SBNのUNOCFでの解析

ここでは、SBN, NSBNのUNOCFでの解析を示す。ただし、UNOCFは不完全な定義であるため、完全に定義された時に予想される大きさで示す。
\(\newcommand{\p}{\psi}
\newcommand{\a}{\{0}
\newcommand{\b}{\{1}
\newcommand{\c}{\{2}
\newcommand{\A}{\{0\}}
\newcommand{\B}{\{1\}}
\newcommand{\C}{\{2\}}
\newcommand{\o}{\p(1)}\)

\(\a[0 \A \A]\} \approx \p(C(1, 0))\)

\(\a[0 \A \A \A]\} \approx \p(C(1; 0))\)

\(\a[0 \A \A \A \A]\} \approx \p(C(2; 0))\)

\(\a[0 \a \A \}]\} \approx \p(C(\o; 0))\)

\(\a[0 \a \A \} \A]\} \approx \p(C(\o + 1; 0))\)

\(\a[0 \a \A \} \A \A]\} \approx \p(C(\o + 2; 0))\)

\(\a[0 \a \A \} \a \A \}]\} \approx \p(C(\o + \o; 0))\)

\(\a[0 \a \A \A \}]\} \approx \p(C(\p(2); 0))\)

\(\a[0 \a \a \A \} \}]\} \approx \p(C(\p(\o); 0))\)

\(\a[0 \a \a \A \A \} \}]\} \approx \p(C(\p(\p(2)); 0))\)

\(\a[0 \a \a \a \A \} \} \}]\} \approx \p(C(\p(\p(\o)); 0))\)

\(\a[0 [0 \A]]\} \approx \p(C(C(0); 0))\)

\(\a[0 [0 \A \A]]\} \approx \p(C(C(1, 0); 0))\)

\(\a[0 [0 \A \A \A]]\} \approx \p(C(C(1; 0); 0))\)

\(\a[0 [0 \a \A \}]]\} \approx \p(C(C(\o; 0); 0))\)

\(\a[0 [0 \a \A \} \a \A \}]]\} \approx \p(C(C(\o + \o; 0); 0))\)

\(\a[0 [0 \a \A \A \}]]\} \approx \p(C(C(\p(2); 0); 0))\)

\(\a[0 [0 \a \a \A \} \}\}]]\} \approx \p(C(C(\p(\o); 0); 0))\)

\(\a[0 [0 [0 \A ]]]\} \approx \p(C(C(C(0); 0); 0))\)

\(\a[0 [0 [0 \a \A \} ]]]\} \approx \p(C(C(C(\o; 0); 0); 0))\)

\(\a[0 [0 [0 [0 \A ]]]]\} \approx \p(C(C(C(C(0); 0); 0); 0))\)

\(\a[0 [1]]\} \approx \p(C(1, 0; 0))\)

\(\a[0 [1] \A]\} \approx \p(C(1, 1; 0))\)

\(\a[0 [1] \A \A]\} \approx \p(C(1, 2; 0))\)

\(\a[0 [1] \a \A \}]\} \approx \p(C(1, \o; 0))\)

\(\a[0 [1] \a \A \A \}]\} \approx \p(C(1, \p(2); 0))\)

\(\a[0 [1] \a \a \A \} \}]\} \approx \p(C(1, \p(\o); 0))\)

\(\a[0 [1] [0 \A]]\} \approx \p(C(1, C(0); 0))\)

\(\a[0 [1] [0 \a \A \}]]\} \approx \p(C(1, C(\o; 0); 0))\)

\(\a[0 [1] [0 \a \A \A \}]]\} \approx \p(C(1, C(\p(2); 0); 0))\)

\(\a[0 [1] [0 \a \a \A \} \}]]\} \approx \p(C(1, C(\p(\o); 0); 0))\)

\(\a[0 [1] [0 [0 \A]]]\} \approx \p(C(1, C(C(0); 0); 0))\)

\(\a[0 [1] [0 [0 \a \A \}]]]\} \approx \p(C(1, C(C(\o); 0); 0))\)

\(\a[0 [1] [0 [0 [0 \A]]]]\} \approx \p(C(1, C(C(0); 0); 0))\)

\(\a[0 [1] [0 [1]]]\} \approx \p(C(1, C(1, 0; 0); 0))\)

\(\a[0 [1] [0 [1]]] [0 [1]]]\} \approx \p(C(1, C(1, 0; 0) + C(1, 0; 0); 0))\)

