Research Article A Unified Model of Complex Specified Information George D. Montanez*˜ Department of Computer Science, Harvey Mudd College, Claremont, CA, USA Abstract A mathematical theory of complex specified information is introduced which unifies several prior methods of computing specified complexity. Similar to how the exponential family of probability distributions have dissimilar surface forms yet share a common underlying mathematical identity, we define a model that allows us to cast Dembski’s semiotic specified complexity, Ewert et al.’s algorithmic specified complexity, Hazen et al.’s functional information, and Behe’s irreducible complexity into a common mathematical form. Adding additional constraints, we introduce canonical specified complexity models, for which one-sided conservation bounds are given, showing that large specified complexity values are unlikely under any given continuous or discrete distribution and that canonical models can be used to form statistical hypothesis tests, by bounding tail probabilities for arbitrary distributions. Cite As: Montanez˜ GD (2018) A Unified Model of Complex Specified Information. BIO-Complexity 2018 (4):1-26. doi:10.5048/BIO-C.2018.4. Editor: Robert J. Marks II Received: June 29, 2018; Accepted: November 30, 2018; Published: December 14, 2018 Copyright: © 2018 George D. Montanez.˜ This open-access article is published under the terms of the Creative Commons Attribution License, which permits free distribution and reuse in derivative works provided the original author(s) and source are credited. Notes: A Critique of this paper, when available, will be assigned doi:10.5048/BIO-C.2018.4.c. *Email:
[email protected] \Life must depend on a higher level of complexity, structure without predictable repetition, he argued." - James Gleick, \The Information: A History, a Theory, a Flood", ch.