Introduction to Finite Automata

Transcription

1 Introduction to Finite Automata Our First Machine Model Captain Pedro Ortiz Department of Computer Science United States Naval Academy SI-340 Theory of Computing Fall 2012 Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

2 References Unless otherwise noted, all the information in this presentation was taken from the course notes or the course suggested text created and maintained by Associate Professor Chris Brown, USNA Kinber, Efim and Smith, Carl, Theory of Computing: A Gentle Introduction. Prentice Hall, Upper Saddle River, NJ, Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

3 Outline 1 Finite Automata 2 Diagram Definition 3 Finite Automata Rules 4 JFLAP Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

4 Assumptions Memory is : Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

5 Assumptions Memory is : 1 Fixed Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

6 Assumptions Memory is : 1 Fixed 2 Finite Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

7 Assumptions Memory is : 1 Fixed 2 Finite 3 Relatively small Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

8 What is a Finite Automaton? Definition Simple type of computer Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

9 What is a Finite Automaton? Definition Simple type of computer Input string w over alphabet Σ Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

10 What is a Finite Automaton? Definition Simple type of computer Input string w over alphabet Σ Memory the current state of the machine Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

11 What is a Finite Automaton? Definition Simple type of computer Input string w over alphabet Σ Memory the current state of the machine Consists of a finite set of states Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

12 What is a Finite Automaton? Definition Simple type of computer Input string w over alphabet Σ Memory the current state of the machine Consists of a finite set of states Transitions from state to state as it reads the characters of w Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

13 States Some definitions to remember: Definition start state or initial state - one state will be designated as the start ( initial ) state. This is the state the machine starts in i.e. before it reads any symbols. Definition accepting state - Some states will be designated as accepting. If a machine M exhausts all its input and is in an accepting state, M accepts that string. The set of strings accepted by M is referred to as the language accepted by M. Notation L(M) = the language accepted by M Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

14 Diagram Definition Definition Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

15 Diagram Definition Definition 1 We represent a finite automaton with a directed graph Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

16 Diagram Definition Definition 1 We represent a finite automaton with a directed graph 2 Vertices represent machine states Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

17 Diagram Definition Definition 1 We represent a finite automaton with a directed graph 2 Vertices represent machine states 3 Edges represent transitions from state to state Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

18 Diagram Definition Definition 1 We represent a finite automaton with a directed graph 2 Vertices represent machine states 3 Edges represent transitions from state to state Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

19 Diagram Definition Definition 1 We represent a finite automaton with a directed graph 2 Vertices represent machine states 3 Edges represent transitions from state to state Edges from one state to another are labeled with characters from Σ Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

20 Diagram Definition Definition 1 We represent a finite automaton with a directed graph 2 Vertices represent machine states 3 Edges represent transitions from state to state Edges from one state to another are labeled with characters from Σ When the machine is in a one state and it reads a character it goes into state pointed to by the edge with the character Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

21 Diagram Example 1 Example Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

22 Diagram Example 1 Example L(M) = {ab, ba} Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

23 Diagram Example 2 Example Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

24 Diagram Example 2 Example L(M) = {ɛ, abc, abcabc, abcabcabc,...} Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

25 Finite Automata Rules Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

26 Finite Automata Rules 1 Σ must be defines Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

27 Finite Automata Rules 1 Σ must be defines 2 Each state must have an outbound transition for each character in Σ Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

28 Finite Automata Rules 1 Σ must be defines 2 Each state must have an outbound transition for each character in Σ 3 States can only have one outbound transition for each character in Σ Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

29 Finite Automata Rules 1 Σ must be defines 2 Each state must have an outbound transition for each character in Σ 3 States can only have one outbound transition for each character in Σ 4 A machine can have zero or more accepting state, but only one start state Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11

30 JFLAP A tool for exploring machine models Installed in the CS department labs Freely available at Captain Pedro Ortiz (US Naval Academy) Introduction to Finite Automata SI-340 Fall / 11