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1 parent 0ddd8f9 commit 67ff01b82efc04235ae721081c4592e379f934be Jeffrey Kegler committed Feb 27, 2014
Showing with 50 additions and 3 deletions.
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53 recce.ltx
@@ -149,8 +149,8 @@ Marpa is
a practical and fully implemented
algorithm for the recognition,
parsing and evaluation of context-free grammars.
-The Marpa recognizer is based on Earley's algorithm
-as modified in Joop Leo's 1991 paper
+The Marpa recognizer is based on Jay Earley's algorithm,
+as modified by Joop Leo
to have \On{} time complexity for all
LR-regular grammars.
An feature new with Marpa is that its parse engine
@@ -2053,10 +2053,57 @@ the previous two equalities.
\subsection{Preliminaries}
+Intuitively,
+a \dfn{finite derivation grammar} is an unambiguous grammar
+which can be parsed by considering, at any location
+in the input, at most some finite number
+of rightmost derivations.
+
\begin{definition}
-Channelled LR($\pi$).
+\Var{g} is
+a \dfn{finite derivation grammar} if \var{g}
+is an unambiguous grammar,
+and if,
+for any input string \CVwstr{0,\var{i}},
+there is a finite set of rightmost derivations, \var{rm-deriv},
+one of which must be the prefix of the rightmost derivation
+of any successful parse.
\end{definition}
+\begin{theorem}
+Let \var{g} be a finite derivation grammar.
+The number of YIM's for it in the Earley set \var{cut},
+excluding right recursions,
+is at most some constant \var{c},
+where \var{c} is a finite constant,
+which may be a function of the grammar.
+\end{theorem}
+
+\begin{theorem}
+Let \var{g} be a finite derivation grammar.
+The number of prediction YIM's for it in the Earley set \var{cut},
+is at most some constant \var{c},
+where \var{c} is a finite constant,
+which may be a function of the grammar.
+\end{theorem}
+
+\begin{theorem}
+Let \var{g} be a finite derivation grammar.
+The number of medial YIM's for it in the Earley set \var{cut},
+is at most some constant \var{c},
+where \var{c} is a finite constant,
+which may be a function of the grammar.
+\end{theorem}
+
+\begin{theorem}
+Let \var{g} be a finite derivation grammar.
+The number of completed YIM's for it in the Earley set \var{cut},
+excluding right recursions,
+is at most some constant \var{c},
+where \var{c} is a finite constant,
+which may be a function of the grammar.
+\end{theorem}
+
\subsection{Complexity of each Earley item}
For the complexity proofs,

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