Wednesday, April 30, 2014

On the algebra of processes III


Let us now assume that the graphs may be infinite. We will however make some finiteness assumptions
which correspond to discrete aspects of the processes.

Consider a cospan of graphs labelled in alphabet A,  X ← G → Y. First we will take the alphabet A to be finite. We could make a less drastic assumption but I want to concentrate attention on X, Y, and G.
A consequence of the fact that A is finite is that G breaks up into subgraphs Ga, one for each element a of A, but all with the same vertex set vert(G).
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Tuesday, April 29, 2014

On the algebra of processes II

I have decided to write a sequence of short posts explaining the ideas behind the abstract I recently posted. I forgot to mention in the abstract that there is a 2009 paper on Arxiv by Luisa de Francesco Albasini, Nicoletta Sabadini and me with some more explanation of our ideas (arXiv:0909.4136 ). It was a summary of thoughts over the summer holiday in Santa Caterina Valfurva that year and was never published. It lacks the distributive laws, and promises to later "fill out details of matters sketched" which promise I hope to partially fulfill in these posts.
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Tuesday, April 22, 2014

On the algebra of processes

The following is an abstract submitted to a conference (only half a page was permitted). I would like expand a little here on the matter in the next day or so.

Abstract: On the algebra of processes
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Sunday, April 20, 2014

Villa Carlotta, Lake Como

To visit in late April.


Monday, April 14, 2014

How to coil a hose

I just bought a hose to water the newly planted roses at our mountain house.  Here is one Nicoletta planted last year:
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