Open Graphs and Computational Reasoning
Abstract
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of halfedges (edges which are drawn with an unconnected end) and enjoy rich compositional principles by connecting graphs along these halfedges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.
 Publication:

arXiv eprints
 Pub Date:
 July 2010
 arXiv:
 arXiv:1007.3794
 Bibcode:
 2010arXiv1007.3794D
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Mathematical Software;
 Computer Science  Symbolic Computation
 EPrint:
 In Proceedings DCM 2010, arXiv:1006.1937