'Tume et Consider the following DFA M= (IGo, Gi} {0, 1}, &, %0 {Gh) S(qt, @) s(q 1) The string 01101 € L(M) Select one:- 0 True 0 False'
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Let $L_{i}$ be the set of strings accepted by the finite-state automaton $A_{i}=\left(\mathcal{I}, \mathcal{S}_{i}, f_{i}, \mathcal{A}_{i}, \sigma_{i}\right), i=1,2 .$ Let $$A=\left(\mathcal{I}, \mathcal{S}_{1} \times \mathcal{S}_{2}, f, \mathcal{A}, \sigma\right)$$ where $$\begin{aligned}f\left(\left(S_{1}, S_{2}\right), x\right) &=\left(f_{1}\left(S_{1}, x\right), f_{2}\left(S_{2}, x\right)\right) \\\mathcal{A} &=\left\{\left(A_{1}, A_{2}\right) \mid A_{1} \in \mathcal{A}_{1} \text { or } A_{2} \in \mathcal{A}_{2}\right\} \\\sigma &=\left(\sigma_{1}, \sigma_{2}\right)\end{aligned}$$ Show that $\operatorname{Ac}(A)=L_{1} \cup L_{2}$.
Automata, Grammars, and Languages
Finite-State Automata
i. Given a deterministic finite automata (DFA) as in Figure 2. a) List all the components of S, I, qo, F. b) Find the sequence of configurations and state if the string 0011101100 is accepted by the DFA. ii. Construct a DFA that accepts the set of all bit strings that contain three consecutive 1s.
Shaiju T.
Let $L_{i}$ be the set of strings accepted by the finite-state automaton $A_{i}=\left(\mathcal{I}, \mathcal{S}_{i}, f_{i}, \mathcal{A}_{i}, \sigma_{i}\right), i=1,2$. Let $$A=\left(\mathcal{I}, \mathcal{S}_{1} \times \mathcal{S}_{2}, f, \mathcal{A}, \sigma\right)$$ where $$\begin{aligned}f\left(\left(S_{1}, S_{2}\right), x\right) &=\left(f_{1}\left(S_{1}, x\right), f_{2}\left(S_{2}, x\right)\right) \\\mathcal{A} &=\left\{\left(A_{1}, A_{2}\right) \mid A_{1} \in \mathcal{A}_{1} \text { and } A_{2} \in \mathcal{A}_{2}\right\} \\\sigma &=\left(\sigma_{1}, \sigma_{2}\right)\end{aligned}$$ Show that $\operatorname{Ac}(A)=L_{1} \cap L_{2}$.
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