1.4. finite automaton with ε moves
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1) An epsilon-NFA (ε-NFA) allows instantaneous transitions between states without reading an input symbol, represented by epsilon (ε) labels on arcs. 2) An ε-NFA is formally defined as a 5-tuple (Q, Σ, δ, q0, F) where Q is states, Σ is the alphabet, δ is the transition function, q0 is the initial state, and F are final states. Epsilon is not a member of the alphabet. 3) The epsilon-closure of a state p is the set of all states reachable from p through epsilon transitions.
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1.4. finite automaton with ε moves
- 1. Finite Automaton with ε - Moves -Sampath Kumar S, AP/CSE, SECE
- 2. Finite Automaton with ε - Moves We extend the class of NFAs by allowing instantaneous (ε) transitions: 1. The automaton may be allowed to change its state without reading the input symbol. 2. In diagrams, such transitions are depicted by labeling the appropriate arcs with ε. 3. Note that this does not mean that ε has become an input symbol. On the contrary, we assume that the symbol ε does not belong to any alphabet 11/21/20172 Sampath Kumar S, AP/CSE, SECE
- 3. Formal definition of ε-NFA: A NFA can be represented by a 5-tuples (Q, ∑, δ, q0, F) where − Q is a finite set of states. ∑ is a finite set of symbols, called the alphabet of the automaton. δ: Q × Σε → P(Q) is the transition function . q0 is the initial state from where any input is processed (q0 ∈ Q). F is a set of final state/states of Q (F ⊆ Q). Note: Note ε is never a member of Σ 11/21/20173 Sampath Kumar S, AP/CSE, SECE
- 4. ε-Closure: The ε-Closure is a set of all states which are reachable from state p on ε-transitions such that: 1. ε-Closure (p) = p where p ∈ Q. 2. If there exist ε-Closure (p) ={q} and δ (q, ε) = r then ε-Closure (p) = {q, r} 11/21/20174 Sampath Kumar S, AP/CSE, SECE
- 5. Example 20. Find the ε-Closure for the following NFA with ε. 11/21/20175 Sampath Kumar S, AP/CSE, SECE
- 6. Example 21. Find the ε-Closure for the following NFA with ε. 11/21/20176 Sampath Kumar S, AP/CSE, SECE
- 7. 11/21/2017 Sampath Kumar S, AP/CSE, SECE 7
- 8. நன்றி 11/21/2017 Sampath Kumar S, AP/CSE, SECE 8
Editor's Notes
- #2: School of EECS, WSU