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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 lowercase 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?
- 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. In this case, recovery means it must get back to a normal state and
continue its analysis of the input program. This step is required so that the
compiler finds as many errors as possible during a single analysis of the input
program. If it is not done well, error recovery may create more errors, or at
least more error messages. 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. The parse tree (or its trace) is used as the basis
for translation.
9. Describe the differences between top-down and bottom-up parsers.
- Top-down, meaning they construct left most derivations and a parse tree in top-down order, which mean the tree is built from the root downward to leaves. In bottom-up order the parse tree is built from 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 non terminal, and y is a mixed string. Because x contains only terminals, A is the leftmost non terminal 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.
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Problem Set :
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6. 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
7. 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.
Stack Input Action
0 id * (id + id) $ Shift 5
0id5 * (id + id) $ Reduce 6 (Use GOTO[0, F])
0F3 * (id + id) $ Reduce 4 (Use GOTO[0, T])
0T2 * (id + id) $ Reduce 2 (Use GOTO[0, E])
0T2*7 (id + id) $ Shift 7
0T2*7(4 id + id ) $ Shift 4
0T2*7(4id5 + id ) $ Shift 5
0T2*7(4F3 + id ) $ Reduce 6 (Use GOTO[4, F])
0T2*7(4T2 + id ) $ Reduce 4 (Use GOTO[4, T])
0T2*7(4E8 + id ) $ Reduce 2 (Use GOTO[4, E])
0T2*7(4E8+6 id ) $ Shift 6
0T2*7(4E8+6id5 ) $ Shift 5
0T2*7(4E8+6F3 ) $ Reduce 6 (Use GOTO[6, F])
0T2*7(4E8+6T9 ) $ Reduce 4 (Use GOTO[6, T])
0T2*7(4E8 ) $ Reduce 1 (Use GOTO[4, E])
0T2*7(4E8)11 $ Shift 11
0T2*7F10 $ Reduce 5 (Use GOTO[7, F])
0T2 $ Reduce 5 (Use GOTO[0, T])
0E1 $ Reduce 2 (Use GOTO[0, E])
–ACCEPT–
0 id * (id + id) $ Shift 5
0id5 * (id + id) $ Reduce 6 (Use GOTO[0, F])
0F3 * (id + id) $ Reduce 4 (Use GOTO[0, T])
0T2 * (id + id) $ Reduce 2 (Use GOTO[0, E])
0T2*7 (id + id) $ Shift 7
0T2*7(4 id + id ) $ Shift 4
0T2*7(4id5 + id ) $ Shift 5
0T2*7(4F3 + id ) $ Reduce 6 (Use GOTO[4, F])
0T2*7(4T2 + id ) $ Reduce 4 (Use GOTO[4, T])
0T2*7(4E8 + id ) $ Reduce 2 (Use GOTO[4, E])
0T2*7(4E8+6 id ) $ Shift 6
0T2*7(4E8+6id5 ) $ Shift 5
0T2*7(4E8+6F3 ) $ Reduce 6 (Use GOTO[6, F])
0T2*7(4E8+6T9 ) $ Reduce 4 (Use GOTO[6, T])
0T2*7(4E8 ) $ Reduce 1 (Use GOTO[4, E])
0T2*7(4E8)11 $ Shift 11
0T2*7F10 $ Reduce 5 (Use GOTO[7, F])
0T2 $ Reduce 5 (Use GOTO[0, T])
0E1 $ Reduce 2 (Use GOTO[0, E])
–ACCEPT–
8.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.
9. 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>} ‘}’
10. 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> ‘}’
