can you help me in automata questions, Theory of Computation

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i have some questions in automata, can you please help me in solving in these questions?

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Decision problems of regular languages, We'll close our consideration of re...

We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.

Recognition problem, The Recognition Problem for a class of languages is th...

The Recognition Problem for a class of languages is the question of whether a given string is a member of a given language. An instance consists of a string and a (?nite) speci?cat

Example of finite state automaton, The initial ID of the automaton given in...

The initial ID of the automaton given in Figure 3, running on input ‘aabbba' is (A, aabbba) The ID after the ?rst three transitions of the computation is (F, bba) The p

Language accepted by a nfa, The language accepted by a NFA A = (Q,Σ, δ, q 0...

The language accepted by a NFA A = (Q,Σ, δ, q 0 , F) is NFAs correspond to a kind of parallelism in the automata. We can think of the same basic model of automaton: an inpu

Find regular grammar : a(a+b)*(ab*+ba*)b, Find the Regular Grammar for the ...

Find the Regular Grammar for the following Regular Expression:                    a(a+b)*(ab*+ba*)b.

Non-determinism - recognizable language, Our DFAs are required to have exac...

Our DFAs are required to have exactly one edge incident from each state for each input symbol so there is a unique next state for every current state and input symbol. Thus, the ne

Reducibility among problems, A common approach in solving problems is to tr...

A common approach in solving problems is to transform them to different problems, solve the new ones, and derive the solutions for the original problems from those for the new ones

Class of recognizable languages, Proof (sketch): Suppose L 1 and L 2 are ...

Proof (sketch): Suppose L 1 and L 2 are recognizable. Then there are DFAs A 1 = (Q,Σ, T 1 , q 0 , F 1 ) and A 2 = (P,Σ, T 2 , p 0 , F 2 ) such that L 1 = L(A 1 ) and L 2 = L(

Closure properties of recognizable languages, We got the class LT by taking...

We got the class LT by taking the class SL and closing it under Boolean operations. We have observed that LT ⊆ Recog, so certainly any Boolean combination of LT languages will also

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