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Fix bug in dynamic step in CYK_for_CFPQ.tex #29

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Fix bug in dynamic step in CYK_for_CFPQ.tex #29

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2 changes: 1 addition & 1 deletion tex/CYK_for_CFPQ.tex
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Expand Up @@ -44,7 +44,7 @@ \section{Алгоритм CYK}\label{sect:lin_CYK}
Далее используем динамику: на шаге $m > 1$ предполагаем, что ячейки матрицы $M[i', j', A]$ заполнены для всех нетерминалов $A$ и пар $i', j': j' - i' < m$.
Тогда можно заполнить ячейки матрицы $M[i, j, A] \text{, где } j - i = m$ следующим образом:

\[ M[i, j, A] = \bigvee_{A \to B C}^{}{\bigvee_{k=i}^{j-1}{M[i, k, B] \wedge M[k, j, C]}} \]
\[ M[i, j, A] = \bigvee_{A \to B C}^{}{\bigvee_{k=i}^{j-1}{M[i, k, B] \wedge M[k+1, j, C]}} \]

По итогу работы алгоритма значение в ячейке $M[0, |\omega|, S]$, где $S$ --- стартовый нетерминал грамматики, отвечает на вопрос о выводимости цепочки $\omega$ в грамматике.

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