Line 489: |
Line 489: |
| | | |
| <br> | | <br> |
| + | |
| + | ===TeX Tables=== |
| + | |
| + | <pre> |
| + | \tableofcontents |
| + | |
| + | \subsection{Table A1. Propositional Forms on Two Variables} |
| + | |
| + | Table A1 lists equivalent expressions for the Boolean functions of two variables in a number of different notational systems. |
| + | |
| + | \begin{quote}\begin{tabular}{|c|c|c|c|c|c|c|} |
| + | \multicolumn{7}{c}{\textbf{Table A1. Propositional Forms on Two Variables}} \\ |
| + | \hline |
| + | $\mathcal{L}_1$ & |
| + | $\mathcal{L}_2$ && |
| + | $\mathcal{L}_3$ & |
| + | $\mathcal{L}_4$ & |
| + | $\mathcal{L}_5$ & |
| + | $\mathcal{L}_6$ \\ |
| + | \hline |
| + | & & $x =$ & 1 1 0 0 & & & \\ |
| + | & & $y =$ & 1 0 1 0 & & & \\ |
| + | \hline |
| + | $f_{0}$ & |
| + | $f_{0000}$ && |
| + | 0 0 0 0 & |
| + | $(~)$ & |
| + | $\operatorname{false}$ & |
| + | $0$ \\ |
| + | $f_{1}$ & |
| + | $f_{0001}$ && |
| + | 0 0 0 1 & |
| + | $(x)(y)$ & |
| + | $\operatorname{neither}\ x\ \operatorname{nor}\ y$ & |
| + | $\lnot x \land \lnot y$ \\ |
| + | $f_{2}$ & |
| + | $f_{0010}$ && |
| + | 0 0 1 0 & |
| + | $(x)\ y$ & |
| + | $y\ \operatorname{without}\ x$ & |
| + | $\lnot x \land y$ \\ |
| + | $f_{3}$ & |
| + | $f_{0011}$ && |
| + | 0 0 1 1 & |
| + | $(x)$ & |
| + | $\operatorname{not}\ x$ & |
| + | $\lnot x$ \\ |
| + | $f_{4}$ & |
| + | $f_{0100}$ && |
| + | 0 1 0 0 & |
| + | $x\ (y)$ & |
| + | $x\ \operatorname{without}\ y$ & |
| + | $x \land \lnot y$ \\ |
| + | $f_{5}$ & |
| + | $f_{0101}$ && |
| + | 0 1 0 1 & |
| + | $(y)$ & |
| + | $\operatorname{not}\ y$ & |
| + | $\lnot y$ \\ |
| + | $f_{6}$ & |
| + | $f_{0110}$ && |
| + | 0 1 1 0 & |
| + | $(x,\ y)$ & |
| + | $x\ \operatorname{not~equal~to}\ y$ & |
| + | $x \ne y$ \\ |
| + | $f_{7}$ & |
| + | $f_{0111}$ && |
| + | 0 1 1 1 & |
| + | $(x\ y)$ & |
| + | $\operatorname{not~both}\ x\ \operatorname{and}\ y$ & |
| + | $\lnot x \lor \lnot y$ \\ |
| + | \hline |
| + | $f_{8}$ & |
| + | $f_{1000}$ && |
| + | 1 0 0 0 & |
| + | $x\ y$ & |
| + | $x\ \operatorname{and}\ y$ & |
| + | $x \land y$ \\ |
| + | $f_{9}$ & |
| + | $f_{1001}$ && |
| + | 1 0 0 1 & |
| + | $((x,\ y))$ & |
| + | $x\ \operatorname{equal~to}\ y$ & |
| + | $x = y$ \\ |
| + | $f_{10}$ & |
| + | $f_{1010}$ && |
| + | 1 0 1 0 & |
| + | $y$ & |
| + | $y$ & |
| + | $y$ \\ |
| + | $f_{11}$ & |
| + | $f_{1011}$ && |
| + | 1 0 1 1 & |
| + | $(x\ (y))$ & |
| + | $\operatorname{not}\ x\ \operatorname{without}\ y$ & |
| + | $x \Rightarrow y$ \\ |
| + | $f_{12}$ & |
| + | $f_{1100}$ && |
| + | 1 1 0 0 & |
| + | $x$ & |
| + | $x$ & |
