## CSci 3501 Algorithms and Computability - Lab 12.

#### Due Wednesday, November 30 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 push-down automata,
the pumping lemma for context-free languages, and Turing machines.

#### Task 1: push-down automata (6 points)

Please refer to Constructing
a push-down automaton section in JFLAP.

- 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.

#### Task 2: Play the context-free "pumping lemma game" (7 points)

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. Clearly describe the strategy.

- 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

#### Task 3: Turing machines (12 points)

Use JFLAP tutorial on Turing machines to construct and test a Turing machine that decides the language a^n b^n c^n, where n >= 0.

#### 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.

The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota.