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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
Revision as of 13:25, 9 March 2009
, 13:25, 9 March 2009→Note 5: use \texttt for cactus code
==Note 5==
==Note 5==
For a slightly more interesting example, let's suppose that we have a dynamic system that is known by its state space <math>X,\!</math> and we have a boolean state variable <math>x : X \to \mathbb{B}.</math> In addition, we are given an initial condition <math>\texttt{x = dx}</math> and a law <math>\texttt{d}^\texttt{2}\texttt{x = (x)}.</math>
For a slightly more interesting example, let's suppose that we have a dynamic system that is known by its state space <math>X,\!</math> and we have a boolean state variable <math>x : X \to \mathbb{B}.</math> In addition, we are given an initial condition <math>\texttt{x~=~dx}</math> and a law <math>\begin{matrix}\texttt{d}^\texttt{2}\texttt{x~=~(x)}.\end{matrix}</math>
The initial condition has two cases: either <math>x = dx = 0\!</math> or <math>x = dx = 1.\!</math>
The initial condition has two cases: either <math>x = dx = 0\!</math> or <math>x = dx = 1.\!</math>