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Computer Science > Logic in Computer Science

arXiv:1007.3794v1 (cs)
[Submitted on 22 Jul 2010]

Title:Open Graphs and Computational Reasoning

Authors:Lucas Dixon (University of Edinburgh), Ross Duncan (University of Oxford), Aleks Kissinger (University of Oxford)
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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 half-edges (edges which are drawn with an unconnected end) and enjoy rich compositional principles by connecting graphs along these half-edges. 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.
Comments: In Proceedings DCM 2010, arXiv:1006.1937
Subjects: Logic in Computer Science (cs.LO); Mathematical Software (cs.MS); Symbolic Computation (cs.SC)
Cite as: arXiv:1007.3794 [cs.LO]
  (or arXiv:1007.3794v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.1007.3794
Journal reference: EPTCS 26, 2010, pp. 169-180
Related DOI: https://doi.org/10.4204/EPTCS.26.16

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Thu, 22 Jul 2010 03:31:39 UTC (28 KB)
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