Moment Semantics for Reversible Rule-Based Systems

We develop a notion of stochastic rewriting over marked graphs – i.e. directed multigraphs with degree constraints. The approach is based on double-pushout (DPO) graph rewriting. Marked graphs are expressive enough to internalize the ‘no-dangling-edge’ condition inherent in DPO rewriting. Our main result is that the linear span of marked graph occurrence-counting functions – or motif functions – form an algebra which is closed under the infinitesimal generator of (the Markov chain associated with) any such rewriting system. This gives a general procedure to derive the moment semantics of any such rewriting system, as a countable (and recursively enumerable) system of differential equations indexed by motif functions. The differential system describes the time evolution of moments (of any order) of these motif functions under the rewriting system. We illustrate the semantics using the example of preferential attachment networks; a well-studied complex system, which meshes well with our notion of marked graph rewriting. We show how in this case our procedure obtains a finite description of all moments of degree counts for a fixed degree.


Editor(s):
Krivine, Jean
Stefani, Jean-Bernard
Published in:
Reversible Computation 7th International Conference, RC 2015, Grenoble, France, July 16-17, 2015, Proceedings, 3-26
Presented at:
7th International Conference on Reversible Computation, Grenoble, France, July 16-17, 2015
Year:
2015
Publisher:
Switzerland, Springer International Publishing
ISSN:
0302-9743
ISBN:
978-3-319-20859-6
Keywords:
Note:
Invited paper. This work was sponsored by the European Research Council (ERC) under the grants DOPPLER (587327) and RULE (320823).
Laboratories:




 Record created 2015-07-26, last modified 2018-04-20

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