession power of k to be the set of strings of length K, each of which symbols is in summession symbol.

Example : If  summession symbol = {0, 1}, then power of 1 summession symbol = {0,1}

                             power of 2 summession symbol = {00, 01, 10, 11}
                            power of 3 summession symbol = {000, 001, 010, 011, 100, 101, 110, 111}
And so on.