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Automaton (NFA) (with ε-transitions) is a 5-tuple: (Q,Σ, δ, q0, Fi where Q, Σ, q0 and F are as in a DFA and T ⊆ Q × Q × (Σ ∪ {ε}).
We must also modify the de?nitions of the directly computes relation and the path function to allow for the possibility that ε-transitions may occur anywhere in a computation or path. The ε-transition from state 1 to state 3 in the example, for instance, allows the automaton on input ‘a' to go from state 0 not only to state 1 but also to immediately go on to state 3. Similarly, it allows the automaton, when in state 1 with input ‘b', to move ?rst to state 3 and then take the ‘b' edge to state 0 or, when in state 0 with input ‘a', to move ?rst to state 2 and then take the ‘a' edge to state 3. Thus, on a given input ‘σ', the automaton can take any sequence of ε-transitions followed by exactly one σ-transition and then any sequence of ε-transitions. To capture this in the de?nition of δ we start by de?ning the function ε-Closure which, given a state, returns the set of all states reachable from it by any sequence of ε-transitions.
proof ogdens lemma .with example i am not able to undestand the meaning of distinguished position .
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Automaton (NFA) (with ε-transitions) is a 5-tuple: (Q,Σ, δ, q 0 , F i where Q, Σ, q 0 and F are as in a DFA and T ⊆ Q × Q × (Σ ∪ {ε}). We must also modify the de?nitions of th
Intuitively, closure of SL 2 under intersection is reasonably easy to see, particularly if one considers the Myhill graphs of the automata. Any path through both graphs will be a
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construct a social network from the real-world data, perform some simple network analyses using Gephi, and interpret the results.
De?nition (Instantaneous Description) (for both DFAs and NFAs) An instantaneous description of A = (Q,Σ, δ, q 0 , F) , either a DFA or an NFA, is a pair h q ,w i ∈ Q×Σ*, where
Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''s encountered is even or odd.
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