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CSC445, Quiz #2 on PDA’s Instructor: Dr. Hasmik Gharibyan Name________________________________________Score ______________ Total points 15 (1 point each). 1) (0.5 point)Give the sets from where the values of arguments of the transition function of a standard PDA M = (Q, , , , q0, F) are taken (list the sets in the order of arguments) Q, {}, {} 2)(0.5 point)The result of the transition function of a standard PDA M=(Q, , , , q0, F) is an element of the set P (Q ({}) ) 3) (0.5 point) Give the starting machine configuration of the PDA M = (Q, , , , q0, F) with an input string w*. [q0 , w, ] 4) (0.5 point) Give the machine configuration of the PDA M = (Q, , , , q0, F) after successful computation of the input string wL(M). (if you use any element other than , also give the set to whom the element belongs): [qf , , ], where qf F Picture: Diagram of a PDA M = (Q, , , , q0, F) M: a / b /A q0 /A q1 5) Given the PDA M in the picture. a) Define the transition depicted by the loop on q1 (i.e. the arc going from node q1 back to q1) in the picture: (q1, b, ) = ___{[ q1, A ]}____ b) Let the PDA in the picture is specified by the machine configuration [q1, baa, AA] at a particular moment. Define the machine configuration of M after one step of computation is performed (look at the state diagram of the machine): [q1, baa, AA] ├ __ [q1, aa, AAA] ___ c) Are the two transitions depicted in the picture by the two arcs starting in q0 compatible? (yes/no) yes d) Specify the language of the PDA in the picture, if acceptance is standard: by final state and empty stack. (You can give the implicit definition of the set or, if possible, a regular expression): L (M) =____ e) Specify the language of the PDA in the picture, if acceptance is by final state. (You can give the implicit definition of the set or, if possible, a regular expression): LF (M) = {aibj | i,j0} // or a*b* f) Specify the language of the PDA in the picture, if acceptance is by empty stack. (You can give the implicit definition of the set or, if possible, a regular expression): LE (M) = {ai | i >0} // or a+ 6) Given the following piece of diagram of a standard PDA. Give the equivalent piece (using two nodes only) of diagram for an extended PDA : Standard PDA: Extended PDA: b /AA b /A /A a A/ A/ A/ a AAA/ 7) Given the following piece of diagram of a standard PDA. Give the equivalent piece of diagram for an atomic PDA: Standard PDA: Atomic PDA: a /A b A/ /A a / b / A/ 8) For any regular language L there is a Push-Down Automaton (PDA) M such that L(M) = L. (true/false) true 9) There is a language that can be accepted by a PDA but cannot be accepted by a finite state automaton (DFA, NFA, NFA-). (true/false) true 10) (1 point: 0.5 point each) Given two context-free languages: L1 and L2. a) Is the language L=(L1L2)* context-free ?(yes/no/not necessarily)_not necessarily_ b) Is the language L = (L1L2) context-free?(yes/no/not necessarily) _not necessarily_ 11) (2 points: 0.5 points each) Given a context-free language L. According to Pumping Lemma for context-free languages, there is a number k depending on L, such that any string zL , with length(z)k , can be decomposed into five parts z = uvwxy etc. a) Is it possible that k=0 (yes/no) ?____no_______ b) Is it possible that v and x both are (yes/no)?___no_______ c) Let’s say z = abkc. Can v substring contain the a and x substring contain the c? (yes/no)__no____ d) Is the string z’ = uwy a string of the language L (yes/no)?___yes___//0 time pumping

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posted: | 8/26/2011 |

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