Question

1. Consider the following BNF grammar: NEW STRUCTURE: Non Terminals --> <0> | <1> | <> | <~> | < > | <\/> | </> Terminals --> P | Q | R | I | U | W | X I previously had: I had the terminals and non-terminals labelled backwards Terminals --> <0> | <1> | <> | <~> | < > | <\/> | </> Non - Terminals --> P | Q | R | I | U | W | X Now consider the function F defined by the following structures: <F> --> 0 | 1 | <V> | ~<F> | (<F> \ <F>) | (<F> / <F>) <V> --> P | Q | R | I | U | W | X (2 points) Part 1: Give both the terminal and non-terminal vocabulary of this grammar. Describe the language that this grammar defines, and discuss whether or not you think the grammar is ambiguous. I gave you the terminals and non-terminals, so discuss whether the language is ambiguous or non-ambiguous. Definition of ambiguous: A grammar is ambiguous if and only if it generates a sentential form that has two or more distinct parse trees. HINT: What are the derivations of the language? What are the possibility based on the terminals and the non- terminal values? (2 points) Part 2: Show a parse tree for the sentence "(~(P \/ Q) \/ R)".

          1. Consider the following BNF grammar:
NEW STRUCTURE:
Non Terminals --> <0> | <1> | <> | <~> | < > | <\/> | </>
Terminals --> P | Q | R | I | U | W | X
I previously had: I had the terminals and non-terminals labelled
backwards
Terminals --> <0> | <1> | <> | <~> | < > | <\/> | </>
Non - Terminals --> P | Q | R | I | U | W | X
Now consider the function F defined by the following structures:
<F> --> 0 | 1 | <V> | ~<F> | (<F> \ <F>) | (<F> / <F>)
<V> --> P | Q | R | I | U | W | X
(2 points)
Part 1: Give both the terminal and non-terminal vocabulary of this
grammar. Describe the language that this grammar defines, and discuss
whether or not you think the grammar is ambiguous. I gave you the
terminals and non-terminals, so discuss whether the language is
ambiguous or non-ambiguous.
Definition of ambiguous: A grammar is ambiguous if and only if it
generates a sentential form that has two or more distinct parse trees.
HINT: What are the derivations of the language? What
are the possibility based on the terminals and the non-
terminal values?
(2 points)
Part 2: Show a parse tree for the sentence "(~(P \/ Q) \/ R)".

1. Consider the following BNF grammar:
NEW STRUCTURE:
Non Terminals –> <0> | <1> | <> | < > | < > | <> | </>
Terminals –> P | Q | R | I | U | W | X
I previously had: I had the terminals and non-terminals labelled
backwards
Terminals –> <0> | <1> | <> | < > | < > | <> | </>
Non - Terminals –> P | Q | R | I | U | W | X
Now consider the function F defined by the following structures:
<F> –> 0 | 1 | <V> | <F> | (<F> <F>) | (<F> / <F>)
<V> –> P | Q | R | I | U | W | X
(2 points)
Part 1: Give both the terminal and non-terminal vocabulary of this
grammar. Describe the language that this grammar defines, and discuss
whether or not you think the grammar is ambiguous. I gave you the
terminals and non-terminals, so discuss whether the language is
ambiguous or non-ambiguous.
Definition of ambiguous: A grammar is ambiguous if and only if it
generates a sentential form that has two or more distinct parse trees.
HINT: What are the derivations of the language? What
are the possibility based on the terminals and the non-
terminal values?
(2 points)
Part 2: Show a parse tree for the sentence "( (P Q) R)".

Added by Allison M.

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