LARA

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sav08:atomic_diagram_normal_form [2009/05/12 23:28]
vkuncak
sav08:atomic_diagram_normal_form [2009/05/12 23:30]
vkuncak
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     x_1 = f(x) \land s_1 = x_1 + y \land s_1 < z     x_1 = f(x) \land s_1 = x_1 + y \land s_1 < z
 \] \]
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 **Example:​** When we have relation symbols $<$ and no function symbols, and consider 3 variables $x$,​$y$,​$z$,​ possible atomic formulas are: **Example:​** When we have relation symbols $<$ and no function symbols, and consider 3 variables $x$,​$y$,​$z$,​ possible atomic formulas are:
-  * $x=y$, $y=x$, $x=z$, $z=x$, $y=z$, $z=y$ +  * $x=x$, $y=y$, $z=z$, ​$x=y$, $y=x$, $x=z$, $z=x$, $y=z$, $z=y$ 
-  * $x<y$, $y<x$, $x<z$, $z<x$, $y<z$, $z<y$+  * $x<x$, $y<y$, $z<​z$, ​$x<y$, $y<x$, $x<z$, $z<x$, $y<z$, $z<y$ 
 +and there are 3^2+3^2=18 atomic formulas.
  
 ===== Atomic Diagram Normal Form ===== ===== Atomic Diagram Normal Form =====