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Finite Automata
 

Finite Automata

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Finite Automata

Finite Automata

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    Finite Automata Finite Automata Presentation Transcript

    • 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.
      • Test if a string matches some pattern.
      • Scan for virus signatures.
      • Process natural language.
      • Search for information using Google.
      • Search for markers in human genome.
      • Access information in digital libraries.
      • Search-and-replace in a word processors.
      • Filter text (spam, NetNanny).
      • Validate data-entry fields (dates, email, URL, credit card).
      Why study regular expression and DFA?
    • Deterministic Finite Automata
      • Theoreticians have developed a number of theoretical models to describe "computing"
      • Simplest model is known as a DFA
      • Deterministic : Machine will be in a state. Upon receipt of a certain symbol, it will go to a known state
      • Finite : The machines only have a certain number of states
      • Automata : Machine, robot
    • DFA's
      • DFA's recognize strings.
      • If the input ends and the DFA is in an accept state then the string is "recognized"
      • A "language" can be described as a set of strings
      • A language is called a regular language if some finite automaton recognizes it.
      • There is a precise mathematical definition of exactly what is meant by a finite automaton
    • 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
      • Design a DFA to recognize strings that start out with k zeros followed by k ones.
      • Design a DFA to recognize strings with an equal number of ones and zeros.
      • Design a DFA to recognize strings with an equal number of strings "01" and "10". Impossible?
        • 1 yes
        • 2 No
    • 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