3 Homework 10 points
Note, these exercises may be done in groups of one, two, or three. Working with someone else is strongly recommended. If more than one person is involved, list all the names on ONE set of answers. Groups may change throughout the term. Working in groups is a BIG plus for you. Take advantage of it. If you work in groups, you must work in the group for the ENTIRE assignment. It is considered cheating if you work with someone else for some of the answers, but turn in an individual copy of the answers. It is an all or nothing situation. You can't work together on some questions and alone on some. Sometimes I see an individual whose name is listed in two groups. This is strictly forbidden and is considered cheating. You cannot work in two groups. Assignments are due at the beginning of class and should be typed.
For this assignment, use the following notation for regular expressions
o o o o o o
a|b (or) ab (and - concatenation) (a) (grouping) a* (kleene closure - zero or more repetitions) a+ (one or more repetitions) a? (optional)
Some extensions to make writing easier (PERL) [abc] one of a or b or c [a-z] anything from a to z inclusive [a-zA-Z] anything from a to z or A to Z inclusive [^abc] anything but a, b, or c . Any character except newline Other pattern matching capabilities are NOT part of regular expressions and should not be used.
Chapter 4 Syntax
1. Write the following regular expressions Write the regular expression which defines a language in which the total number of b's is divisible by two, such as aabaabbaba Write the regular expression which defines a language in which three b's never occur together. Note that you must show that every string that fits the description can be generated and nothing that does not fit the description is generated.
1
2. Consider the grammar below where , , and are some unspecified binary operators. E TE | E T |T T F T |F F (E) |a What kind of associativity does have? What kind of associativity does have? What kind of associativity does have? What operation has higher precedence or are they equal? 3. In English, what language is generated by the following grammar? Be as precise as possible. indicates the empty string. T aTb|bTa| 4. Here is a simple grammar for conditionals in a language. I've turned some nonterminals into terminals for simplicity. Demonstrate the grammar is ambiguous. Notice that ::== is used in place of the . The meaning is the same
Statement ::= Conditional | OTHER Conditional ::= IF TEST THEN Statement | IF TEST Statement THEN ELSE Statement
5. In C and Java, expressions have the form
exp
exp '-' sub_exp
| sub_exp
sub_exp
'(' type_name ')' sub_exp
| | | | '-' sub_exp id literal '(' exp ')'
type_name
id
| more_complex_type_descriptions
This allows expressions like: 1, a, a - 1, ( a ), ( a - 1 ), - a, ( int ) a . Demonstrate that the grammar is ambiguous. 6. In English, describe what language is generated by the following grammar? Be as precise as possible. indicates the empty string. B BB|(B) |
2
7. A nested comment is a comment within a comment. Many programming languages do not allow nested comments. Given what you know about grammars, why is this restriction made? 8. Consider the grammar G represented by the four tuple = ({E,T,F},={+,*,(,),a}, P,E) where P is the set of productions E E + T |T TT * F |F F (E) |NUM For this grammar, draw a parse tree and an abstract syntax tree (in which only the terminal symbols are shown) for 3 *(4 + 5)+(6+7) 9. Using the BNF grammar for expressions (as in the previous problem), add operators % for mod and ^ for exponentiation. Recall that mod is left-associative (like division) and that power is right associative. Test out your grammar to verify that it works. 10. Syntax diagrams show the rules in a railroad diagram. A variable declaration section in Pascal has the following form:
var <identifier>, <identifier>,...,<identifier>:<type_name>; <identifier>, <identifier>,...,<identifier>:<type_name>; ... <identi...