CSci 3501 Algorithms and Computability - Lab 11.
Due Wednesday, November 10th at 11:59pm
What to submit and when:
- All submissions are electronic: by e-mail to elenam at morris.umn.edu and CC to all lab
partners. Please do not delete your e-mail from "Sent mail" or your
mailbox until the end of the semester.
- When working on the lab, please comment your work so that it is
clear what contributions of each person are.
- At the end of the lab each group should send me the results of their
in-class work. Please indicate if this is your final submission.
- If your submission at the end of the lab time was not final,
please send me(CC to the lab partner(s)) a final copy before the due
time. Please use the subject "3501 Lab N", where N is the lab
number.
Lab assignment
Work in pairs
Lab overview and goals
The goal of the lab is to get practice with context-free grammars,
push-down automata, and the pumping lemma for context-free languages.
Context-free grammars and pushdown automata (20 points)
Please refer to the corresponding sections of
the JFLAP tutorial,
namely Entering
grammars (just pressing "enter" in RHS enters an empty
string),
Brute
Force Parser for constructing parse trees,
and Constructing
a push-down automaton.
Your tasks are as follows:
- A context-free grammar for odd-length strings of alternating zeros and ones
- A context-free grammar of strings of a,b that has more
occurrences of "a" than occurrences of "b". The order of letters is
arbitrary. Test your automaton on strings baaba and aaab and export
the corresponding parse trees as jpg files.
- A context-free grammar for a language of 0, 1, true, false,
operations
<,
>, ==
, a ternary conditional operator ?:
, and parentheses.
The comparison operations have higher precedence than the
conditional.
The conditional operator is defined as following:
e1? e2 : e3
evalautes e1, and if it is true then it evaluates and returns e2,
otherwise e3. For example:
0 < 1? 0 : 1
returns 0. <, >, ==
are left-associative, i.e.
0 == 1 == true
should be interpreted as
(0 == 1) == true
(and is expected to return false).
The conditional is right-associative:
0 > 1 ? 0 : 0 == 0 ? 1 : 0
is interpreted as
0 > 1 ? 0 : (0 == 0 ? 1 : 0)
and is expected to return 1.
Test your grammar on all of the test cases above and two more cases that
check for precedence, associativity, and parentheses. Submit jpg files
for the parse trees. Note that
language designers
don't always get the associativity
right.
Important: your grammar must enforce the right
precedence and associativity for all operations. Your write-up for
this problem should briefly explain how this is done.
- A pushdown automaton for the language of strings a^k followed by
any number of b followed by c^k (do not convert your grammar from
the previous question into an automaton or vice versa)
- A pushdown automaton for the language of strings a^n b^m where n
<= m.
- A pushdown automaton for strings w1 w2 where w2 contains a
reversed w1 as a substring. The alphabet is 0,1. Assume that w1 has
at least one symbol.
Convert context-free grammars to pushdown automata (3 points)
Use the option
Convert
CFG to PDA (LL) for this problem. In a plain-text file explain
what rules were added to the PDA and why.
- Convert the grammar for the language of palindromes to a
PDA. The alphabet is 0,1. Submit the resulting PDA.
Play the context-free "pumping lemma game" (7 points) -- moved to
the next lab
Use the tutorial
for the pumping lemma. Play the "pumping lemma game" for the
following examples. For each example state whether the language is
context-free; justify it based on which side has a winning strategy in
the pumping lemma game.
- The third language (a^n b^j a^n b^j, n >= 0, j >= 0) -- computer
goes first.
- The eighth language (a^k b^n c^n d^j: j not equal to k) -- you go
first
What to submit
- Submit your JFLAP files as attachments, CC your group. Make sure
to submit your automata
files (as .jff) and your input data (as .txt). Make sure to follow the naming requirements! Make it clear which
data refers to which automaton.
CSci 3501
course web site.