Use top-down parsing to determine whether each of the...

Use top-down parsing to determine whether each of the following strings belongs to the language generated by the grammar in Example $12 .$
$$
\begin{array}{ll}{\text { a) } b a b a} & {\text { b) } a b a b} \\ {\text { c) } c b a b a} & {\text { d) } b b b c b a}\end{array}
$$

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Key Concepts

Top-Down Parsing

Top-down parsing is a strategy for analyzing a string by starting from the start symbol of the grammar and progressively applying production rules to generate the input string. In this approach, the parser attempts to construct a parse tree from the root down to the leaves, matching the generated string with the input. It often involves recursive descent techniques and can utilize backtracking if multiple productions are possible.

Context-Free Grammar

A context-free grammar (CFG) is a formal system for generating strings in a language. It consists of a set of production rules that describe how non-terminal symbols can be replaced by groups of terminal and/or non-terminal symbols. CFGs are widely used in programming language design and natural language processing because they provide a structured way to represent language syntax.

Leftmost Derivation

Leftmost derivation is a method of deriving a string in which the leftmost non-terminal is always the one expanded during each step of the derivation. This form of derivation is closely related to top-down parsing since the parser makes decisions based on expanding the leftmost unprocessed symbol, thereby maintaining a systematic approach to generating the parse tree.

Transcript

00:01 Before deriving the string, we would go over the set of production p.

00:11 We have that s can be derived to a -b.

00:19 A can be derived as c -a.

00:23 B can be derived as b -a.

00:25 B can be derived as c -b.

00:28 B can be derived as b.

00:34 C can be derived as c -b.

00:38 B, c can be derived as b.

00:42 Okay, so for our first string, we have b -a -ba, b .a.

00:49 So we would, bottom parsing is when you start with a, sorry, we start with s, and then using the set of production p to derive the string.

00:59 So we have s.

01:03 S can be right as a and b.

01:10 And a b can be right as sorry, a can be right as c a capital b c a capital b can be c can be right as b so therefore we have b a capital b and b capital b can be right as capital b and a so capital b can be again be right as smaller b.

01:46 So therefore we know that b -a -b -a belongs to the language generated by the grandma.

02:03 So for the next string which is ab ab we're using top -down parsing we would have starting from s as as as is can be right as a -b.

02:22 As c small a capital b but however we know that c can only be used the production step c b or c would go to b which imply that the string string has to start with a b or a c c so therefore oh so i messed up here for a bit.

03:08 So the string has to start with either a c or a b...

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