GATE CS 2023 Set 1 — Question 19
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Compiler Design → Finite Automata & Regular Languages → Lexer Construction (DFA/NFA)
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Question
Consider the following definition of a lexical token id for an identifier in a programming language, using extended regular expressions:letter [A-Za-z]
digit [0-9]
id letter (letter | digit).Which one of the following Non-deterministic Finite-state Automata with -transitions accepts the set of valid identifiers? (A double-circle denotes a final state)
digit [0-9]
id letter (letter | digit).Which one of the following Non-deterministic Finite-state Automata with -transitions accepts the set of valid identifiers? (A double-circle denotes a final state)
Correct answer
(C) [figure]
Solution
The regular expression for the identifier is given as . To construct an NFA with -transitions for this expression:
1.Initial Transition: The automaton must first consume a
letter. This is shown in options (B), (C), and (D).2.Kleene Star and Union: The part requires a structure that can handle zero or more occurrences of either a
letter or a digit.3.Thompson Construction:
- The union is represented by two parallel paths.
- The Kleene star is represented by a loop that allows returning to the start of via an -transition and a skip path that allows bypassing entirely via an -transition.
- It starts with a
lettertransition. - It then enters a sub-structure for , where parallel paths for
letteranddigitare enclosed in -transitions that provide both the looping (repetition) and the skip (zero occurrences) functionality.
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