Parser Hierarchy and Grammar Handling Power Explained

This section details the relative power of various grammar parsers used in compiler construction. Parser power signifies a parser's ability to recognize and process grammars within a specific class. A parser with greater power can handle a broader set of grammars. We analyze the hierarchy for $LL(0)$, $LR(0)$, $SLR$, $LALR(1)$, and $LR(1)$ parsers.

Analyzing Individual Parser Capabilities

LL(0) Parsers

$LL(0)$ parsers operate top-down. They are highly constrained, requiring unambiguous grammars without left recursion and using zero lookahead. Consequently, $LL(0)$ can only parse extremely simple context-free grammars.

LR(0) Parsers

$LR(0)$ parsers work bottom-up. As the most basic type of LR parser, they build states from grammar items but lack lookahead for resolving shift/reduce conflicts. While superior to $LL(0)$, their grammar handling capacity remains limited.

SLR Parsers

$SLR$, or Simple LR, enhances $LR(0)$ by incorporating FOLLOW sets. These sets help in resolving shift/reduce conflicts. The use of FOLLOW sets gives $SLR(1)$ parsers greater power than $LR(0)$ parsers, enabling them to handle more grammars.

LALR(1) Parsers

$LALR(1)$ (Look-Ahead LR) strikes a balance between $LR(1)$'s power and $SLR$'s state efficiency. It merges states from an $LR(1)$ parser that share identical item sets (disregarding lookaheads). This merging process allows $LALR(1)$ to handle more grammars than $SLR$.

LR(1) Parsers

$LR(1)$ parsers represent the most powerful deterministic type among the common LR parsers. They utilize a lookahead symbol effectively for action decisions. Unlike $LALR(1)$, $LR(1)$ maintains distinct states even for identical item sets if their lookaheads differ. This characteristic enables $LR(1)$ parsers to handle the broadest range of unambiguous context-free grammars.

Determining the Increasing Order of Parser Power

The hierarchy of parser power, from least capable to most capable, is determined by the class of grammars each parser type can handle:

• Least Powerful: $LL(0)$ has the most restrictive capabilities.
• Following LL(0): $LR(0)$, utilizing a bottom-up strategy, surpasses $LL(0)$ in power.
• Enhanced Power: $SLR$ builds upon $LR(0)$ using FOLLOW sets, increasing its grammar handling scope.
• Further Capability: $LALR(1)$ is more powerful than $SLR$ due to its state merging strategy derived from $LR(1)$.
• Most Powerful: $LR(1)$ offers the highest level of power among these deterministic parsers, thanks to its detailed lookahead mechanism.

The correct sequence representing the increasing order of parser power is:

$LL(0)$ $\rightarrow$ $LR(0)$ $\rightarrow$ $SLR$ $\rightarrow$ $LALR(1)$ $\rightarrow$ $LR(1)$