Assignment 4
Review questions
6.What is a state transition diagram?
A state transition diagram is a directed graph. Where the nodes of a state diagram are labeled with state names.
7. Why are character classes used, rather than individual characters, for the letter and digit transitions of a state diagram for a lexical analyzer?
Suppose we need a lexical analyzer that recognizes only arithmetic expressions, including variable names and integer literals as operands. Assume that the variable names consist of strings of uppercase letters, lowercase letters, and digits but must begin with a letter. Names have no length limitation. The first thing to observe is that there are 52 different characters (any uppercase or low- ercase letter) that can begin a name, which would require 52 transitions from the transition diagram’s initial state. However, a lexical analyzer is interested only in determining that it is a name and is not concerned with which specific name it happens to be. Therefore, we define a character class named LETTER for all 52 letters and use a single transition on the first letter of any name.
8. What are the two distinct goals of syntax analysis?
The two distinct goals of syntax analysis are first, the syntax analyzer must check the input program to determine whether it is syntactically correct. When an error is found, the analyzer must produce a diagnostic message and recover. The second goal of syntax analysis is to produce a complete parse tree, or at least trace the structure of the complete parse tree, for syntactically correct input.
9. Describe the differences between top-down and bottom-up parsers.
Parsers are categorized according to the direction in which they build parse trees. Top-down parsers is in which the tree is built from the root downward to the leaves. While bottom-up parsers, in which the parse tree is built from the leaves upward to the root.
10. Describe the parsing problem for a top-down parser. The general form of a left sentential form is xAy, whereby our notational conventions x is a string of terminal symbols, A is a nonterminal, and y is a mixed string. Because x contains only terminals, A is the leftmost nonterminal in the sentential form, so it is the one that must be expanded to get the next sentential form in a left- most derivation. Determining the next sentential form is a matter of choosing the correct grammar rule that has A as its LHS. For example, if the current sentential form is
xAy
and the A-rules are A → bB, A → cBb, and A → a, a top-down parser must choose among these three rules to get the next sentential form, which could be xbBy, xcBby, or xay. This is the parsing decision problem for top-down parsers.
Problem Sets
1.Given the following grammar and the right sentential form, draw a parse tree and show the phrases and simple phrases, as well as the handle.
S→AbB | bAc A→Ab | aBB B→Ac | cBb | c a.
a. aAcccbbc
S -> AbB -> aBBbB -> aAcBbB -> aAccBbbB -> aAcccbbc
b. AbcaBccb
S -> AbB -> AbcBb -> AbcAcb -> AbcaBBcb -> AbcaBccb
c. baBcBbbc
S -> bAc -> baBBc -> baBcBbc -> baBcBbbc
2. Show a complete parse, including the parse stack contents, input string, and action for the string id * (id + id), using the grammar and parse table in Section 4.5.3.
3. Show a complete parse, including the parse stack contents, input string, and action for the string (id + id) * id, using the grammar and parse table in Section 4.5.3.
4. Write an EBNF rule that describes the while statement of Java or C++. Write the recursive-descent subprogram in Java or C++ for this rule.
<while_stmt> -> WHILE ‘(‘ (<arith_expr> | <logic_expr>) ‘)’ <block> <block> -> <stmt> | ‘{‘ <stmt> {<stmt>} ‘}’
5. Write an EBNF rule that describes the for statement of Java or C++. Write the recursive-descent subprogram in Java or C++ for this rule.
Assume the following non-terminals are given: <type>, <id>, <literal>, <assign>, <expr>, and <stmt_list>.
<for> -> for ‘(‘ [[<type>] <id> = <expr> {, [<type>] <id> = <expr>}] ; [<expr>] ; [<expr> {, <expr>}] ‘)’ ‘{‘ <stmt_list> ‘}’
