CS 434 Exam 1
Spring 2004
Solution
1. Show this grammar is ambiguous by drawing 3 distinct parse trees for the string xyz.
S
A
B
C
D
E
F
→
→
→
→
→
→
→
AB | CD | E
xAy | 
zB | 
xC | 
yDz | 
xEz | F
yF | 
2. List every string with length exactly 6 that is generated by the grammar of problem 1.
xxxxxx
xxxxyz
yyyyyy
xyyyyz
zzzzzz
xyzzzz
xxxyyy
yyyzzz
xxxzzz
xxyyzz
3. Construct a context-free grammar that generates arithmetic expressions using
operators –, +, /, * with the precedence levels and associativities as specified below.
Assume that arbitrary operands are denoted by id, so this string could be generated:
id+(id–id*id)/id
Operator Precedence Associativity
–
1st (highest)
left
+
2nd
right
/
3rd
right
th
*
4 (lowest)
left
S
T
U
V
W
→
→
→
→
→
S*T
U/T
V+U
V–W
(S)
|
|
|
|
|
T
U
V
W
id
4. List every string with length at most 5 that is accepted by this finite-state machine:
01
10
0001
1110
0010
1101
0100
1011
1000
0111
5. Draw a deterministic finite-state machine that accepts strings over alphabet {@, #, $}
such that the difference (number of @’s minus number of #’s) is not a multiple of 3.
Example: @$@#$@#$@ should be accepted because (4 – 2) is not a multiple of 3.
Hint: this DFSM can be drawn with as few as 3 states.
6. List every string with length at most 4 that is generated by this regular expression:
(ba*c | ca*b)+
bc
cb
bac
cab
baac
caab
bcbc
cbcb
bccb
cbbc
7. Construct a regular expression that generates the strings over alphabet {a, b} that do
not contain substring aa and also do not contain substring bb.
(ab)* | (ab)*a | (ba)* | (ba)*b
8. Suppose you have downloaded from the Internet a de-compiler that converts MIPS
machine code into Java, and this de-compiler is written in MIPS machine code. Suppose
you also have access to a MIPS machine. Draw a tombstone diagram that shows how to
construct a de-compiler from MIPS to Java that is written in Java.
MIPS
 Java
MIPS
MIPS
MIPS
 Java
 Java
Java
MIPS
MIPS
9. Identify a syntax error, a scope error, and a type error in this C++ code. Briefly but
precisely describe each error.
class B {
int w;
public:
void g ( )
B (int a) { w=a; }
B * j ( ) { return w; }
int f ( ) { return a; }
};
// Syntax error: missing ‘;’ or ‘{}’
// Type error: ‘w’ is int, not B*
// Scope error: ‘a’ is undefined
10. First explain a restriction in the C++ language that seems to indicate that a single-pass
compiler will be used. Next explain a feature of the C++ language that appears to
indicate that a multi-pass compiler must be used. Briefly justify your answers.
Single-pass: Most names must be declared before they can be used.
– C++ ordinary functions must be declared before they can be called.
– C++ classes must be declared before they can be used as type names.
Multi-pass: Some names can be used before they are declared (forward references).
– C++ instance variables can be accessed before they are declared.
– C++ member functions can be invoked before they are declared.