Pertemuan 5 non deterministic finite automata with transition nfa
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Pertemuan 5 Non Deterministic Finite Automata with  Transition (NFA-  ) . Matakuliah: T0162/Teori Bahasa dan Automata Tahun: 2009. Finite Automata with ε Transition. NFA that allow a transition on ε , the empty string ( ε -NFA).

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Pertemuan 5 Non Deterministic Finite Automata with  Transition (NFA-  )

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Pertemuan 5 non deterministic finite automata with transition nfa

Pertemuan 5Non Deterministic Finite Automata with  Transition (NFA- )

Matakuliah: T0162/Teori Bahasa dan Automata

Tahun: 2009


Finite automata with transition

Finite Automata with ε Transition

  • NFA that allow a transition on ε, the empty string (ε-NFA).

  • In effect, NFA is allowed to make a transition spontaneusly without receiving an input symbol.


Example

Example


Example1

example


Formal notation nfa

Formal Notation ε-NFA


Example2

example


Epsilon closure

Epsilon closure


Reguler expression

Reguler expression

  • Regular expressions describe regular languages in formal language theory

    Given a finite alphabet Σ, the following constants are defined:

  • (empty set) ∅ denoting the set ∅.

  • (empty string) ε denoting the set containing only the "empty" string, which has no characters at all.


Reguler expression1

Reguler expression

  • (concatenation) RS denoting the set { αβ | α in R and β in S }. For example {"ab", "c"}{"d", "ef"} = {"abd", "abef", "cd", "cef"}.

  • (alternation) R | S denoting the set union of R and S. For example {"ab", "c"}|{"ab", "d", "ef"} = {"ab", "c", "d", "ef"}.

  • (Kleene star) R* denoting the smallest superset of R that contains ε and is closed under string concatenation. This is the set of all strings that can be made by concatenating any finite number (including zero) of strings from R. For example, {"0","1"}* is the set of all finite binary strings (including the empty string), and {"ab", "c"}* = {ε, "ab", "c", "abab", "abc", "cab", "cc", "ababab", "abcab", ... }.


Examples

Examples

  • a|b* denotes {ε, a, b, bb, bbb, ...}

  • (a|b)* denotes the set of all strings with no symbols other than a and b, including the empty string: {ε, a, b, aa, ab, ba, bb, aaa, ...}

  • ab*(c|ε) denotes the set of strings starting with a, then zero or more bs and finally optionally a c: {a, ac, ab, abc, abb, abbc, ...}


Converting re to automata

Converting RE to Automata


Induction

induction


Example3

example


Exercise

exercise

The RE (a|b)c is mapped to the following NFA:


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