| + | $x$ \\ |
| + | $f_{13}$ & |
| + | $f_{1101}$ && |
| + | 1 1 0 1 & |
| + | $((x)\ y)$ & |
| + | $\operatorname{not}\ y\ \operatorname{without}\ x$ & |
| + | $x \Leftarrow y$ \\ |
| + | $f_{14}$ & |
| + | $f_{1110}$ && |
| + | 1 1 1 0 & |
| + | $((x)(y))$ & |
| + | $x\ \operatorname{or}\ y$ & |
| + | $x \lor y$ \\ |
| + | $f_{15}$ & |
| + | $f_{1111}$ && |
| + | 1 1 1 1 & |
| + | $((~))$ & |
| + | $\operatorname{true}$ & |
| + | $1$ \\ |
| + | \hline |
| + | \end{tabular}\end{quote} |
| + | |
| + | \subsection{Table A2. Propositional Forms on Two Variables} |
| + | |
| + | Table A2 lists the sixteen Boolean functions of two variables in a different order, grouping them by structural similarity into seven natural classes. |
| + | |
| + | \begin{quote}\begin{tabular}{|c|c|c|c|c|c|c|} |
| + | \multicolumn{7}{c}{\textbf{Table A2. Propositional Forms on Two Variables}} \\ |
| + | \hline |
| + | $\mathcal{L}_1$ & |
| + | $\mathcal{L}_2$ && |
| + | $\mathcal{L}_3$ & |
| + | $\mathcal{L}_4$ & |
| + | $\mathcal{L}_5$ & |
| + | $\mathcal{L}_6$ \\ |
| + | \hline |
| + | & & $x =$ & 1 1 0 0 & & & \\ |
| + | & & $y =$ & 1 0 1 0 & & & \\ |
| + | \hline |
| + | $f_{0}$ & |
| + | $f_{0000}$ && |
| + | 0 0 0 0 & |
| + | $(~)$ & |
| + | $\operatorname{false}$ & |
| + | $0$ \\ |
| + | \hline |
| + | $f_{1}$ & |
| + | $f_{0001}$ && |
| + | 0 0 0 1 & |
| + | $(x)(y)$ & |
| + | $\operatorname{neither}\ x\ \operatorname{nor}\ y$ & |
| + | $\lnot x \land \lnot y$ \\ |
| + | $f_{2}$ & |
| + | $f_{0010}$ && |
| + | 0 0 1 0 & |
| + | $(x)\ y$ & |
| + | $y\ \operatorname{without}\ x$ & |
| + | $\lnot x \land y$ \\ |
| + | $f_{4}$ & |
| + | $f_{0100}$ && |
| + | 0 1 0 0 & |
| + | $x\ (y)$ & |
| + | $x\ \operatorname{without}\ y$ & |
| + | $x \land \lnot y$ \\ |
| + | $f_{8}$ & |
| + | $f_{1000}$ && |
| + | 1 0 0 0 & |
| + | $x\ y$ & |
| + | $x\ \operatorname{and}\ y$ & |
| + | $x \land y$ \\ |
| + | \hline |
| + | $f_{3}$ & |
| + | $f_{0011}$ && |
| + | 0 0 1 1 & |
| + | $(x)$ & |
| + | $\operatorname{not}\ x$ & |
| + | $\lnot x$ \\ |
| + | $f_{12}$ & |
| + | $f_{1100}$ && |
| + | 1 1 0 0 & |
| + | $x$ & |
| + | $x$ & |
| + | $x$ \\ |
| + | \hline |
| + | $f_{6}$ & |
| + | $f_{0110}$ && |
| + | 0 1 1 0 & |
| + | $(x,\ y)$ & |
| + | $x\ \operatorname{not~equal~to}\ y$ & |
| + | $x \ne y$ \\ |
| + | $f_{9}$ & |
| + | $f_{1001}$ && |
| + | 1 0 0 1 & |
| + | $((x,\ y))$ & |
| + | $x\ \operatorname{equal~to}\ y$ & |
| + | $x = y$ \\ |
| + | \hline |
| + | $f_{5}$ & |
| + | $f_{0101}$ && |
| + | 0 1 0 1 & |
| + | $(y)$ & |
| + | $\operatorname{not}\ y$ & |