\(\a[0 [1] [0 [1]] \A]\} \approx \p(C(1, \p(C(1, 0; 0) + 1); 0))\)

\(\a[0 [1] [0 [1]] \a \A \}]\} \approx \p(C(1, \p(C(1, 0; 0) + \o); 0))\)

\(\a[0 [1] [0 [1]] [0 \A]]\} \approx \p(C(1, \p(C(1, 0; 0) + C(0)); 0))\)

\(\a[0 [1] [0 [1]] [0 [1]]]\} \approx \p(C(1, \p(C(1, 0; 0) + C(1, 0; 0)); 0))\)

\(\a[0 [1] [0 [1] \A]]\} \approx \p(C(1, \p(\p(C(1, 0; 0) + 1)); 0))\)

\(\a[0 [1] [0 [1] \A \A]]\} \approx \p(C(1, \p(\p(C(1, 0; 0) + 2)); 0))\)

\(\a[0 [1] [0 [1] [0 \A]]\} \approx \p(C(1, \p(\p(C(1, 0; 0) + C(0))); 0))\)

\(\a[0 [1] [0 [1] [0 [1]]]\} \approx \p(C(1, \p(\p(C(1, 0; 0) + 1)) + C(1, 0; 0); 0))\)

\(\a[0 [1] [0 [1] [0 [1]] [0 [1]]]\} \approx \p(C(1, \p(\p(C(1, 0; 0) + 1)) + \p(C(1, 0; 0) + 1)); 0))\)

\(\a[0 [1] [0 [1] [0 [1] \A]]\} \approx \p(C(1, \p(\p(\p(C(1, 0; 0) + 1))); 0))\)

\(\a[0 [1] [1]]\} \approx \p(C(1, C(1, 1; 0); 0))\)

### \(\p(C(1, C(1, 1; 0); 0))\)~\(\p(C(2, 0; 0))\)

\(\a[0 [1] [1]]\} \approx \p(C(1, C(1, 1; 0); 0))\)

\(\a[0 [1] [1] [0 [1]]]\} \approx \p(C(1, C(1, 1; 0) + C(1, 0; 0); 0))\)

\(\a[0 [1] [1] [0 [1] [0 [1] \A]]]\} \approx \p(C(1, C(1, 1; 0) + \p(\p(C(1, 0; 0) + 1)); 0))\)

\(\a[0 [1] [1] [0 [1] [1]]]\} \approx \p(C(1, C(1, 1; 0) + C(1, 1; 0); 0))\)

\(\a[0 [1] [1] [0 [1] [1] [0 [1] [1] \A]]]\} \approx \p(C(1, \p(\p(C(1, 1; 0) + 1)); 0))\)

\(\a[0 [1] [1] [1]]\} \approx \p(C(1, C(1, 2; 0); 0))\)

\(\a[0 [1 \A]]\} \approx \p(C(1, C(1, \o; 0); 0))\)

\(\a[0 [1 \A \A]]\} \approx \p(C(1, C(1, \p(2); 0); 0))\)

\(\a[0 [1 \a \A \}]]\} \approx \p(C(1, C(1, \p(\o); 0); 0))\)

\(\a[0 [1 [0 \A]]]\} \approx \p(C(1, C(1, C(0); 0); 0))\)

\(\a[0 [1 [0 [1]]]]\} \approx \p(C(1, C(1, C(1, 0; 0); 0); 0))\)

\(\a[0 [1 [0 [1] [0 [1]]]]]\} \approx \p(C(1, C(1, \p(\p(C(1, 0; 0) + 1)); 0))\)

\(\a[0 [1 [0 [1] [1]]]]\} \approx \p(C(1, C(1, C(1, 1; 0); 0); 0))\)

\(\a[0 [1 [0 [1] [1] [1]]]]\} \approx \p(C(1, C(1, C(1, 2; 0); 0); 0))\)

\(\a[0 [1 [0 [1 \A]]]]\} \approx \p(C(1, C(1, C(1, \o; 0); 0); 0))\)

\(\a[0 [1 [0 [1 [0 \A]]]]]\} \approx \p(C(1, C(1, C(1, C(0); 0); 0); 0))\)

\(\a[0 [1 [0 [1 [0 [1]]]]]]\} \approx \p(C(1, C(1, C(1, C(1, 0; 0); 0); 0); 0))\)

