On some invariance properties of the asynchronous flows

On some invariance properties of the asynchronous flows, ICMA 2015, The 14th International Conference on Mathematics and its Applications, Timișoara, November 5-7, 2015, Proceedings, Ioan Goleț, Liviu Cădariu editors, editura Politehnica Timișoara, 2016, pp. 145-150

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Mathematical Subject Classification (2010): 94C10

Keywords and phrases: Boolean function, asynchronous flow, invariance, connectedness, path connectedness

The asynchronous circuits from electronics are modeled by Boolean functions Φ:{0,1}ⁿ→{0,1}ⁿ that iterate their coordinates Φ₁,...,Φ_n independently on each other, giving the so-called asynchronous flows. The bibliography is mainly related to the (real, usual) dynamical systems theory and we use analogies. The invariance of a set A⊂{0,1}ⁿ is the most important property addressed in the paper and we define some concepts (connectedness, path connectedness) compatible with it. We initiate a study in this framework and we show in the end that several other possibilities of defining invariance exist, giving several other concepts (connectedness, path connectedness) compatible with them, that require their own study.