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User:Jon Awbrey/Figures and Tables 1 (view source)

Revision as of 12:14, 18 October 2025

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+ Table 13. Algorithmic Translation Rules
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==Format Samples==
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 +
<ul>
 +
<li><math>\rightsquigarrow</math></li>
 +
 
 +
<li><math>\leftrightsquigarrow</math></li>
 +
 
 +
<li><math>\xrightarrow{\mathrm{Parse}}</math></li>
 +
 
 +
<li><math>\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Parse}}</math></li>
 +
</ul>
 +
 
 +
==Table 13. Algorithmic Translation Rules==
 +
 
 +
<br>
 +
 
 +
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%"
 +
|+ style="height:30px" | <math>\text{Table 13. Algorithmic Translation Rules}</math>
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|- style="height:40px; background:ghostwhite"
 +
|
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{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; text-align:center; width:100%"
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| width="33%" | <math>\text{Sentence in PARCE}</math>
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| width="33%" | <math>\xrightarrow{\mathrm{Parse}}</math>
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| width="33%" | <math>\text{Graph in PARC}</math>
 +
|}
 +
|-
 +
|
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{| align="center" border="0" cellpadding="8" cellspacing="0" style="text-align:center; width:100%"
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| width="33%" | <math>\mathrm{Conc}^0</math>
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| width="33%" | <math>\xrightarrow{\mathrm{Parse}}</math>
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| width="33%" | <math>\mathrm{Node}^0</math>
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|-
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| width="33%" | <math>\mathrm{Conc}_{j=1}^k s_j</math>
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| width="33%" | <math>\xrightarrow{\mathrm{Parse}}</math>
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| width="33%" | <math>\mathrm{Node}_{j=1}^k \mathrm{Parse} (s_j)</math>
 +
|}
 +
|-
 +
|
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{| align="center" border="0" cellpadding="8" cellspacing="0" style="text-align:center; width:100%"
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| width="33%" | <math>\mathrm{Surc}^0</math>
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| width="33%" | <math>\xrightarrow{\mathrm{Parse}}</math>
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| width="33%" | <math>\mathrm{Lobe}^0</math>
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|-
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| width="33%" | <math>\mathrm{Surc}_{j=1}^k s_j</math>
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| width="33%" | <math>\xrightarrow{\mathrm{Parse}}</math>
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| width="33%" | <math>\mathrm{Lobe}_{j=1}^k \mathrm{Parse} (s_j)</math>
 +
|}
 +
|}
 +
 
 +
<br>
 +
 
 +
==Table 14. Semantic Translation &bull; Functional Form==
 +
 
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<br>
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%"
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|+ style="height:30px" | <math>\text{Table 14. Semantic Translation : Functional Form}</math>
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|- style="height:40px; background:ghostwhite"
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|
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{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; width:100%"
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| width="20%" | <math>\mathrm{Sentence}</math>
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| width="20%" | <math>\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Parse}}</math>
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| width="20%" | <math>\mathrm{Graph}</math>
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| width="20%" | <math>\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Denotation}}</math>
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| width="20%" | <math>\mathrm{Proposition}</math>
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|}
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|-
 +
|
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{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
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| width="20%" | <math>s_j</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
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| width="20%" | <math>C_j</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
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| width="20%" | <math>q_j</math>
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|}
 +
|-
 +
|
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{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 +
| width="20%" | <math>\mathrm{Conc}^0</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
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| width="20%" | <math>\mathrm{Node}^0</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
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| width="20%" | <math>1</math>
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|-
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| width="20%" | <math>\mathrm{Conc}^k_j s_j</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
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| width="20%" | <math>\mathrm{Node}^k_j C_j</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
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| width="20%" | <math>\mathrm{Conj}^k_j q_j</math>
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|}
 +
|-
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|
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{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 +
| width="20%" | <math>\mathrm{Surc}^0</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
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| width="20%" | <math>\mathrm{Lobe}^0</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
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| width="20%" | <math>0</math>
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|-
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| width="20%" | <math>\mathrm{Surc}^k_j s_j</math>
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| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
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| width="20%" | <math>\mathrm{Lobe}^k_j C_j</math>
 +
| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
 +
| width="20%" | <math>\mathrm{Surj}^k_j q_j</math>
 +
|}
 +
|}
 +
 
