CSci 3501 Algorithms and Computability - Lab 10.

Due Wednesday, December 10th at 11:59pm

What to submit and when:

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 (13 points)

Please refer to the corresponding sections of the JFLAP tutorial, namely Entering grammars (just pressing "enter" on the right hand side enters an empty string), Brute Force Parser for constructing parse trees, and Constructing a push-down automaton.

Your tasks are as follows:

  1. A context free grammar for the language of strings a^n b^m, where n >= m
  2. A context free grammar for the language of strings a^k followed by any number of b followed by c^k
  3. A context-free grammar for a language of 0, 1, true, false, operations <, >, == , a ternary conditional operator ?:, and parentheses. The order of precedence is as follows: parentheses, the comparison operations, the conditional operator and then 0, 1, true and false (all at the same level).

    The conditional operator is defined as following:

    e1? e2 : e3
    evalautes e1, and if it is true then it evaluates and returns e2, otherwise it evaluates and returns e3. For example:
     0 < 1? 0 : 1
    would be interpreted as
    (0 < 1) ? 0 : 1
    which becomes
    true ? 0 : 1 
    after the condition is evaluated, which would in turn result in 0.

    The comparison operators <, >, == are left-associative, i.e. i.e.

    0 == 1 == false
    should be interpreted as
    (0 == 1) == false
    which evaluates to
    false == false
    which is true.

    The conditional is right-associative:

     0 > 1 ? 0 : 0 == 0 ? 1 : 0
    is interpreted as
    (0 > 1) ? 0 : ((0 == 0) ? 1 : 0) 
    then evaluated as
    false ? 0 : ((0 == 0) ? 1 : 0)
    then as
    false ? 0 : (true ? 1 : 0)
    then as
    false ? 0 : 1
    which will 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 correct precedence and associativity for all operations. Your write-up for this problem should briefly explain how this is done.

  4. 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)
  5. A pushdown automaton for the language of strings a^n b^m where n <= m.

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.

What to submit

CSci 3501 course web site.

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