1. [4 marks] Consider the grammar:
MethodDecl ? %f)d ParamList R Block
ParamList ? ?
ParamList ? Param ParamListTail
ParamListTail ? ?

ParamListTail ? , Param ParamListTail
Param ? id
Block ? Ñ Statements R
Statements ? ?
Statements ? Statement Statements
Statement ? IfStatement
Statement ? Expression
IfStatement ? f ( xpression )…xpression ? Blockid J.J Expression
Expression ? id
Expression ? id ArgList R
ArgList ? ?
ArgList ? Arg ArgListTail
ArgListTail ? ?
ArgListTail ? Arg ArgListTail
Arg ? Expression
Give a parse tree for the following program fragment. (An id is an identifier, e.g., node.)
def visit(node, func) {
if (node) {
func(node)
if (node.next) {
visit(node.next, func)
}
}
}
2. For each of the following languages, give (i) a context free grammar and (ii) a PDA that
recognizes the language, along with a brief explanation of how the PDA works.
Use the automaton simulator https://automatonsimulator.com/ to create the PDAs. Submit the PDA encodings and and a diagram picture (screenshot) of the PDA.
(a) [8 marks] L = {xny2 mxmy3 n | n ? 0, m > 0}
(b) [8 marks] L = {w ? {x, y, z}? : |w| x = |w| y }
3. [5 marks] Use the pumping lemma to show that the language of strings whose length is a
perfect square is not regular. I.e., L = {w ? {a}? : |a| = n2 , n ? Z}
1
Marking Scheme
1. Marking scheme for Question 1:
Structure
4 points
3 points
2 points
1 points
0 points
Parse tree follows
grammar
productions
Parse
tree
mostly
follows
grammar
productions
Parse tree follows some grammar productions
Parse tree does
not follow grammar productions
Parse tree is not
present
2. Marking scheme for Question 2 (each part):
3 points
2 points
1 points
0 points
Grammar
Grammar is correct or
mostly correct
Approach is correct,
but incorrect grammar
Attempt at grammar
made
No answer provided
PDA
Automaton passes all
tests
Automaton
passes
75% of the tests
Automaton
passes
50% of the tests
Automaton passes
50% of the tests
Explanation
of automaton provided
Partial
explanation
provided
Explanation makes no
sense or not provided
Explanation
3. Marking scheme for Question 3.
3 points
Technique
Argument Follows logically
Clarity
2 points
Has a few gaps
2
1 point
Approrpriate
Has major gaps
Easy to read
0 poin ts
Inappropriate or no proof
No proof
Hard to read or no proof
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