 +
<br>
 +
 
 +
==Table 15. Semantic Translation &bull; Equational Form==
 +
 
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<br>
 +
 
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%"
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|+ style="height:30px" | <math>\text{Table 15. Semantic Translation : Equational Form}</math>
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|- style="height:40px; background:ghostwhite"
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|
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{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; width:100%"
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| width="20%" | <math>\downharpoonleft \mathrm{Sentence} \downharpoonright</math>
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| width="20%" | <math>\stackrel{\mathrm{Parse}}{=}</math>
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| width="20%" | <math>\downharpoonleft \mathrm{Graph} \downharpoonright</math>
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| width="20%" | <math>\stackrel{\mathrm{Denotation}}{=}</math>
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| width="20%" | <math>\mathrm{Proposition}</math>
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|}
 +
|-
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|
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{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 +
| width="20%" | <math>\downharpoonleft s_j \downharpoonright</math>
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| width="20%" | <math>=</math>
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| width="20%" | <math>\downharpoonleft C_j \downharpoonright</math>
 +
| width="20%" | <math>=</math>
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| width="20%" | <math>q_j</math>
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|}
 +
|-
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|
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{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
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| width="20%" | <math>\downharpoonleft \mathrm{Conc}^0 \downharpoonright</math>
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| width="20%" | <math>=</math>
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| width="20%" | <math>\downharpoonleft \mathrm{Node}^0 \downharpoonright</math>
 +
| width="20%" | <math>=</math>
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| width="20%" | <math>1</math>
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|-
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| width="20%" | <math>\downharpoonleft \mathrm{Conc}^k_j s_j \downharpoonright</math>
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| width="20%" | <math>=</math>
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| width="20%" | <math>\downharpoonleft \mathrm{Node}^k_j C_j \downharpoonright</math>
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| width="20%" | <math>=</math>
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| width="20%" | <math>\mathrm{Conj}^k_j q_j</math>
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|}
 +
|-
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|
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{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
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| width="20%" | <math>\downharpoonleft \mathrm{Surc}^0 \downharpoonright</math>
 +
| width="20%" | <math>=</math>
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| width="20%" | <math>\downharpoonleft \mathrm{Lobe}^0 \downharpoonright</math>
 +
| width="20%" | <math>=</math>
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| width="20%" | <math>0</math>
 +
|-
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| width="20%" | <math>\downharpoonleft \mathrm{Surc}^k_j s_j \downharpoonright</math>
 +
| width="20%" | <math>=</math>
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| width="20%" | <math>\downharpoonleft \mathrm{Lobe}^k_j C_j \downharpoonright</math>
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| width="20%" | <math>=</math>
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| width="20%" | <math>\mathrm{Surj}^k_j q_j</math>
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|}
 +
|}
 +
 
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<br>
 +
 
 +
==Table 16. Boolean Functions on Zero Variables==
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<br>
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 +
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%"
 +
|+ style="height:30px" | <math>\text{Table 16. Boolean Functions on Zero Variables}</math>
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|- style="height:40px; background:ghostwhite"
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| width="14%" | <math>F</math>
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| width="14%" | <math>F</math>
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| width="48%" | <math>F()</math>
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| width="24%" | <math>F</math>
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|-
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| <math>0</math>
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| <math>F_0^{(0)}</math>
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| <math>0</math>
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| <math>\texttt{( )}</math>
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|-
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| <math>1</math>
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| <math>F_1^{(0)}</math>
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| <math>1</math>
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| <math>\texttt{(( ))}</math>
 +
|}
 +
 
 +
<br>
 +
 
 +
==Table 17. Boolean Functions on One Variable==
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<br>
 +
 
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{| align="center" border="1" cellpadding="6" cellspacing="0" style="text-align:center; width:60%"
 +
|+ style="height:30px" | <math>\text{Table 17. Boolean Functions on One Variable}</math>
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|- style="height:40px; background:ghostwhite"
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| width="14%" | <math>F</math>
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| width="14%" | <math>F</math>
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| colspan="2" | <math>F(x)</math>
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| width="24%" | <math>F</math>
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|- style="height:40px; background:ghostwhite"
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| width="14%" | &nbsp;
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| width="14%" | &nbsp;
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| width="24%" | <math>F(1)</math>
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| width="24%" | <math>F(0)</math>
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| width="24%" | &nbsp;
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|-
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| <math>F_0^{(1)}</math>
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| <math>F_{00}^{(1)}</math>
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| <math>0</math>
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| <math>0</math>
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| <math>\texttt{( )}</math>
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|-
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| <math>F_1^{(1)}</math>
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| <math>F_{01}^{(1)}</math>
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| <math>0</math>
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| <math>1</math>
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| <math>\texttt{(} x \texttt{)}</math>
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|-
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| <math>F_2^{(1)}</math>
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| <math>F_{10}^{(1)}</math>
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| <math>1</math>
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| <math>0</math>
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| <math>x</math>
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|-
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| <math>F_3^{(1)}</math>
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| <math>F_{11}^{(1)}</math>
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| <math>1</math>
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| <math>1</math>
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| <math>\texttt{(( ))}</math>
 +
|}
 +
 