| + | $\lnot y$ \\ |
| + | $f_{10}$ & |
| + | $f_{1010}$ && |
| + | 1 0 1 0 & |
| + | $y$ & |
| + | $y$ & |
| + | $y$ \\ |
| + | \hline |
| + | $f_{7}$ & |
| + | $f_{0111}$ && |
| + | 0 1 1 1 & |
| + | $(x\ y)$ & |
| + | $\operatorname{not~both}\ x\ \operatorname{and}\ y$ & |
| + | $\lnot x \lor \lnot y$ \\ |
| + | $f_{11}$ & |
| + | $f_{1011}$ && |
| + | 1 0 1 1 & |
| + | $(x\ (y))$ & |
| + | $\operatorname{not}\ x\ \operatorname{without}\ y$ & |
| + | $x \Rightarrow y$ \\ |
| + | $f_{13}$ & |
| + | $f_{1101}$ && |
| + | 1 1 0 1 & |
| + | $((x)\ y)$ & |
| + | $\operatorname{not}\ y\ \operatorname{without}\ x$ & |
| + | $x \Leftarrow y$ \\ |
| + | $f_{14}$ & |
| + | $f_{1110}$ && |
| + | 1 1 1 0 & |
| + | $((x)(y))$ & |
| + | $x\ \operatorname{or}\ y$ & |
| + | $x \lor y$ \\ |
| + | \hline |
| + | $f_{15}$ & |
| + | $f_{1111}$ && |
| + | 1 1 1 1 & |
| + | $((~))$ & |
| + | $\operatorname{true}$ & |
| + | $1$ \\ |
| + | \hline |
| + | \end{tabular}\end{quote} |
| + | |
| + | \subsection{Table A3. $\operatorname{E}f$ Expanded Over Differential Features $\{ \operatorname{d}x, \operatorname{d}y \}$} |
| + | |
| + | \begin{quote}\begin{tabular}{|c|c||c|c|c|c|} |
| + | \multicolumn{6}{c}{\textbf{Table A3. $\operatorname{E}f$ Expanded Over Differential Features $\{ \operatorname{d}x, \operatorname{d}y \}$}} \\ |
| + | \hline |
| + | & & |
| + | $\operatorname{T}_{11}$ & |
| + | $\operatorname{T}_{10}$ & |
| + | $\operatorname{T}_{01}$ & |
| + | $\operatorname{T}_{00}$ \\ |
| + | & $f$ & |
| + | $\operatorname{E}f|_{\operatorname{d}x\ \operatorname{d}y}$ & |
| + | $\operatorname{E}f|_{\operatorname{d}x (\operatorname{d}y)}$ & |
| + | $\operatorname{E}f|_{(\operatorname{d}x) \operatorname{d}y}$ & |
| + | $\operatorname{E}f|_{(\operatorname{d}x)(\operatorname{d}y)}$ \\ |
| + | \hline |
| + | $f_{0}$ & $(~)$ & $(~)$ & $(~)$ & $(~)$ & $(~)$ \\ |
| + | \hline |
| + | $f_{1}$ & $(x)(y)$ & $x\ y$ & $x\ (y)$ & $(x)\ y$ & $(x)(y)$ \\ |
| + | $f_{2}$ & $(x)\ y$ & $x\ (y)$ & $x\ y$ & $(x)(y)$ & $(x)\ y$ \\ |
| + | $f_{4}$ & $x\ (y)$ & $(x)\ y$ & $(x)(y)$ & $x\ y$ & $x\ (y)$ \\ |
| + | $f_{8}$ & $x\ y$ & $(x)(y)$ & $(x)\ y$ & $x\ (y)$ & $x\ y$ \\ |
| + | \hline |
| + | $f_{3}$ & $(x)$ & $x$ & $x$ & $(x)$ & $(x)$ \\ |
| + | $f_{12}$ & $x$ & $(x)$ & $(x)$ & $x$ & $x$ \\ |
| + | \hline |
| + | $f_{6}$ & $(x,\ y)$ & $(x,\ y)$ & $((x,\ y))$ & $((x,\ y))$ & $(x,\ y)$ \\ |
| + | $f_{9}$ & $((x,\ y))$ & $((x,\ y))$ & $(x,\ y)$ & $(x,\ y)$ & $((x,\ y))$ \\ |
| + | \hline |
| + | $f_{5}$ & $(y)$ & $y$ & $(y)$ & $y$ & $(y)$ \\ |
| + | $f_{10}$ & $y$ & $(y)$ & $y$ & $(y)$ & $y$ \\ |
