Converting a Grammar Into Deterministic Grammar
Duration: 4 min
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This educational video provides a detailed lecture on converting non-deterministic grammars into deterministic grammars using the process of left factoring, a fundamental concept in compiler design. The instructor begins by presenting a specific problem on the screen: "Consider the following non-deterministic grammar and convert them into deterministic grammar by the process of left factoring." The initial grammar given is $S
ightarrow aSb / abS / ab$. He demonstrates the left factoring technique by first factoring out the common 'a', rewriting the production as $S
ightarrow aS'$. He then defines the new non-terminal $S'$ with the remaining suffixes: $S'
ightarrow Sb / bS / b$. He points out that $S'$ still has a common prefix 'b' in the second and third alternatives. He proceeds to factor out 'b' again, rewriting $S'$ as $S'
ightarrow Sb / bS''$ and defining $S''
ightarrow S / \epsilon$.
Chapters
0:00 – 2:00 00:00-02:00
The video begins with a clear problem statement displayed on the screen: "Consider the following non-deterministic grammar and convert them into deterministic grammar by the process of left factoring." The specific grammar provided is $S ightarrow aSb / abS / ab$. The instructor explains that this grammar is non-deterministic because the first two productions share a common prefix 'a'. He proceeds to apply the left factoring technique. First, he identifies the common prefix 'a' and rewrites the production rule as $S ightarrow aS'$. He then defines the new non-terminal $S'$ with the remaining parts of the original productions: $S' ightarrow Sb / bS / b$. However, he observes that the productions for $S'$ still contain a common prefix 'b' in the second and third alternatives ($bS$ and $b$). To resolve this, he factors out 'b' again, rewriting $S'$ as $S' ightarrow Sb / bS''$. Finally, he defines the new non-terminal $S''$ with the remaining parts: $S'' ightarrow S / \epsilon$.
2:00 – 4:23 02:00-04:23
The lecture transitions to a second example to reinforce the concept. The new grammar is $S ightarrow ab / abc / abcd / b$. The instructor starts by identifying the common prefix 'a' in the first three productions. He factors this out, rewriting the rule as $S ightarrow aS' / b$, and defines $S' ightarrow b / bc / bcd$. He then notices that $S'$ has a common prefix 'b' in all its alternatives. He factors out 'b' to get $S' ightarrow bS''$ and defines $S'' ightarrow \epsilon / c / cd$. The process continues as he identifies a common prefix 'c' in the last two alternatives of $S''$. He rewrites $S''$ as $S'' ightarrow cS''' / \epsilon$ and defines $S''' ightarrow d$. The video concludes with a slide titled "Simplification or Minimization of CFG," introducing the next topic of eliminating useless symbols, unit productions, and null productions.
The video effectively demonstrates the algorithmic approach to left factoring through two distinct examples, moving from a grammar with recursive structures to one with string literals. The instructor emphasizes the iterative nature of the process, showing that multiple levels of common prefixes may need to be factored out sequentially.