Computing FIRST and FOLLOW Sets for Grammars

Lecture 18 of CS606 Compiler Construction details the fixed-point iterative algorithms used to compute FIRST and FOLLOW sets for any context-free grammar. FIRST(alpha) is defined as the set of all terminal symbols that can appear as the first symbol of a string derived from alpha, including epsilon if alpha can derive the empty string. Students examine the three rules for computing FIRST sets: if X is a terminal, FIRST(X) is {X}; if X -> epsilon is a production, epsilon is in FIRST(X); and for a production X -> Y1 Y2 ... Yk, terminals from FIRST(Yi) are added iteratively as long as preceding symbols are nullable. FOLLOW(A) is defined as the set of all terminal symbols that can appear immediately to the right of non-terminal A in any sentential form derived from the start symbol S, with the input end-marker $ placed in FOLLOW(S). Students master the iterative calculation of FOLLOW sets, learning how nullable productions propagate follow sets and providing the exact mathematical inputs required for parsing table construction. By engaging with solved past papers by Moaaz and Waqar Siddhu, learners gain actionable insights into recurrent university exam questions. Interactive quiz assessments on VU SIGMA facilitate rapid knowledge verification and retention of critical compiler engineering terminology. Comprehensive coverage of IEEE and ACM curricula standards ensures learners communicate with technical precision across global systems engineering teams. Detailed analysis of machine code selection highlights the imperative of generating instruction sequences that maximize hardware pipeline throughput. Intermediate representation taxonomy categorizes structural formats into graphical ASTs, linear tuples, and hybrid tree-address models. The strategic role of peephole optimization is evaluated as a final localized pass to eliminate redundant loads, stores, and jumps. In this lecture, students examine formal language translation principles and architectural compiler pipelines to understand automated code generation. Through detailed theoretical derivations and algorithmic walkthroughs, the lesson explores lexical tokenization, grammatical parse trees, and syntax trees. Special emphasis is placed on formal grammar transformations, eliminating left recursion, and establishing unambiguous predictive parsing tables.