\(\a[0 [1 [1]]]\} \approx \p(C(2, 0; 0))\)

## \(\p(C(2, 0; 0))\)~\(\p(C(1; 0; 0))\)

### \(\p(C(2, 0; 0))\)~\(\p(C(1, 0, 0; 0))\)

\(\a[0 [1 [1]]]\} \approx \p(C(2, 0; 0))\)

\(\a[0 [1 [1]] \A]\} \approx \p(C(2, 1; 0))\)

\(\a[0 [1 [1]]] \a \A \}\} \approx \p(C(2, \o; 0))\)

\(\a[0 [1 [1]]] [0 \A]\} \approx \p(C(2, C(0); 0))\)

\(\a[0 [1 [1]]] [0 [1]]\} \approx \p(C(2, C(1, 0; 0); 0))\)

\(\a[0 [1 [1]]] [0 [1][0 [1]]\} \approx \p(C(2, C(1, C(1, 0; 0); 0)); 0))\)

\(\a[0 [1 [1]]] [0 [1][1]]\} \approx \p(C(2, C(1, C(1, 1; 0); 0)); 0))\)

\(\a[0 [1 [1]]] [0 [1][0 [1]]]\} \approx \p(C(2, C(1, C(1, C(1, 0; 0); 0); 0)) 0))\)

\(\a[0 [1 [1]]] [0 [1 [1]]]\} \approx \p(C(2, C(2, 0; 0); 0))\)

\(\a[0 [1 [1]]] [0 [1 [1]] \A]\} \approx \p(C(2, C(2, 0; 0); 0))\)

\(\a[0 [1 [1]]] [0 [1 [1]] [0 [1]]]\} \approx \p(C(2, C(2, C(1, 0; 0); 0); 0))\)

\(\a[0 [1 [1]]] [0 [1 [1]] [0 [1][1]]]\} \approx \p(C(2, C(2, C(1, 1; 0); 0); 0))\)

\(\a[0 [1 [1]]] [0 [1 [1]] [0 [1 [1]]]]\} \approx \p(C(2, C(2, C(2, 0; 0); 0); 0))\)

\(\a[0 [1 [1]] [1]]\} \approx \p(C(3, 0; 0))\)

\(\a[0 [1 [1]] [1] [0 [1 [1]] [1]]]\} \approx \p(C(3, C(3, 0; 0); 0))\)

\(\a[0 [1 [1]] [1] [0 [1 [1]] [1] [0 [1 [1]] [1]]]]\} \approx \p(C(3, C(3, C(3, 0; 0); 0); 0))\)

\(\a[0 [1 [1]] [1] [1]]\} \approx \p(C(4, 0; 0))\)

\(\a[0 [1 [1]] [1 \A]]\} \approx \p(C(\o, 0; 0))\)

\(\a[0 [1 [1]] [1 [0 \A]]]\} \approx \p(C(C(0), 0; 0))\)

\(\a[0 [1 [1]] [1 [0 [1]]]]\} \approx \p(C(C(1, 0; 0), 0; 0))\)

\(\a[0 [1 [1]] [1 [0 [1][1]]]]\} \approx \p(C(C(1, C(1, 1; 0); 0), 0; 0))\)

\(\a[0 [1 [1]] [1 [0 [1 [1]]]]]\} \approx \p(C(C(2, 0; 0), 0; 0))\)

\(\a[0 [1 [1]] [1 [0 [1 [1]] [1]]]]\} \approx \p(C(C(3, 0; 0), 0; 0))\)

\(\a[0 [1 [1]] [1 [0 [1 [1]] [1 \A]]]]]\} \approx \p(C(C(\o, 0; 0), 0; 0))\)

\(\a[0 [1 [1]] [1 [0 [1 [1]] [1 [0 [\A]]]]]]]\} \approx \p(C(C(C(0), 0; 0), 0; 0))\)

\(\a[0 [1 [1]] [1 [0 [1 [1]] [1 [0 [1]]]]]]]\} \approx \p(C(C(C(1, 0; 0), 0; 0), 0; 0))\)

\(\a[0 [1 [1]] [1 [0 [1 [1]] [1 [0 [1 [1]]]]]]]]\} \approx \p(C(C(C(2, 0; 0), 0; 0), 0; 0))\)

\(\a[0 [1 [1]] [1 [1]]]\} \approx \p(C(1, 0, 0; 0))\)

