lec1128 - Deterministic Finite Automata (a specific finite...

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Deterministic Finite Automata (a specific finite state machine) We have already talked about one way to specify a regular language: through a regular expression. Now, I will show you another way, using a more “visual” representation. In the textbook, they talk about finite state machines in sections 6.2 and 6.3. DFA’s are a specific type of finite state machine. In particular, a DFA does not have output, as a general FSM does. That is pretty much the only difference. Both in the book and in Dr. Lang’s notes(around 4-10 through 4-16) there is a formal definition of a DFA and FSM respectively. Since we have so little time to deal with these, I won’t get into the formal definition, which usually confuses people. If you are interested in it, look at Dr. Lang’s notes. I think they do a good job of explaining the mechanics of the definition. I will draw a whole bunch of pictures, and give you a basic idea of how one works. The basic idea behind a DFA is this: Its goal is to read in a string and determine whether or not the string is in the language that the DFA describes. But, there are some restrictions. It may only have a finite amount of memory. In particular, this machine reads in one letter at a time. But after it has “read” in a letter of the string, it can not “remember” what it read in. Rather, it can only “remember” what state it is in, and there is only a finite amount of these states.
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So, the machine has these components: 1) An alphabet that the strings in the language are made up of. 2) A set of states, each of which I will denote with a circle. 3) A start state, which I will denote with an shaded arrow 4) A set of final states, which I will denote with a circle inside of a circle 5) A set of transitions in between each of the states, which is essentially a list of rules that govern how you “move” from
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This document was uploaded on 06/09/2011.

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lec1128 - Deterministic Finite Automata (a specific finite...

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