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

1. Pertemuan 5Non Deterministic Finite Automata with  Transition (NFA- ) Matakuliah : T0162/Teori Bahasa dan Automata Tahun : 2009

2. 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.

3. Example

5. example

6. Formal Notation ε-NFA

7. example

8. Epsilon closure

9. 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.

10. 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", ... }.

11. 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, ...}

12. Converting RE to Automata

15. induction

17. example

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