Development of the Notion of Formal Data-Flow System as an Interpretation Instrument for Discrete Attractors.

<div>The praxis of network information technology and parallel calculations requires</div><div>&nbsp;</div><div>an extension of the concept of algorithmic system and construction of algorithmic&nbsp;</div><div>&nbsp;</div><div>systems with distributed control. The concept of the thread, developed by Brauer&nbsp;</div><div>&nbsp;</div><div>and his followers, can be considered as basis for such systems development. The&nbsp;</div><div>&nbsp;</div><div>results of embedding the production formal systems into the Brauer thread by&nbsp;</div><div>&nbsp;</div><div>the example of graph grammarsare reviewed in this work. As a result we get a&nbsp;</div><div>&nbsp;</div><div>new type of formal systems &mdash; the threading formal systems. The basis of the&nbsp;</div><div>&nbsp;</div><div>process lies in embedding the discrete attractor into the thread mechanism at the&nbsp;</div><div>&nbsp;</div><div>first choice law D1 level. And the second choice law D2 interprets the attractor&rsquo;s&nbsp;</div><div>&nbsp;</div><div>behavior as productions of the formal system. There is also a review of open&nbsp;</div><div>&nbsp;</div><div>threading systems that are managed with the Godel numbering mechanism.</div>