| + | \hline |
| + | $f_{7}$ & $(x\ y)$ & $((x)(y))$ & $((x)\ y)$ & $(x\ (y))$ & $(x\ y)$ \\ |
| + | $f_{11}$ & $(x\ (y))$ & $((x)\ y)$ & $((x)(y))$ & $(x\ y)$ & $(x\ (y))$ \\ |
| + | $f_{13}$ & $((x)\ y)$ & $(x\ (y))$ & $(x\ y)$ & $((x)(y))$ & $((x)\ y)$ \\ |
| + | $f_{14}$ & $((x)(y))$ & $(x\ y)$ & $(x\ (y))$ & $((x)\ y)$ & $((x)(y))$ \\ |
| + | \hline |
| + | $f_{15}$ & $((~))$ & $((~))$ & $((~))$ & $((~))$ & $((~))$ \\ |
| + | \hline |
| + | \multicolumn{2}{|c||}{\PMlinkname{Fixed Point}{FixedPoint} Total:} & 4 & 4 & 4 & 16 \\ |
| + | \hline |
| + | \end{tabular}\end{quote} |
| + | |
| + | \subsection{Table A4. $\operatorname{D}f$ Expanded Over Differential Features $\{ \operatorname{d}x, \operatorname{d}y \}$} |
| + | |
| + | \begin{quote}\begin{tabular}{|c|c||c|c|c|c|} |
| + | \multicolumn{6}{c}{\textbf{Table A4. $\operatorname{D}f$ Expanded Over Differential Features $\{ \operatorname{d}x, \operatorname{d}y \}$}} \\ |
| + | \hline |
| + | & $f$ & |
| + | $\operatorname{D}f|_{\operatorname{d}x\ \operatorname{d}y}$ & |
| + | $\operatorname{D}f|_{\operatorname{d}x (\operatorname{d}y)}$ & |
| + | $\operatorname{D}f|_{(\operatorname{d}x) \operatorname{d}y}$ & |
| + | $\operatorname{D}f|_{(\operatorname{d}x)(\operatorname{d}y)}$ \\ |
| + | \hline |
| + | $f_{0}$ & $(~)$ & $(~)$ & $(~)$ & $(~)$ & $(~)$ \\ |
| + | \hline |
| + | $f_{1}$ & $(x)(y)$ & $((x,\ y))$ & $(y)$ & $(x)$ & $(~)$ \\ |
| + | $f_{2}$ & $(x)\ y$ & $(x,\ y)$ & $y$ & $(x)$ & $(~)$ \\ |
| + | $f_{4}$ & $x\ (y)$ & $(x,\ y)$ & $(y)$ & $x$ & $(~)$ \\ |
| + | $f_{8}$ & $x\ y$ & $((x,\ y))$ & $y$ & $x$ & $(~)$ \\ |
| + | \hline |
| + | $f_{3}$ & $(x)$ & $((~))$ & $((~))$ & $(~)$ & $(~)$ \\ |
| + | $f_{12}$ & $x$ & $((~))$ & $((~))$ & $(~)$ & $(~)$ \\ |
| + | \hline |
| + | $f_{6}$ & $(x,\ y)$ & $(~)$ & $((~))$ & $((~))$ & $(~)$ \\ |
| + | $f_{9}$ & $((x,\ y))$ & $(~)$ & $((~))$ & $((~))$ & $(~)$ \\ |
| + | \hline |
| + | $f_{5}$ & $(y)$ & $((~))$ & $(~)$ & $((~))$ & $(~)$ \\ |
| + | $f_{10}$ & $y$ & $((~))$ & $(~)$ & $((~))$ & $(~)$ \\ |
| + | \hline |
| + | $f_{7}$ & $(x\ y)$ & $((x,\ y))$ & $y$ & $x$ & $(~)$ \\ |
| + | $f_{11}$ & $(x\ (y))$ & $(x,\ y)$ & $(y)$ & $x$ & $(~)$ \\ |
| + | $f_{13}$ & $((x)\ y)$ & $(x,\ y)$ & $y$ & $(x)$ & $(~)$ \\ |
| + | $f_{14}$ & $((x)(y))$ & $((x,\ y))$ & $(y)$ & $(x)$ & $(~)$ \\ |
| + | \hline |
| + | $f_{15}$ & $((~))$ & $(~)$ & $(~)$ & $(~)$ & $(~)$ \\ |
| + | \hline |
| + | \end{tabular}\end{quote} |
| + | |
| + | \subsection{Table A5. $\operatorname{E}f$ Expanded Over Ordinary Features $\{ x, y \}$} |
| + | |