### \(\p(C(1, 0, 0; 0))\)~\(\p(C(1; 0; 0))\)

\(\a[0 [1 [1]] [1 [1]] [1]]\} \approx \p(C(1, 1, 0; 0))\)

\(\a[0 [1 [1]] [1 [1]] [1] [1]]\} \approx \p(C(1, 2, 0; 0))\)

\(\a[0 [1 [1]] [1 [1]] [1 [0 \A]]]\} \approx \p(C(1, C(1, 0; 0), 0; 0))\)

\(\a[0 [1 [1]] [1 [1]] [1 [1]]]\} \approx \p(C(1, C(2, 0; 0), 0; 0))\)

\(\a[0 [1 [1]] [1 [1]] [1 [1]] [1]]\} \approx \p(C(1, C(2, 1; 0), 0; 0))\)

\(\a[0 [1 [1]] [1 [1]] [1 [1]] [1] [1]]\} \approx \p(C(1, C(2, 2; 0), 0; 0))\)

\(\a[0 [1 [1]] [1 [1]] [1 [1]] [1 [0 \A]]]\} \approx \p(C(1, C(1, C(1, 0; 0), 0; 0), 0; 0))\)

\(\a[0 [1 [1]] [1 [1]] [1 [1]] [1 [1]]]\} \approx \p(C(1, C(1, C(2, 0; 0), 0; 0), 0; 0))\)

\(\a[0 [1 [1] \A ]]\} \approx \p(C(2, 0, 0; 0))\)

\(\a[0 [1 [1] \A ] [1]]\} \approx \p(C(2, 1, 0; 0))\)

\(\a[0 [1 [1] \A ] [1 [1]]]\} \approx \p(C(2, C(2, 0; 0), 0; 0))\)

\(\a[0 [1 [1] \A ] [1 [1]] [1]]\} \approx \p(C(2, C(2, 1; 0), 0; 0))\)

\(\a[0 [1 [1] \A ] [1 [1]] [1 [0 \A]]]\} \approx \p(C(2, C(1, C(1, 0; 0), 0; 0), 0; 0))\)

\(\a[0 [1 [1] \A ] [1 [1]] [1 [1]]]\} \approx \p(C(2, C(1, C(2, 0; 0), 0; 0), 0; 0))\)

\(\a[0 [1 [1] \A ] [1 [1]] [1 [1]] [1]]\} \approx \p(C(2, C(1, C(2, 1; 0), 0; 0), 0; 0))\)

\(\a[0 [1 [1] \A ] [1 [1]] [1 [1]] [1 [0 \A]]]\} \approx \p(C(2, C(1, C(1, C(1, 0, 0), 0; 0), 0; 0), 0; 0))\)

\(\a[0 [1 [1] \A ] [1 [1]] [1 [1]] [1 [1]]]\} \approx \p(C(2, C(1, C(1, C(2, 0, 0), 0; 0), 0; 0), 0; 0))\)

\(\a[0 [1 [1] \A ] [0 [1 [1] \A ]]]\} \approx \p(C(2, C(2, 0, 0; 0), 0; 0))\)

\(\a[0 [1 [1] \A ] [0 [1 [1] \A ] [1 [1]]]]\} \approx \p(C(2, C(2, C(2, 0; 0), 0; 0), 0; 0))\)

\(\a[0 [1 [1] \A ] [0 [1 [1] \A ] [1 [1]] [1 [1]]]]\} \approx \p(C(2, C(2, C(1, C(2, 0, 0), 0; 0), 0; 0), 0; 0))\)

\(\a[0 [1 [1] \A ] [0 [1 [1] \A ] [0 [1 [1] \A ]]]]\} \approx \p(C(2, C(2, C(2, 0, 0; 0), 0; 0), 0; 0))\)

\(\a[0 [1 [1] \A \A ]]\} \approx \p(C(3, 0, 0; 0))\)

\(\a[0 [1 [1] \A \A ] [1 [1] \A \A ]]\} \approx \p(C(3, C(3, 0, 0; 0), 0; 0))\)

\(\a[0 [1 [1] \a \A \} ]]\} \approx \p(C(\o, 0, 0; 0))\)

\(\a[0 [1 [1] [0 [1]]]]\} \approx \p(C(C(1, 0; 0), 0, 0; 0))\)

\(\a[0 [1 [1] [0 [1][1]]]]\} \approx \p(C(C(2, 0; 0), 0, 0; 0))\)

