LALR(1) Part-3

Duration: 8 min

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The video presents a comprehensive lecture on constructing an SLR(1) parsing table for a specific context-free grammar. The instructor begins by defining the grammar rules, which include productions for S, A, and B. He then introduces the concept of grammar augmentation by adding a new start symbol S' and the production S' -> S. The core of the lecture involves building the canonical collection of LR(0) items, which forms the states of the DFA used in parsing. The instructor systematically derives each state (I0 through I12) by computing closures and transitions. Finally, he constructs the parsing table, mapping states to actions (shift, reduce, accept) and goto transitions based on the derived items and lookahead symbols. This process is crucial for compiler design and understanding how parsers work.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the grammar with productions S -> Aa, S -> bAc, S -> Bc, S -> bBa, A -> d, and B -> d. He explains the need for grammar augmentation to handle the start symbol correctly, adding S' -> S. He then begins constructing the initial state I0. He writes down the closure of the augmented production S' -> .S, $, which includes S -> .Aa, $, S -> .bAc, $, S -> .Bc, $, and S -> .bBa, $. He further expands the closure by adding productions for non-terminals A and B that appear after the dot, resulting in A -> .d, a and B -> .d, c. This state I0 serves as the starting point for the state machine, containing all possible initial moves. The items are written clearly on the board, showing the dot position and lookahead symbols.

  2. 2:00 – 5:00 02:00-05:00

    The instructor proceeds to build the transitions from state I0. He identifies transitions on terminals 's', 'A', 'B', 'b', and 'd'. The transition on 's' leads to state I1, which contains the completed item S' -> S., $. The transition on 'A' leads to state I2 with S -> A.a, $. The transition on 'B' leads to state I3 with S -> B.c, $. The transition on 'b' leads to state I4, which contains S -> b.Ac, $, S -> b.Ba, $, A -> .d, c, and B -> .d, a. The transition on 'd' leads to state I5, containing A -> d., a and B -> d., c. He carefully writes out the items for each new state, ensuring the lookahead symbols are correctly propagated from the parent state. This step-by-step derivation is essential for building the correct state machine. The closure of I4 is particularly important as it includes multiple productions.

  3. 5:00 – 7:53 05:00-07:53

    The lecture continues with the construction of the remaining states and the final parsing table. From state I4, transitions on 'A' and 'B' lead to states I6 (S -> bA.c, $) and I7 (S -> bB.a, $) respectively. Transitions on 'c' from I6 and 'a' from I7 lead to states I11 (S -> bAc., $) and I12 (S -> bBa., $). The instructor then draws the parsing table with rows for states I0 to I12 and columns for terminals a, b, c, d, and $. He fills in the action and goto entries. For example, I0 has goto entries for s, A, B, b, and d. I1 has an accept action on $. He fills in shift actions (S) and reduce actions (R) based on the completed items in each state, such as reducing A -> d in state I5 on input 'a'. The video concludes with a nearly complete parsing table ready for analysis, showing the full structure of the parser. The table entries are filled systematically.

The video provides a step-by-step walkthrough of SLR(1) parsing table construction. It starts with the fundamental grammar definition and moves through the critical steps of augmentation, state machine construction (DFA), and finally table population. The instructor emphasizes the importance of tracking lookahead symbols to resolve conflicts and correctly identify reduce actions. The progression from I0 to the final states I12 demonstrates the systematic nature of the algorithm, showing how each production rule contributes to the parsing structure. The final table serves as a complete specification for a parser to recognize strings generated by the given grammar.