| + | \begin{quote}\begin{tabular}{|c|c||c|c|c|c|} |
| + | \multicolumn{6}{c}{\textbf{Table A5. $\operatorname{E}f$ Expanded Over Ordinary Features $\{ x, y \}$}} \\ |
| + | \hline |
| + | & $f$ & |
| + | $\operatorname{E}f|_{x\ y}$ & |
| + | $\operatorname{E}f|_{x (y)}$ & |
| + | $\operatorname{E}f|_{(x) y}$ & |
| + | $\operatorname{E}f|_{(x)(y)}$ \\ |
| + | \hline |
| + | $f_{0}$ & |
| + | $(~)$ & |
| + | $(~)$ & |
| + | $(~)$ & |
| + | $(~)$ & |
| + | $(~)$ \\ |
| + | \hline |
| + | $f_{1}$ & |
| + | $(x)(y)$ & |
| + | $\operatorname{d}x\ \operatorname{d}y$ & |
| + | $\operatorname{d}x\ (\operatorname{d}y)$ & |
| + | $(\operatorname{d}x)\ \operatorname{d}y$ & |
| + | $(\operatorname{d}x)(\operatorname{d}y)$ \\ |
| + | $f_{2}$ & |
| + | $(x)\ y$ & |
| + | $\operatorname{d}x\ (\operatorname{d}y)$ & |
| + | $\operatorname{d}x\ \operatorname{d}y$ & |
| + | $(\operatorname{d}x)(\operatorname{d}y)$ & |
| + | $(\operatorname{d}x)\ \operatorname{d}y$ \\ |
| + | $f_{4}$ & |
| + | $x\ (y)$ & |
| + | $(\operatorname{d}x)\ \operatorname{d}y$ & |
| + | $(\operatorname{d}x)(\operatorname{d}y)$ & |
| + | $\operatorname{d}x\ \operatorname{d}y$ & |
| + | $\operatorname{d}x\ (\operatorname{d}y)$ \\ |
| + | $f_{8}$ & |
| + | $x\ y$ & |
| + | $(\operatorname{d}x)(\operatorname{d}y)$ & |
| + | $(\operatorname{d}x)\ \operatorname{d}y$ & |
| + | $\operatorname{d}x\ (\operatorname{d}y)$ & |
| + | $\operatorname{d}x\ \operatorname{d}y$ \\ |
| + | \hline |
| + | $f_{3}$ & |
| + | $(x)$ & |
| + | $\operatorname{d}x$ & |
| + | $\operatorname{d}x$ & |
| + | $(\operatorname{d}x)$ & |
| + | $(\operatorname{d}x)$ \\ |
| + | $f_{12}$ & |
| + | $x$ & |
| + | $(\operatorname{d}x)$ & |
| + | $(\operatorname{d}x)$ & |
| + | $\operatorname{d}x$ & |
| + | $\operatorname{d}x$ \\ |
| + | \hline |
| + | $f_{6}$ & |
| + | $(x,\ y)$ & |
| + | $(\operatorname{d}x,\ \operatorname{d}y)$ & |
| + | $((\operatorname{d}x,\ \operatorname{d}y))$ & |
| + | $((\operatorname{d}x,\ \operatorname{d}y))$ & |
| + | $(\operatorname{d}x,\ \operatorname{d}y)$ \\ |
| + | $f_{9}$ & |
| + | $((x,\ y))$ & |
| + | $((\operatorname{d}x,\ \operatorname{d}y))$ & |
| + | $(\operatorname{d}x,\ \operatorname{d}y)$ & |
| + | $(\operatorname{d}x,\ \operatorname{d}y)$ & |
| + | $((\operatorname{d}x,\ \operatorname{d}y))$ \\ |
| + | \hline |
| + | $f_{5}$ & |
| + | $(y)$ & |
| + | $\operatorname{d}y$ & |
| + | $(\operatorname{d}y)$ & |
| + | $\operatorname{d}y$ & |
| + | $(\operatorname{d}y)$ \\ |
| + | $f_{10}$ & |
| + | $y$ & |
| + | $(\operatorname{d}y)$ & |
| + | $\operatorname{d}y$ & |
| + | $(\operatorname{d}y)$ & |
