Sergio A. Alvarez web: http://www.cs.wpi.edu/ alvarez/
Department of Computer Science e-mail: alvarez@cs.wpi.edu
Worcester Polytechnic Institute phone: (508) 831-5118
Worcester, MA 01609, USA fax: (508) 831-5776

CS 3133, A Term 1998
Midterm Exam Practice Problems

Solutions now available

1. Find a regular expression for each of the following languages over the alphabet :
   1. all strings in which any a's precede all b's (in a left-to-right scan).
   2. all strings that do not contain the substring bb.
2. Construct a context-free grammar over the alphabet that generates the language . Use three nonterminal symbols .
3. Is the language defined in the preceding problem regular? If you answer yes, give a regular expression that describes the language. Otherwise, prove that the language is not regular.
4. Consider the machine M over having state set , start state A, accepting state set , and transition function satisfying and for all other pairs .
   1. Draw the state transition diagram of the machine M.
   2. Find a regular expression for the language L(M).
5. Define a context-free grammar G over as follows.

   

   1. Give a leftmost derivation in G for the string acaacb.
   2. Find a regular expression for the language L(G).
   3. Construct a nondeterministic finite automaton M with possible lambda transitions (i.e., an NFA- ) that accepts L(G).
   4. Construct a deterministic finite automaton (DFA) equivalent to the NFA- that you found above in part (3) of this problem.

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