Vanishment this world!$
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A thing is a 3-tuple $(G,A,\delta)$ such that:
- $G=(V,E)$ is a directed graph;
- $A,V$ are two nonempty sets;
- $\delta:A \times V\to\GF(2)$.
The directed graph $G$ is called the world of the thing. A vertex of $G$ is called a state of world that the thing thinks existing. An element of $A$ is called an another thing that the thing thinks existing. For $a \in
A$ and $v \in V$, we
say the thing senses
$a$ in $v$ if $\delta(a,v)=1$, and the opposite if $\delta(a,v)=0$.
In the rest of this daydream, $(G,A,\delta)$ is a thing as defined above, where $G=(V,E)$.
A subjective world of the thing is a walk in $G$.
Let $w=(v_0,v_1,\dots)$ be a subjective world of the thing as defined above.
For $u,v$ two vertices of $w$, if there exists a finite sub-walk of $w$ which starts at $u$ and ends at $v$, then $u$ is called a past of $v$, and $v$ is called a future of $u$.
If there exists $e \in A$ such that $\forall v \in w$, $\delta(e,v)=1$, the thing is then called a living thing, and $e$ is called its ego.
In the rest of this daydream, we focus on a living thing $L = (T, w, e)$ as defined above, where $T = (G,A,\delta)$ is the thing itself, $w=(v_0,v_1,\dots)$ is one of its subjective worlds, and $e \in A$ is one of its egos corresponding to
$w$.
$L$ is called mortal (immortal) if $w$ is finite (infinite).