Wirth–Weber precedence relationship について

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Wirth–Weber precedence relationship ：ウィキペディア英語版

Wirth–Weber precedence relationship

The Wirth–Weber relationship between a pair of symbols

(V_t \cup V_n)

is necessary to determine if a formal grammar is a simple precedence grammar, and in such case the simple precedence parser can be used.
The goal is to identify the when the viable prefixes have the pivot and must be reduced. A

\gtrdot

means that the pivot is found, a

\lessdot

means that a potential pivot is starting, and a

\dot =

means that we are still in the same pivot.
==Formal definition==

G =

X \dot = Y \iff \begin A \to \alpha X Y \beta \in P  \\  A \in V_n \\ \alpha , \beta \in (V_n \cup V_t)^* \\ X, Y \in (V_n \cup V_t) \end

X \lessdot Y \iff \begin A \to \alpha X B \beta \in P \\ B \Rightarrow^+ Y \gamma \\ A, B \in V_n \\ \alpha , \beta, \gamma \in (V_n \cup V_t)^* \\ X, Y \in (V_n \cup V_t) \end

X \gtrdot a \iff \begin A \to \alpha B Y \beta \in P \\ B \Rightarrow^+ \gamma X \\ Y \Rightarrow^* a \delta \\ A, B \in V_n \\ \alpha , \beta, \gamma, \delta \in (V_n \cup V_t)^* \\ X, Y \in (V_n \cup V_t) \\ a \in V_t \end

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