Theory of Computation — CSE 105
Regular Languages
Study Guide and Homework I
Homework I:
Solutions to the following problems should be turned in
class
on
July 12, 1999.
Instructions:
Write your answers clearly and completely.
Please use 8.5
11 inches paper.
Use a
stapler or a clip to attach the individual pages. Write your name.
When presenting any construction, for example, an algorithm or an automaton, please
give an overview of the main ideas and then present the construction. Always support the
correctness of your construction with a short informal proof.
1. For each of the languages given below, design finite state automata and regular expressions
to recognize them. In all cases the alphabet is
.
(a)
does not contain the substring 110
(b)
contains an even number of 0’s, or exactly two 1’s
2. Problem 1.26, Page 88.
3. Problem 1.42, Page 90. Provide a short proof of the correctness of your construction.
4. Prove the following languages nonregular:
(a)
is a prime ;
(b) Let
Here,
contains all columns of 0’s and 1’s of height two. A string of symbols in
gives two rows of 0’s and 1’s. Consider each row to be a binary number and let
the bottom row of
is the reverse of the top row of
1
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Study Guide:
In the following, the material on regular languages (chapter 1) is broken down
into a number of short topics. For each topic, a list of specific items and problems are provided.
If you understand these items and solve the problems, you would do very well in the course.
1
Deterministic Finite Automata (DFA)
Topics:
The notion and definition of DFA, presentation of DFA by transition diagrams, the
notion of acceptance by a DFA, the class of regular languages, techniques for designing DFAs,
and closure operations.
Designing DFAs
1. 1.1, 1.2, and 1.3, pages 83 and 84.
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 Summer '99
 Paturi
 Formal language, Regular expression, Regular language, Nondeterministic finite state machine, Automata theory

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