difference between top down and bottom up parsing techniques?

I guess the same logic is applied in both of them, i.e replacing the matched strings with the corresponding no开发者_运维知识库n-terminal elements as provided in the production rules.

Why do they categorize LL as top down and LR as bottom-up?

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Bottom up parsing:

Bottom-up parsing (also known as shift-reduce parsing) is a strategy for analyzing unknown data relationships that attempts to identify the most fundamental units first, and then to infer higher-order structures from them. It attempts to build trees upward toward the start symbol.

Top-down parsing:

Top-down parsing is a strategy of analyzing unknown data relationships by hypothesizing general parse tree structures and then considering whether the known fundamental structures are compatible with the hypothesis.

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Top down parsing involves to generating the string from first non-terminal. Example: recursive descent parsing,non-recursive descent parsing, LL parsing, etc. The grammars with left recursive and left factoring do not work. Might occur backtracking. Use of left most derivation

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Things Of Interest Blog The difference between top-down parsing and bottom-up parsing

Given a formal grammar and a string produced by that grammar, parsing is figuring out the production process for that string.

In the case of the context-free grammars, the production process takes the form of a parse tree. Before we begin, we always know two things about the parse tree: the root node, which is the initial symbol from which the string was originally derived, and the leaf nodes, which are all the characters of the string in order. What we don't know is the layout of nodes and branches between them.

For example, if the string is acddf, we know this much already:

S

/|\

???

| | | | | a c d d f

Example grammar for use in this article

S → xyz | aBC
B → c | cd
C → eg | df

Bottom-up parsing

This approach is not unlike solving a jigsaw puzzle. We start at the bottom of the parse tree with individual characters. We then use the rules to connect the characters together into larger tokens as we go. At the end of the string, everything should have been combined into a single big S, and S should be the only thing we have left. If not, it's necessary to backtrack and try combining tokens in different ways.

With bottom-up parsing, we typically maintain a stack, which is the list of characters and tokens we've seen so far. At each step, we shift a new character onto the stack, and then reduce as far as possible by combining characters into larger tokens. Example

String is acddf. Steps

ε can't be reduced
a can't be reduced
ac can be reduced, as follows:
reduce ac to aB
    aB can't be reduced
    aBd can't be reduced
    aBdd can't be reduced
    aBddf can be reduced, as follows:
    reduce aBddf to aBdC
        aBdC can't be reduced
        End of string. Stack is aBdC, not S. Failure! Must backtrack.
    aBddf can't be reduced
ac can't be reduced
acd can be reduced, as follows:
reduce acd to aB
    aB can't be reduced
    aBd can't be reduced
    aBdf can be reduced, as follows:
    reduce aBdf to aBC
        aBC can be reduced, as follows:
        reduce aBC to S
            End of string. Stack is S. Success!

Parse trees

| a

| | a c

B | | a c

B | | | a c d

B | | | | a c d d

B | | | | | a c d d f

B C | | | |\ a c d d f

| | a c

| | | a c d

B

| /| a c d

B

| /| | a c d d

B

| /| | | a c d d f

B C

| /| |\ a c d d f

S

/|\ / | | / B C | /| |\ a c d d f

Example 2

If all combinations fail, then the string cannot be parsed.

String is acdg. Steps

ε can't be reduced
a can't be reduced
ac can be reduced, as follows:
reduce ac to aB
    aB can't be reduced
    aBd can't be reduced
    aBdg can't be reduced
    End of string. Stack is aBdg, not S. Failure! Must backtrack.
ac can't be reduced
acd can be reduced, as follows:
reduce acd to aB
    aB can't be reduced
    aBg can't be reduced
    End of string. stack is aBg, not S. Failure! Must backtrack.
acd can't be reduced
acdg can't be reduced
End of string. Stack is is acdg, not S. No backtracking is possible. Failure!

Parse trees

| a

| | a c

B | | a c

B | | | a c d

B | | | | a c d g

| | a c

| | | a c d

B

| /| a c d

B

| /| | a c d g

| | | a c d

| | | | a c d g

Top-down parsing

For this approach we assume that the string matches S and look at the internal logical implications of this assumption. For example, the fact that the string matches S logically implies that either (1) the string matches xyz or (2) the string matches aBC. If we know that (1) is not true, then (2) must be true. But (2) has its own further logical implications. These must be examined as far as necessary to prove the base assertion. Example

String is acddf. Steps

Assertion 1: acddf matches S
    Assertion 2: acddf matches xyz:
    Assertion is false. Try another.
    Assertion 2: acddf matches aBC i.e. cddf matches BC:
        Assertion 3: cddf matches cC i.e. ddf matches C:
            Assertion 4: ddf matches eg:
            False.
            Assertion 4: ddf matches df:
            False.
        Assertion 3 is false. Try another.
        Assertion 3: cddf matches cdC i.e. df matches C:
            Assertion 4: df matches eg:
            False.
            Assertion 4: df matches df:
            Assertion 4 is true.
        Assertion 3 is true.
    Assertion 2 is true.
Assertion 1 is true. Success!

Parse trees

S
|

S

/|\ a B C | |

S

/|\ a B C | | c

S

/|\ a B C /| | c d

S

/|\ a B C /| |\ c d d f

Example 2

If, after following every logical lead, we can't prove the basic hypothesis ("The string matches S") then the string cannot be parsed.

String is acdg. Steps

Assertion 1: acdg matches S:
    Assertion 2: acdg matches xyz:
    False.
    Assertion 2: acdg matches aBC i.e. cdg matches BC:
        Assertion 3: cdg matches cC i.e. dg matches C:
            Assertion 4: dg matches eg:
            False.
            Assertion 4: dg matches df:
            False.
        False.
        Assertion 3: cdg matches cdC i.e. g matches C:
            Assertion 4: g matches eg:
            False.
            Assertion 4: g matches df:
            False.
        False.
    False.
Assertion 1 is false. Failure!

Parse trees

S
|

S

/|\ a B C | |

S

/|\ a B C | | c

S

/|\ a B C /| | c d

Why left-recursion is a problem for top-down parsers

If our rules were left-recursive, for example something like this:

S → Sb

Then notice how our algorithm behaves: Steps

Assertion 1: acddf matches S:
    Assertion 2: acddf matches Sb:
        Assertion 3: acddf matches Sbb:
            Assertion 4: acddf matches Sbbb:
                ...and so on forever

Parse trees

S |

S |\ S b |

S |\ S b |\ S b |

S |\ S b |\ S b |\ S b |

...