2011/07/31 by David Balduzzi
Computer Science · Mathematics · Physics and Astronomy · #cs.IT #cs.DC #cs.NE #math.CT #math.IT #nlin.CG
paper · pdf · doi:10.4204/eptcs.88.3
published as EPTCS 88, 2012, pp. 28-42 · In Proceedings DCM 2011, arXiv:1207.6821
arxiv created 2012/07/31 · arxiv updated 2012/08/01
The internal structure of a measuring device, which depends on what its components are and how they are organized, determines how it categorizes its inputs. This paper presents a geometric approach to studying the internal structure of measurements performed by distributed systems such as probabilistic cellular automata. It constructs the quale, a family of sections of a suitably defined presheaf, whose elements correspond to the measurements performed by all subsystems of a distributed system. Using the quale we quantify (i) the information generated by a measurement; (ii) the extent to which a measurement is context-dependent; and (iii) whether a measurement is decomposable into independent submeasurements, which turns out to be equivalent to context-dependence. Finally, we show that only indecomposable measurements are more informative than the sum of their submeasurements.