1 research outputs found
Span(Graph): a Canonical Feedback Algebra of Open Transition Systems
We show that Span(Graph)*, an algebra for open transition systems introduced
by Katis, Sabadini and Walters, satisfies a universal property. By itself, this
is a justification of the canonicity of this model of concurrency. However, the
universal property is itself of interest, being a formal demonstration of the
relationship between feedback and state. Indeed, feedback categories, also
originally proposed by Katis, Sabadini and Walters, are a weakening of traced
monoidal categories, with various applications in computer science. A state
bootstrapping technique, which has appeared in several different contexts,
yields free such categories. We show that Span(Graph)* arises in this way,
being the free feedback category over Span(Set). Given that the latter can be
seen as an algebra of predicates, the algebra of open transition systems thus
arises - roughly speaking - as the result of bootstrapping state to that
algebra. Finally, we generalize feedback categories endowing state spaces with
extra structure: this extends the framework from mere transition systems to
automata with initial and final states.Comment: 48 pages, 33 figures, journal versio