<commit_before>#+title: Automata
#+AUTHOR: <NAME>
#+DESCRIPTION: Notes on automata theory, from theoretical computer science.
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These are my notes from this year's study of automata, which is an important branch of theoretical computer science.  It is surprisingly mathematical in its form and content.
* Alphabets

An alphabet \Sigma is a non-empty, finite set.

Automata theory uses linguistic terminology for its basic ideas, but an alphapet doesn't have to consist of letters.  For instance, if you consider a vending machine as an automaton, the letters are actually the different coins that the machine recognizes.

* Deterministic Finite Automata<commit_msg>automata.org<commit_after>#+title: Automata
#+AUTHOR: <NAME>
#+DESCRIPTION: Notes on automata theory, from theoretical computer science.
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These are my notes from this year's study of automata, which is an important branch of theoretical computer science.  It is surprisingly mathematical in its form and content. 

* Alphabets

An alphabet \Sigma is a non-empty, finite set.[fn:Carroll_Long]

For a given alphabet \Sigma and a natural number /n/, a sequence of symbols a_{1}a_{2}...a_{n} is a /word/ if and only if a_{i} \in \Sigma \forall i \in 1 .. /n/. [fn:Carroll_Long]

Automata theory uses linguistic terminology for its basic ideas, but an alphabet doesn't have to consist of letters.  For instance, if you consider a vending machine as an automaton, the letters are actually the different coins that the machine recognizes.

* Deterministic Finite Automata

* Footnotes

[fn:Carroll_Long]/Theory of Finite Automata with and  Introduction to Formal Languages/, <NAME> and Darrell Long, Prentice Hall, Englewood Cliffs New Jersey, 1989

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