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Finite Automata Mukesh N. Tekwani Elphinstone College Mumbai, India 2006 Finite Automata Finite Automata
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.
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Why study regular expression and DFA?
Deterministic Finite Automata ,[object Object],[object Object],[object Object],[object Object],[object Object]
DFA's ,[object Object],[object Object],[object Object],[object Object],[object Object]
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
DFA Examples Example. 1  Accept all strings that end in  a 1 q 0 q 1 0 1 1 0 Start
DFA Examples Strings with an odd number of ones. Even Odd 0 0 1 1 Start
DFA Examples Strings containing the substring 001 '001' 0 0 1 1 '0' '00' 0 1 0,1
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”
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
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”
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”
Finite State Machine (DFA) 0 1 3 2 start 4 A DFA that recognizes the strings  “ and”, &  “any” a n d ACCEPTED y
Finite State Machine (DFA) 0 1 3 2 start 4 A DFA that recognizes the strings  “ and”, &  “any” a n ACCEPTED
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
Examples ,[object Object],[object Object],[object Object],[object Object],[object Object]
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

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Finite Automata

  • 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.
  • 3.
  • 4.
  • 5.
  • 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
  • 17.
  • 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