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First Midterm Exam
CS164, Fall 2007
Oct 2, 2007
Please read all instructions (including these) carefully. Write your name, login, and SID. No electronic devices are allowed, including cell phones used as watches. Silence your cell phones and place them in your bag. The exam is closed book, but you may refer to one (1) page of handwritten notes. Solutions will be graded on correctness and clarity. Each problem has a relatively simple and straightforward solution. Partial solutions will be graded for partial credit. There are 9 pages in this exam and 5 questions, each with multiple parts. If you get stuck on a question move on and come back to it later. You have 1 hour and 20 minutes to work on the exam. Please write your answers in the space provided on the exam, and clearly mark your solutions. You may use the backs of the exam pages as scratch paper. Do not use any additional scratch paper.
LOGIN: _______________________
NAME: _______________________
SID: _______________________
Problem Max points Points
1 17
2 24
3 20 4 15
5 24
TOTAL 100
Problem 1: Miscellaneous [XYZ points]
1) [XYZ points] Circle pairs of regular expressions that are equivalent (in that they
describe the same sets of strings):
a. (ab)+ (ab)*ab
b. ab* (ab)*
c. (a|b+) (a|(b)+)
d. a+* a+
2) [XYZ points] Tokenize the following fragments of Java programs. Each fragment
contains an error but tokenization is still possible. Indicate tokenization by drawing ‘|’ characters between lexemes.
a. int j = a ++ b;
b. int j = a+++++b;
c. int $foo ( int a ) { return 1; }
3) [XYZ points] CYK parser accepts arbitrary context-free grammars. This is because
the CYK parser implicitly disambiguates these grammars.
True or False
4) [XYZ points] A language is a set of strings. REGEX is the set of all languages that
can be described with regular expressions and CFG is the set of all languages that
can be described by context free grammars. Which relationship holds? Circle all
applicable smileys. Answer: A B C D E F
A REGEX is a strict subset of CFG
B REGEX is a subset of CFG
C REGEX is equal to CFG
D REGEX is a superset of CFG
E REGEX is a strict superset of CFG
F None of the above
5) There are grammars that can be represented by NFAs but not by DFAs.
True or False
Part 1. [XYZ points] Show the edges added for this string by the Earley parser:
int Fun int id ( P ) { B } P id | P , P E id | E ( A ) A E | E , A B E
int Fun int id ( P ) { B } P id | P , P E id | E ( A ) A E | E , A B E
id Fun int id ( P ) { B } P id | P , P E id | E ( A ) A E | E , A B E
( Fun int id ( P ) { B } P id | P , P E id | E ( A ) A E | E , A B E
id Fun int id ( P ) { B } P id | P , P E id | E ( A ) A E | E , A B E
, Fun int id ( P ) { B } P id | P , P E id | E ( A ) A E | E , A B E
id Fun int id ( P ) { B } P id | P , P E id | E ( A ) A E | E , A B E
) Fun int id ( P ) { B } P id | P , P E id | E ( A ) A E | E , A B E
{ Fun int id ( P ) { B } P id | P , P E id | E ( A ) A E | E , A B E
id Fun int id ( P ) { B } P id | P , P E id | E ( A ) A E | E , A B E
} Fun int id ( P ) { B } P id | P , P E id | E ( A ) A E | E , A B E
Part 2. [XYZ points] Is the grammar ambiguous? Circle one. YES NO
Part 3. [XYZ points] How many parse trees did the Earley parser discover? _______
Part 4. [XYZ points] Draw below three (3) edges that were would be placed by the
CYK parser but were not placed by the Earley parser. Label the edges in CYK style.
int id ( id , id ) { id }
Problem 3: Left-recursion Elimination [XYZ points]
This is a simplified grammar for regular expressions (we left out concatenation).
R -> R '|' R | R '*' | '(' R ')' | 0 | 1
Part 1. [XYZ points] Write down the formula for eliminating left recursion. The
formula should contain and :
Part 2. [XYZ points] What is and in the above grammar?
Part 3. [XYZ points] Write a non-recursive CFG that recognizes the same language as
the above grammar.
Part 3. [XYZ points] Convert the following automaton into a regular expression. Show
each step: first eliminate node 2, then node 3.
Problem 5: Grammars and Syntax Directed Translation [XYZ points]
In this question we will design and implement (a tiny subset of) a language that will
simplify development of HTML documents. Wikis already come with such a formatting
language but we want something closer to a professional language like LaTeX.
We focus on a single aspect of the formatting language: adding emphasis to text by using
an italics font. The tricky part is nested emphasis: we want to emphasize text that is
already within emphasized text. In the previous sentence, the text “already within” is an
emphasis nested within a bigger enclosing emphasis.
In HTML, the example sentence would need to be written as follows.
The only tricky part is nested emphasis: we want to emphasize text that is already within an emphasized text.
Note that HTML does not support nested emphasis. To support it, we had to turn off
italics before the nested emphasis (before “ already within”). In our language we want to
make things clean and readable; we‟ll indicate beginning and end of emphasis fragments:
The only tricky part is \emph{nested} emphasis: \emph{we want to emphasize text that is \emph{already within} an emphasized text}.
Part 1 [XYZ points]: Write regular expressions for the lexemes in the language. You
want to tokenize the input as indicated below with |.
| The only tricky part is | \emph{ | nested | } | emphasis: | \emph{ | we want to emphasize text that is | \emph{ | already within | } | an emphasized text | } |. |
If the document contains a backslash followed by anything other than “emph”, report a
lexical error. The text lexeme may contain escaped „}‟ and „\‟ characters. That is, it can
contain pairs of characters „}‟ and „\‟.
Lexeme regular expression token \emph{ open } close text Text error -- report error
