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Which of the following problems occur?

i) Does a given program ever produce an output?
ii) If L is a CFL, then is L



                        
                                                                                                
                                        
                                        
                                        
                                            A                                        
                                        
                                        
                                            i, ii, iii, iv                                        
                                    
                                                                    
                                        
                                        
                                        
                                            B                                        
                                        
                                        
                                            i, ii                                        
                                    
                                                                    
                                        
                                        
                                        
                                            C                                        
                                        
                                        
                                            ii, iii, iv                                        
                                    
                                                                    
                                        
                                        
                                        
                                            D                                        
                                        
                                        
                                            iii, iv                                        
                                    
                                                                                    

                        
                            Correct Answer: D
                            i) Is a variation of Turing Machine Halting problem and it is undecidable.



            
                
                    
                    
                        
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                MCQ            
            
        

        
            
                1.
                The definition of a language L with alphabet {a} is given as following. L = { ank | k > 0, and n is a positive integer constant} What is the minimum number of states needed in a DFA to recognize L?
            

            
                                                            
                            
                            A
                            
                                k+1                            
                        
                                            
                            
                            B
                            
                                n+1                            
                        
                                            
                            
                            C
                            
                                2n+1                            
                        
                                            
                            
                            D
                            
                                2k+1                            
                        
                                                

            
                Correct Answer: B
                Note that n is a constant and k is any positive integer. For example, let n=3, then the DFA must be able to accept aaa, aaaaaa, aaaaaaaaa, , .. build such a DFA, 4 states are required.
            
        

        
            
            
                            
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                MCQ            
            
        

        
            
                2.
                Can a DFA simulate NDFA?
            

            
                                                            
                            
                            A
                            
                                No                            
                        
                                            
                            
                            B
                            
                                Yes                            
                        
                                            
                            
                            C
                            
                                Sometimes                            
                        
                                            
                            
                            D
                            
                                Depends on NDFA                            
                        
                                                

            
                Correct Answer: B
                Yes it can be done through power set construction.
            
        

        
            
            
                            
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                3.
                Which of the following problems occur?
i) Does a given program ever produce an output?
ii) If L is a CFL, then is L

            


            
                                                            
                            
                            A
                            
                                i, ii, iii, iv                            
                        
                                            
                            
                            B
                            
                                i, ii                            
                        
                                            
                            
                            C
                            
                                ii, iii, iv                            
                        
                                            
                            
                            D
                            
                                iii, iv                            
                        
                                                

            
                Correct Answer: D
                i) Is a variation of Turing Machine Halting problem and it is undecidable.

            
        


        
            
            
                            
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                4.
                What is the relation between NFA-accepted languages and DFA accepted languages?
            

            
                                                            
                            
                            A
                            
                                >                            
                        
                                            
                            
                            B
                            
                                <                            
                        
                                            
                            
                            C
                            
                                <                            
                        
                                            
                            
                            D
                            
                                <=                            
                        
                                                

            
                Correct Answer: C
                The no of languages accepted by NFA and DFA is equal.
            
        

        
            
            
                            
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                5.
                What is the complement of the language accepted by the NFA shown below? Assume ? = {a} and ? is the empty string.

            

            
                                                            
                            
                            A
                            
                                ?                            
                        
                                            
                            
                            B
                            
                                ?                            
                        
                                            
                            
                            C
                            
                                a                            
                        
                                            
                            
                            D
                            
                                {a, ?}                            
                        
                                                

            
                Correct Answer: B
                The given alphabet ? contains only one symbol {a} and the given NFA accepts all strings with any number of occurrences of 
            
        

        
            
            
                            
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