9 October, Day 13
Chapter 2 – Finite Automata (FA)
A FA is a model of computation. A FA is a mathematical model of H/W.
A FA is an abstraction of H/W.
Consider his “black box” analogy.
Input -> “Black Box” -> Output
Inside functions of black box are hidden
Ex: a TV, we don’t know how it works inside, we give it input (channel
30) and it gives us output
Mathematical definition of FA
Q is a set of “states” (this is hidden in the black box)
Sigma is a set of “input” symbols
delta is a function for “moving” from a state given an input (this is the
hidden portion of the black box)
Q includes an initial state and a final state
An automaton accepts “words” in its language
example for English:
problem: is this string a word?
“NOT” [black box: FA] black box: FA] yes / accept
“OTN” [black box: FA] black box: FA] no
Language we CS people care about is binary form
Thus, words are sequences of 1s / 0s
Job of a FA is to determine if input string is a word in the FA’s
language; if yes then “accept”
example use of an FA – compiler checking syntax
input strings of 1s and 0s – is this input a syntactically valid “word” in
the language C?
He is trying to uncover a pattern for the words that are accepted by
the FA
Pattern that was found was – 01(001)*01
(001)* is shorthand for any number of repetitions of the sequence 001
note that “any number” can also mean 0, thus valid words following
the pattern
01(001)*01 are
01 01
CSC 490 Course Notes and Outline, © Dr. Gary Locklair, Fall 2006