 +
<br>
 +
 
 +
==Table 18. Boolean Functions on Two Variables==
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<br>
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{| align="center" border="1" cellpadding="4" cellspacing="0" style="text-align:center; width:60%"
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|+ style="height:30px" | <math>\text{Table 18. Boolean Functions on Two Variables}</math>
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|- style="height:40px; background:ghostwhite"
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| width="14%" | <math>F</math>
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| width="14%" | <math>F</math>
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| colspan="4" | <math>F(x, y)</math>
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| width="24%" | <math>F</math>
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|- style="height:40px; background:ghostwhite"
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| width="14%" | &nbsp;
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| width="14%" | &nbsp;
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| width="12%" | <math>F(1, 1)</math>
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| width="12%" | <math>F(1, 0)</math>
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| width="12%" | <math>F(0, 1)</math>
 +
| width="12%" | <math>F(0, 0)</math>
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| width="24%" | &nbsp;
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|-
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| <math>F_{0}^{(2)}</math>
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| <math>F_{0000}^{(2)}</math>
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| <math>0</math>
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| <math>0</math>
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| <math>0</math>
 +
| <math>0</math>
 +
| <math>\texttt{( )}</math>
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|-
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| <math>F_{1}^{(2)}</math>
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| <math>F_{0001}^{(2)}</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>\texttt{(} x \texttt{)(} y \texttt{)}</math>
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|-
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| <math>F_{2}^{(2)}</math>
 +
| <math>F_{0010}^{(2)}</math>
 +
| <math>0</math>
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| <math>0</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>\texttt{(} x \texttt{)} y</math>
 +
|-
 +
| <math>F_{3}^{(2)}</math>
 +
| <math>F_{0011}^{(2)}</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>\texttt{(} x \texttt{)}</math>
 +
|-
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| <math>F_{4}^{(2)}</math>
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| <math>F_{0100}^{(2)}</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>x \texttt{(} y \texttt{)}</math>
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|-
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| <math>F_{5}^{(2)}</math>
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| <math>F_{0101}^{(2)}</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>\texttt{(} y \texttt{)}</math>
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|-
 +
| <math>F_{6}^{(2)}</math>
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| <math>F_{0110}^{(2)}</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>\texttt{(} x \texttt{,} y \texttt{)}</math>
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|-
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| <math>F_{7}^{(2)}</math>
 +
| <math>F_{0111}^{(2)}</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>\texttt{(} x y \texttt{)}</math>
 +
|-
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| <math>F_{8}^{(2)}</math>
 +
| <math>F_{1000}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>x y</math>
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|-
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| <math>F_{9}^{(2)}</math>
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| <math>F_{1001}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>\texttt{((} x \texttt{,} y \texttt{))}</math>
 +
|-
 +
| <math>F_{10}^{(2)}</math>
 +
| <math>F_{1010}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>y</math>
 +
|-
 +
| <math>F_{11}^{(2)}</math>
 +
| <math>F_{1011}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>\texttt{(} x \texttt{(} y \texttt{))}</math>
 +
|-
 +
| <math>F_{12}^{(2)}</math>
 +
| <math>F_{1100}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>x</math>
 +
|-
 +
| <math>F_{13}^{(2)}</math>
 +
| <math>F_{1101}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>\texttt{((} x \texttt{)} y \texttt{)}</math>
 +
|-
 +
| <math>F_{14}^{(2)}</math>
 +
| <math>F_{1110}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>\texttt{((} x \texttt{)(} y \texttt{))}</math>
 +
|-
 +
| <math>F_{15}^{(2)}</math>
 +
| <math>F_{1111}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>\texttt{(( ))}</math>
 +
|}
 +
 
 +
<br>
Jon Awbrey
12,117

edits

Retrieved from "https://mywikibiz.com/Special:MobileDiff/481152...481160"