| + | $\operatorname{d}y$ \\ |
| + | \hline |
| + | $f_{7}$ & |
| + | $(x\ y)$ & |
| + | $((\operatorname{d}x)(\operatorname{d}y))$ & |
| + | $((\operatorname{d}x)\ \operatorname{d}y)$ & |
| + | $(\operatorname{d}x\ (\operatorname{d}y))$ & |
| + | $(\operatorname{d}x\ \operatorname{d}y)$ \\ |
| + | $f_{11}$ & |
| + | $(x\ (y))$ & |
| + | $((\operatorname{d}x)\ \operatorname{d}y)$ & |
| + | $((\operatorname{d}x)(\operatorname{d}y))$ & |
| + | $(\operatorname{d}x\ \operatorname{d}y)$ & |
| + | $(\operatorname{d}x\ (\operatorname{d}y))$ \\ |
| + | $f_{13}$ & |
| + | $((x)\ y)$ & |
| + | $(\operatorname{d}x\ (\operatorname{d}y))$ & |
| + | $(\operatorname{d}x\ \operatorname{d}y)$ & |
| + | $((\operatorname{d}x)(\operatorname{d}y))$ & |
| + | $((\operatorname{d}x)\ \operatorname{d}y)$ \\ |
| + | $f_{14}$ & |
| + | $((x)(y))$ & |
| + | $(\operatorname{d}x\ \operatorname{d}y)$ & |
| + | $(\operatorname{d}x\ (\operatorname{d}y))$ & |
| + | $((\operatorname{d}x)\ \operatorname{d}y)$ & |
| + | $((\operatorname{d}x)(\operatorname{d}y))$ \\ |
| + | \hline |
| + | $f_{15}$ & |
| + | $((~))$ & |
| + | $((~))$ & |
| + | $((~))$ & |
| + | $((~))$ & |
| + | $((~))$ \\ |
| + | \hline |
| + | \end{tabular}\end{quote} |
| + | |
| + | \subsection{Table A6. $\operatorname{D}f$ Expanded Over Ordinary Features $\{ x, y \}$} |
| + | |
| + | \begin{quote}\begin{tabular}{|c|c||c|c|c|c|} |
| + | \multicolumn{6}{c}{\textbf{Table A6. $\operatorname{D}f$ Expanded Over Ordinary Features $\{ x, y \}$}} \\ |
| + | \hline |
| + | & $f$ & |
| + | $\operatorname{D}f|_{x\ y}$ & |
| + | $\operatorname{D}f|_{x (y)}$ & |
| + | $\operatorname{D}f|_{(x) y}$ & |
| + | $\operatorname{D}f|_{(x)(y)}$ \\ |
| + | \hline |
| + | $f_{0}$ & |
| + | $(~)$ & |
| + | $(~)$ & |
| + | $(~)$ & |
| + | $(~)$ & |
| + | $(~)$ \\ |
| + | \hline |
| + | $f_{1}$ & |
| + | $(x)(y)$ & |
| + | $\operatorname{d}x\ \operatorname{d}y$ & |
| + | $\operatorname{d}x\ (\operatorname{d}y)$ & |
| + | $(\operatorname{d}x)\ \operatorname{d}y$ & |
| + | $((\operatorname{d}x)(\operatorname{d}y))$ \\ |
| + | $f_{2}$ & |
| + | $(x)\ y$ & |
| + | $\operatorname{d}x\ (\operatorname{d}y)$ & |
| + | $\operatorname{d}x\ \operatorname{d}y$ & |
| + | $((\operatorname{d}x)(\operatorname{d}y))$ & |
| + | $(\operatorname{d}x)\ \operatorname{d}y$ \\ |
| + | $f_{4}$ & |
| + | $x\ (y)$ & |
| + | $(\operatorname{d}x)\ \operatorname{d}y$ & |
| + | $((\operatorname{d}x)(\operatorname{d}y))$ & |
| + | $\operatorname{d}x\ \operatorname{d}y$ & |
| + | $\operatorname{d}x\ (\operatorname{d}y)$ \\ |
| + | $f_{8}$ & |
| + | $x\ y$ & |
