Question

is the language defined by the following regular expression regular? (i.e., can one construct a finite automaton that recognizes strings in this language?) [a-za-z]([a-za-z$0-9]*) true false

Answer 1

The language specified by the regular expression [a-za-z]([a-za-z$0-9]*) is regular, as it describes a set of strings that start with an alphabetic character followed by any combination of alphanumeric characters or the dollar sign, which can be recognized by a finite automaton.

Step-by-step explanation:

The language defined by the regular expression [a-za-z]([a-za-z$0-9]*) is indeed regular. This is because regular expressions are used to describe regular languages, and regular languages are those that can be recognized by a finite automaton. The given regular expression specifies a language that starts with an alphabetical character (either lowercase or uppercase) and is followed by zero or more characters that can be either alphanumeric or the dollar sign ($).

To construct a finite automaton (FA) for this language, one would begin with a start state that transitions to an accept state upon reading an alphabetical character. From this accept state, there would be transitions back to itself for every character in the set [a-zA-Z0-9$], allowing for the concatenation of these characters. Since FAs are capable of capturing this repetitive and concatenative behavior, it confirms that the language is regular.