Spring 2002 91.304 FCS Quiz 1 Announcement

The exam covers through Example 2.4.5, page 36, in TCGI  and material in the lectures.
The exam is closed book.  In outline, the exam is as below. There is no question on Quiz 1
requiring you to use mathematical induction, but it is almost certain that you will be required
to do so on Quiz 2 or the Final Exam.  No further information on Quiz 1 will be provided.

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Spring 2002

91.304, Section 201                            Name: _____________________

Quiz 1 The exam is closed book. Please do not discuss it with anyone until it is returned. Put your
name on both this sheet and the blue book. You can use diagrams in your answers (except
in problem 2(a)) if you prefer. Write your answers on this sheet after working out your
solutions in your blue book, and turn in both this sheet and your blue book.

1.  Consider the domain D = {a,...} and the binary relation R = {<a,b>, ...}.
    What is
     (a) (10 points) the reflexive closure of R on D?    R =
     (b) (10 points) the symmetric closure of R on D? R =
     (c) (10 points) the transitive closure of R on D?   R =
     (d) (10 points) the equivalence (reflexive-symmetric-transitive) closure of
           R on D? R =

2.  Consider the NFA M=<Q,S ,D ,s,F>, where Q={q0,...}, S ={a,b},
    D={<q0,e,q1>, ...}, s=q0, and F={q1,...}.
    (a) (10 points) Write a regular expression re that denotes L(M), the language
        accepted by the NFA M. re =
    (b) (50 points) Using the construction described in the proof of TCGI
        Theorem 2.3.1, construct a DFA M'=<Q',S ,D ',s',F'> that is equivalent
        to the NFA M.