## 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 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.

1. 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)
2. 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.

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.