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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 8 pages in this exam and 4 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 20
2 30
3 25
4 25
TOTAL 100
Problem 1: Miscellaneous [20 points]
1) [4 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) [4 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) [4 points] CYK parser accepts arbitrary context-free grammars. This is because
the CYK parser implicitly disambiguates these grammars.
True or False
4) [4 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) [4 points] There are languages that can be represented by NFAs but not by DFAs.
True or False
Part 1. [15 points] Show the edges added for this string by the Earley parser:
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. [5 points] Is the grammar ambiguous? Circle one. YES NO due to the P P|P rule
Part 3. [5 points] How many parse trees did the Earley parser discover? __ 1_____
Part 4. [5 points] Draw below three (3) edges that 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: Representation Conversions [25 points]
Part 1. [8 points] Convert the following grammar to a regular expression, or concisely
justify why this is not possible. Note: we do not care about the parse tree; the regular
expression must represent the same set of strings as the grammar. Hint: write a few
strings from the language and find a regular pattern, if possible.
ARITHMETIC CFG:
E A | M | 0 | 1
A E + E
M E * E
YOUR REGEX:
Justification:
Part 2. [8 points] Same problem as above but for a different grammar: Hint: write a
few strings from the language and find a regular pattern, if possible.
Reverse Polish Notation CFG:
E E E +| E E * | 0 | 1
YOUR REGEX:
Justification: Due to a mistake on our part, we made this problem
harder than originally intended. As a result, all of you got full credit. Some
of you received an extra credit for making good observations about the
wrong grammar.
As some of you noticed, the grammar in the problem was not a correct
RPM grammar. The correct RPN grammar is given above. The (correct)
RPN grammar cannot be expressed as a regular language. Informally, it is
because the grammar generates strings of the form 00+, 000++, 00+0+,
etc, where the ‘+’s, viewed as binary operators, must always have zeros on
the left; these zeros could be results of the evaluations. So there is a
counting argument: one needs to keep track of the generated zeros in
order to generate the right number of ‘+’s. Similar argument applied to the
more complex grammar in the problem.
Problem 4: Grammars and Syntax Directed Translation [25 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 [7 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 | } |. |
Backslashes may appear in the text lexeme when followed by by „}‟ or „\‟ characters.
Backslashes may also be followed by “emph{”; this forms the open token. Anything else
is a lexical error.
Syntax of regular expressions: you can use Python, including raw strings, but you can
also use JavaScript regexes. Please underline your choice.
Lexeme regular expression Token \emph{ (^) /\emph{/ open } /}/ close Text /(\[}\]|[^\}]|\n)/*^ Text
