Exercises 1

Exercise 1

Assume the following extensions to the regular expressions. In each case describe why the modification does not actually change the expressibility.

• The intersection of two regular expressions.
• The optional expression denoting that expression optional
• Limiting Kleene repetition with a maximum and minimum bound

Design your own operator that extends regular expressions to make it possible to express nested comments.

Exercise 2

Convert the following NFAs to deterministic finite automata.

Exercise 3

Integer literals are in three forms in Scala: decimal, hexadecimal and octal. The compiler discriminates different classes from their beginning. Decimal integers are started with a non-zero digit. Hexadecimal numbers begin with 0x or 0X and may contain the digits from 0 through 9 as well as upper or lowercase digits A to F afterwards. If the integer number starts with zero, it is in octal representation so it can contain only digits 0 through 7. There can be an l or L at the end of the literal to show the number is Long.

• Draw a single DFA that accepts all the allowable integer literals.
• Write the corresponding regular expression.

Exercise 4

Design a DFA which accepts all the binary numbers divisible by 6. For example your automaton should accept the words 0, 110 (6 decimal) and 10010 (18 decimal).

Exercise 5

Let be the language of strings on defined by that is, .

• Construct a DFA that accepts .
• Describe how the lexical analyzer will tokenize the following inputs.
• <=====
• ==<==<==<==<==
• <=====<

Exercise 6

For each of the following languages find the first set. Determine if the language is nullable.

(a|b)*(b|d)((c|a|d)* | a*)