Alphabet (computer science) facts for kids
In computer science, an alphabet is a special kind of set that has a limited number of items. This set is never empty. The items in this set are called letters or symbols. Think of it like the alphabet you use for writing, but in computer science, these "letters" can be anything!
For example, the symbols used in Morse code can be an alphabet: 
(which means a dash and a dot). Another example could be the special words (called keywords) used in a Programming language, like {begin, if, else, for, while}.
The set of natural numbers (like 1, 2, 3, and so on) is not an alphabet. This is because it goes on forever and is not a limited set.
The alphabet used most often in computer science is {0,1}. It's called the binary alphabet because it only has two symbols: 0 and 1.
Alphabets are used to create a string (which is also called a word). A string is a sequence of letters taken from an alphabet. For example, if you use the binary alphabet {0,1}, a string of length 5 could be 01101.
The empty string is a special string that has no letters at all. It's often written as 
. The empty string can be made from any alphabet.
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What is a Kleene Star?
When we have an alphabet, let's call it 
, we can write down all the possible strings that can be made from it. We show this set of all possible strings as 
. This is known as the Kleene star (or Kleene closure) of . It's named after a famous mathematician named Stephen Cole Kleene.
For the binary alphabet {0,1}, its Kleene star would look like this: 
. The "..." at the end means that this list goes on forever. We can't write down every single string because there are an endless number of them!
Why are Alphabets Important in Computer Science?
Alphabets are super important in computer science. They are used to study formal languages, which are like special languages that computers understand. They also help us understand finite automata, which are like simple machines that follow rules.
Alphabets also help computer scientists answer very difficult questions. These questions are about what computers can actually figure out and what they cannot.
Related pages
- Arto Salomaa, Formal Languages, (1973): Chapter 1
- Michael A. Harrison, Introduction to Formal Language Theory, (1978): Chapter 1.2
- John E. Hopcroft and Jeffrey D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley Publishing, Reading Massachusetts, (1979). ISBN: 0201-02988-X.
- György E. Révész, Introduction to Formal Languages, (1991): Chapter 1.1
- Grzegorz Rozenberg and Arto Salomaa, Handbook of Formal Languages: Volume 1. Word, Language, Grammar, (1997): Chapter 2.1
- Dan A. Simovici and Richard L. Tenney, Theory of Formal Languages with Applications, (1999): Chapter 2.1
- Keijo Ruohonen, Formal Languages, (2009): Chapter 1.1
- John Martin: Introduction to Languages and the Theory of Computation (2010): Chapter 1.5
See also
In Spanish: Palabra (matemáticas) para niños
