Thermodynamic Graph-Rewriting
نویسندگان
چکیده
We develop a new thermodynamic approach to stochastic graph-rewriting. The ingredients are a finite set of reversible graph-rewriting rules G (called generating rules), a finite set of connected graphs P (called energy patterns), and an energy cost function which associates real values to each of these energy patterns. The idea is that G defines the qualitative dynamics, by showing which transformations are possible, while P and allow one to attach an energy to the reachable graphs and, thereby, describe their long-term probability distribution π. Given G and P, we construct a finite set of rules GP which (i) has the same qualitative transition system as G; and (ii) when equipped with rates according to , defines a continuous-time Markov chain of which π is the unique fixed point. The construction relies on the use of site graphs and a technique of ‘growth policy’ for quantitative rule refinement which is of independent interest. This division of labour between the qualitative and long-term quantitative aspects of the dynamics leads to intuitive and concise descriptions for realistic models (see §4). It also guarantees thermodynamical consistency (aka detailed balance), otherwise known to be undecidable, which is important for some applications. Finally, it leads to parsimonious parameterizations of models, again an important point in some applications.
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ورودعنوان ژورنال:
- Logical Methods in Computer Science
دوره 11 شماره
صفحات -
تاریخ انتشار 2013