Regular Expressions for Lexical Analyzer Token Classes

To design a lexical analyzer, we typically write regular expression rules that the scanner tries to match against the input stream. Key practical concerns are (1) correctly expressing the token language, and (2) ensuring the scanner prefers the longest match so that operators like $<=$ are not split as $<$ followed by $=$. This “maximal munch” / longest-match behavior is standard in scanner construction.

Below are regular expressions for:

1. Identifiers: begin with a letter; then contain only letters and digits
2. Unsigned integer constants
3. Relational operators: $<, <=, >, >=, ==, !=$

We’ll use a common character-class convention: [A-Za-z] for letters and [0-9] for digits.

Key terms: lexical analyzer, token class, maximal munch, relational operator.

(i) Identifiers (start with letter, then letters/digits)

An identifier starts with one letter and then can be followed by zero or more letters or digits.

Regular expression:

• ([A-Za-z])([A-Za-z0-9])*
• Equivalent compact form: [A-Za-z][A-Za-z0-9]*

Notes

• The * allows identifiers with no trailing characters beyond the first letter (e.g., a).
• If your language forbids keywords as identifiers, you’d typically do a second-stage check: match IDENT via the regex, then remap matched lexemes that equal reserved words.

Key terms: identifier, character class, Kleene star, reserved keyword.

(ii) Unsigned integer constants

An unsigned integer constant is a sequence of one or more digits.

Regular expression:

• [0-9]+

Notes

• + requires at least one digit, so empty strings do not match.
• If you want to restrict leading zeros (e.g., disallow 00), that would require a different regex; the prompt does not impose such restrictions.

Key terms: integer constant, unsigned, digit, quantifier.

(iii) Relational operators: <, <=, >, >=, ==, !=

These are specific multi-character and single-character operators. The crucial scanning issue is that < and <= share a prefix, and similarly > and >= share a prefix, and = could conflict with ==.

A single combined regex (recommended):

• <=|>=|==|!=|<|>

Ordering rationale

• Many scanner generators implement maximal munch, but you still want the rule set to be consistent. Writing <= before <, and >= before >, and so on makes intent explicit. This is aligned with the typical “longest match” principle used during scanning.

Alternative: group by operator family

• < family: <=|<
• > family: >=|>
• equality/inequality: ==|!=

Key terms: operator token, prefix conflict, alternation, escape.