| + | $((\operatorname{d}x)(\operatorname{d}y))$ & |
| + | $(\operatorname{d}x)\ \operatorname{d}y$ & |
| + | $\operatorname{d}x\ (\operatorname{d}y)$ & |
| + | $\operatorname{d}x\ \operatorname{d}y$ \\ |
| + | \hline |
| + | $f_{3}$ & |
| + | $(x)$ & |
| + | $\operatorname{d}x$ & |
| + | $\operatorname{d}x$ & |
| + | $\operatorname{d}x$ & |
| + | $\operatorname{d}x$ \\ |
| + | $f_{12}$ & |
| + | $x$ & |
| + | $\operatorname{d}x$ & |
| + | $\operatorname{d}x$ & |
| + | $\operatorname{d}x$ & |
| + | $\operatorname{d}x$ \\ |
| + | \hline |
| + | $f_{6}$ & |
| + | $(x,\ y)$ & |
| + | $(\operatorname{d}x,\ \operatorname{d}y)$ & |
| + | $(\operatorname{d}x,\ \operatorname{d}y)$ & |
| + | $(\operatorname{d}x,\ \operatorname{d}y)$ & |
| + | $(\operatorname{d}x,\ \operatorname{d}y)$ \\ |
| + | $f_{9}$ & |
| + | $((x,\ y))$ & |
| + | $(\operatorname{d}x,\ \operatorname{d}y)$ & |
| + | $(\operatorname{d}x,\ \operatorname{d}y)$ & |
| + | $(\operatorname{d}x,\ \operatorname{d}y)$ & |
| + | $(\operatorname{d}x,\ \operatorname{d}y)$ \\ |
| + | \hline |
| + | $f_{5}$ & |
| + | $(y)$ & |
| + | $\operatorname{d}y$ & |
| + | $\operatorname{d}y$ & |
| + | $\operatorname{d}y$ & |
| + | $\operatorname{d}y$ \\ |
| + | $f_{10}$ & |
| + | $y$ & |
| + | $\operatorname{d}y$ & |
| + | $\operatorname{d}y$ & |
| + | $\operatorname{d}y$ & |
| + | $\operatorname{d}y$ \\ |
| + | \hline |
| + | $f_{7}$ & |
| + | $(x\ y)$ & |
| + | $((\operatorname{d}x)(\operatorname{d}y))$ & |
| + | $(\operatorname{d}x)\ \operatorname{d}y$ & |
| + | $\operatorname{d}x\ (\operatorname{d}y)$ & |
| + | $\operatorname{d}x\ \operatorname{d}y$ \\ |
| + | $f_{11}$ & |
| + | $(x\ (y))$ & |
| + | $(\operatorname{d}x)\ \operatorname{d}y$ & |
| + | $((\operatorname{d}x)(\operatorname{d}y))$ & |
| + | $\operatorname{d}x\ \operatorname{d}y$ & |
| + | $\operatorname{d}x\ (\operatorname{d}y)$ \\ |
| + | $f_{13}$ & |
| + | $((x)\ y)$ & |
| + | $\operatorname{d}x\ (\operatorname{d}y)$ & |
| + | $\operatorname{d}x\ \operatorname{d}y$ & |
| + | $((\operatorname{d}x)(\operatorname{d}y))$ & |
| + | $(\operatorname{d}x)\ \operatorname{d}y$ \\ |
| + | $f_{14}$ & |
| + | $((x)(y))$ & |
| + | $\operatorname{d}x\ \operatorname{d}y$ & |
| + | $\operatorname{d}x\ (\operatorname{d}y)$ & |
| + | $(\operatorname{d}x)\ \operatorname{d}y$ & |
| + | $((\operatorname{d}x)(\operatorname{d}y))$ \\ |
| + | \hline |
| + | $f_{15}$ & |
| + | $((~))$ & |
| + | $(~)$ & |
| + | $(~)$ & |
| + | $(~)$ & |
| + | $(~)$ \\ |
| + | \hline |
| + | \end{tabular}\end{quote} |
| + | </pre> |
| | | |
| ==Inquiry Driven Systems== | | ==Inquiry Driven Systems== |