The document discusses finite automata including nondeterministic finite automata (NFAs) and deterministic finite automata (DFAs). It provides examples of NFAs and DFAs that recognize particular strings, including strings containing certain substrings. It also gives examples of DFA state machines and discusses using finite automata to recognize regular languages.

1. Finite Automata Mukesh N. Tekwani Elphinstone College Mumbai, India 2006 Finite Automata Finite Automata

2. Nondeterministic Finite Automata A nondeterministic finite automata (NFA) is collection of 5 things or 5 tuple: A set of states S. A set of input symbols ∑ (alphabet) A transition function δ that maps state-symbol pairs to sets of states. A state S 0 (sometimes denoted by Q 0 ) called as the start state or initial state . A set of states F called as the accepting states or final states . An accepting state is denoted by a double circle.

6. Parts of a DFA 1 0 1 1 0 accept state transition start state The alphabet for this example is {0, 1}. Each state has a transition for every symbol in the alphabet 2

7. DFA Examples Example. 1 Accept all strings that end in a 1 q 0 q 1 0 1 1 0 Start

8. DFA Examples Strings with an odd number of ones. Even Odd 0 0 1 1 Start

9. DFA Examples Strings containing the substring 001 '001' 0 0 1 1 '0' '00' 0 1 0,1

10. Finite State Machine (DFA) 0 1 2 3 4 start h e 5 6 8 9 7 ACCEPTED State Machine that recognizes the strings “ he”, “hers”, “his”, and “she”

11. Finite State Machine (DFA) State Machine that recognizes the strings “ he”, “hers”, “his”, and “she” 0 1 2 3 4 start h e 5 6 8 9 7 ACCEPTED r s

12. Finite State Machine (DFA) 0 1 2 3 4 start h 5 6 8 9 7 ACCEPTED i s State Machine that recognizes the strings “ he”, “hers”, “his”, and “she”

13. Finite State Machine (DFA) 0 1 2 3 4 start 5 6 8 9 7 ACCEPTED s h e State Machine that recognizes the strings “ he”, “hers”, “his”, and “she”

14. Finite State Machine (DFA) 0 1 3 2 start 4 A DFA that recognizes the strings “ and”, & “any” a n d ACCEPTED y

15. Finite State Machine (DFA) 0 1 3 2 start 4 A DFA that recognizes the strings “ and”, & “any” a n ACCEPTED

16. Nondeterministic Finite Automata 0 start A NFA that recognizes the strings “and”, & “any” n 1 2 3 4 5 6 d n y a a

18. Actually the third one is regular! DFA to recognize strings with an equal number of strings "01" and "10" 0 0 0 0 0 1 1 1 1 1 1 0 1 0