UNIVERSITY OF CALIFORNIA
Department of Electrical Engineering
and Computer Sciences
Computer Science Division
Prof. R. Fateman
Fall, 2001
Solutions: CS 164 Midterm 1: September 26, 2001, 9:00AM
1. [20 points] Here is a table describing an automaton with 2 states. The start state is S.
a. Draw a diagram of the automaton in the space to the right of the table. I’m not good
at drawing in tex. The expected solution has two states, S and T. From S to itself is an arc
labeled 0,1. From S to T is an arc labeled 0. From T to T is an arc labeled 0. T is a final
stae, S has an incoming arc as the initial state.
b. Write down a simple regular expression that describes the same language that is
recognized by this automaton.
(0 | 1)*0 is the simplest solution.
c. In the space below, draw a DFA that accepts the same language. Use as few states as
possible.
Two states, the same as above except that instead of an arc from S to S labeled 0,1 there
is an arc from T to S labeled 1.
d. Write a context free grammar G0 that describes the same language.
Here’s one.
X -> T0
T -> 0T | 1T | epsilon
2. [5 points] Write down a precise definition of L(G) the language generated by any context
free grammar G.
We expect something like
L(G) = {a1 a2 ...an | ai is in terminals(G), S==>* a1 a2 ... an, S is start(G)}
Or in English.. a set of all strings of terminal symbols derived from the start
symbol S using rules of G.
State Transitions Final State?
0 1
S S,T S
T T yes
1
