Practice Problem on Follow Function

Duration: 3 min

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AI Summary

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This educational video provides a comprehensive lecture on computing Follow sets within the context of formal languages and compiler design. The instructor systematically works through several grammar examples to demonstrate the application of Follow set rules. The session begins with basic grammars involving terminals and non-terminals, progressing to more complex scenarios involving epsilon productions. The lecture culminates in a detailed analysis of a specific GATE 2019 examination question, where the instructor breaks down the problem statement, the provided symbol indexing table, and the step-by-step derivation of the required Follow set. Key concepts covered include the definition of Follow sets, the four fundamental rules for their calculation, and the handling of epsilon transitions.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor starts by analyzing a grammar defined by productions S -> aAb, A -> Ba / b, and B -> d. He writes Follow(S) = {$} on the screen, explaining that the start symbol always includes the end-of-input marker. He then calculates Follow(A) = {b} by observing the production S -> aAb, where b immediately follows A. Next, he determines Follow(B) = {a} based on the production A -> Ba. The lesson transitions to a new grammar S -> S0S1 / epsilon, where he again establishes Follow(S) = {$}. Finally, he introduces a complex grammar S -> AaAb / BaBb with A -> epsilon and B -> epsilon, calculating Follow(S) = {$} and Follow(A) = {a, b} to illustrate handling of multiple productions and epsilon rules.

  2. 2:00 – 3:23 02:00-03:23

    The video shifts to a specific GATE 2019 problem involving the grammar S -> Aa, A -> BD, B -> b | epsilon, and D -> d | epsilon. A table is displayed mapping symbols to indices: a=3, b=2, d=1, and $=0. The instructor presents a slide titled Follow listing four specific rules. Rule 1 states that if A is the start symbol, Follow(A) = {$}. Rule 2 covers A -> alpha B beta where beta is not epsilon, setting Follow(A) = First(beta). Rule 3 addresses S -> alpha A, implying Follow(A) = Follow(S). Rule 4 handles S -> alpha B beta where beta derives epsilon, stating Follow(A) = First(beta) U Follow(S) - epsilon. He applies these rules to the GATE question, explaining that since D can derive epsilon in A -> BD, the Follow set of B must include First(D) and Follow(A).

The lecture effectively bridges theoretical definitions with practical problem-solving. By moving from simple examples to a competitive exam question, the instructor reinforces the importance of understanding epsilon productions and the interaction between First and Follow sets. The structured presentation of rules on the slide serves as a clear reference for students to apply these concepts to various grammar structures.