1. A decimal constant is any sequence of one or more decimal digits (including one
starting with zero). A hexadecimal constant has the form 0xW where W is a sequence of
one or more decimal digits or the letters A-F.
(a) Write a finite-state machine to recognize either decimal or hexadecimal constants.
Label each state with either S (start state), D (decimal constant), H (hexadecimal
constant), or N (neither).
(b) Write a regular expression to recognize either a decimal or hexadecimal constant.
2. Define finite-state machines for the following regular expressions over the characters a
and b. Label each node either S (start), A (accept the string) or R (reject it).
(a) a(a|b)*
(b) aa*b(b|a)*
(c) (b|a)*a*ab(b|a)*
3. (a) Write a regular expression for this language: semicolon-separated lists of aโ and
bโs, in square brackets. Examples of strings in the language are [], [a], and [a;b;a;a].
(b) Then write a finite-state machine for the language. Each state should be labeled either
as S (for the start state), A (for an accepting state), or E (for an error state).
4. Write an ocamllex specification for tokens of this type:
type token = LESSTHAN | LEFTSHIFT | LEFTSHIFTEQ | IDENT of string
where these represent, respectively, the sequence โ<โ, โ<<โ, โ<<=โ, and any string
starting with a letter and consisting solely of letters and digits. Your specification should
return the next token in the input, ignoring any character other than the ones that
constitute tokens.