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 5Non 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).
• In effect, NFA is allowed to make a transition spontaneusly without receiving an input symbol.
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 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
• 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, ...}
exercise

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