\(\a[0 [1 [1] [0 [1 [1]]]]]\} \approx \p(C(C(1, 0, 0; 0), 0, 0; 0))\)

\(\a[0 [1 [1] [0 [1 [1] \A ]]]]\} \approx \p(C(C(2, 0, 0; 0), 0, 0; 0))\)

\(\a[0 [1 [1] [0 [1 [1] [0 [1 [1]]]]]]]\} \approx \p(C(C(C(1, 0, 0, 0), 0, 0; 0), 0, 0; 0))\)

\(\a[0 [1 [1] [1]]]\} \approx \p(C(1, 0, 0, 0; 0))\)

\(\a[0 [1 [1] [1] \A]]\} \approx \p(C(2, 0, 0, 0; 0))\)

\(\a[0 [1 [1] [1] [0 [1]]]]\} \approx \p(C(C(1, 0; 0), 0, 0, 0; 0))\)

\(\a[0 [1 [1] [1] [0 [1 [1]]]]]\} \approx \p(C(C(1, 0, 0; 0), 0, 0, 0; 0))\)

\(\a[0 [1 [1] [1] [0 [1 [1] [1]]]]]\} \approx \p(C(C(1, 0, 0, 0; 0), 0, 0, 0; 0))\)

\(\a[0 [1 [1] [1] [1]]]\} \approx \p(C(1, 0, 0, 0, 0; 0))\)

\(\a[0 [1 [1 [0]]]]\} \approx \p(C(1; 0; 0))\)

## \(\p(C(1; 0; 0))\)~\(\p(C(2; 0; 0))\)

### \(\p(C(1; 0; 0))\)~\(\p(C(1, 0; 0; 0))\)

\(\a[0 [1 [1 [0]]]]\} \approx \p(C(1; 0; 0))\)

\(\a[0 [1 [1 [0]] \A]]\} \approx \p(C(1; 1; 0))\)

\(\a[0 [1 [1 [0]] [0 [1]]]]\} \approx \p(C(1; C(1, 0; 0); 0))\)

\(\a[0 [1 [1 [0]] [0 [1 [1]]]]]\} \approx \p(C(1; C(1, 0, 0; 0); 0))\)

\(\a[0 [1 [1 [0]] [0 [1 [1] [1]]]]]\} \approx \p(C(1; C(1, 0, 0, 0; 0); 0))\)

\(\a[0 [1 [1 [0]] [0 [1 [1 [0]]]]]]\} \approx \p(C(1; C(1; 0; 0); 0))\)

\(\a[0 [1 [1 [0]] [0 [1 [1 [0]] [0 [1 [1 [0]]]]]]]]\} \approx \p(C(1; C(1; C(1; 0; 0); 0); 0))\)

\(\a[0 [1 [1 [0]] [1]]]\} \approx \p(C(1; 1, 0; 0))\)

\(\a[0 [1 [1 [0]] [1] [0 [1 [1 [0]]]]]]\} \approx \p(C(1; 1, C(1; 0; 0); 0))\)

\(\a[0 [1 [1 [0]] [1] [0 [1 [1 [0]] [1]]]]]\} \approx \p(C(1; 2, 0; 0))\)

\(\a[0 [1 [1 [0]] [1] [0 [1 [1 [0]] [1]]] [0 [1 [1 [0]] [1]]]]]\} \approx \p(C(1; 3, 0; 0))\)

\(\a[0 [1 [1 [0]] [1] [0 [1 [1 [0]] [1]] \A ]]]\} \approx \p(C(1; \o, 0; 0))\)

\(\a[0 [1 [1 [0]] [1] [0 [1 [1 [0]] [1]] [0 [1 [1 [0]]]]]]]\} \approx \p(C(1; C(1; 0; 0), 0; 0))\)

\(\a[0 [1 [1 [0]] [1] [0 [1 [1 [0]] [1]] [0 [1 [1 [0]] [1]]]]]]\} \approx \p(C(1; C(1; 1, 0; 0), 0; 0))\)

\(\a[0 [1 [1 [0]] [1] [0 [1 [1 [0]] [1] [1]]]]]\} \approx \p(C(1; 1, 0, 0; 0))\)

\(\a[0 [1 [1 [0]] [1] [0 [1 [1 [0]] [1 [0]]]]]]\} \approx \p(C(2; 0; 0))\)