Publications

A list of my published work is below.  For copyright reasons, I am unable to provide links.  I am, however, able to provide copies on request.

  • Peter Hines, M. V. Lawson, An Application of Polycyclic Monoids to Rings Semigroup Forum (56)  (1996) pp. 146-149
  • Peter Hines, The Algebra of Self-Similarity and its Applications  PhD Thesis, University of Wales, Bangor (1998)
  • Peter Hines, The Categorical Theory of Self-Similarity, Theory and Applications of Categories 6(3)  (1999) pp.33-46
  • Peter Hines, A Short Note on Coherence and Self-Similarity, {Journal of Pure and Applied Algebra (175)  (2002) pp. 135-139
  • Peter Hines, A Categorical Framework for Finite State Machines Mathematical Structures in Computer Science (13)  (2003) pp. 451-480
  • Peter Hines, Physical Systems as Constructive Logics, in Unconventional Computation, C. Calude et. al (ed.s), Springer LNCS  (2006) pp.101-112
  •  Peter Hines, E. Pothos, N. Chater, A Non-Parametric Approach to Simplicity Clustering, Applied Artificial Intelligence 21(8)  (2007) pp. 729-752
  • Peter Hines, Machine Semantics, Theoretical Computer Science 409(1)  (2008) pp. 1-23
  • Peter Hines, Machine Semantics: From Causality to Computational Models,  International Journal of Unconventional Computation 4(3)  (2008) pp. 249-272
  • E. Pothos, A.Perlman, D. Edwards, T. Gureckis, P. Hines, N. Chater Modelling Category Intuitiveness, Cognitive Science Journal  (2008) pp. 415-420
  • Peter Hines, S. Braunstein The Structure of Partial Isometries, in, Semantic Techniques in Quantum Computation, Cambridge University Press  (2010) pp.361-389
  • Peter Hines Quantum circuit oracles for Abstract Machine computations, Theoretical Computer Science 411  (2010) pp. 1501-1520
  • E. Pothos, N. Chater, P. Hines The simplicity model of unsupervised categorization,  in Formal Models of Categorization, A. Mills \& E. Pothos (ed.s)  (2010) Cambridge University Press
  • Peter Hines Can a quantum computer run the von Neumann architecture?  in B. Coecke (ed.) New Structures for Physics, Lect. Notes Phys. 813, Springer Berlin  (2011) pp.941-978
  • V. Kendon, A. Sebald, S. Stepney, M. Bechmann, P. Hines, R. Wagner Heterotic Computing, Unconventional Computation 2011, Turku, Finland. Springer L.N.C.S. 6714  (2011) pp. 113-124
  • E. Pothos, A. Perlman, T. Bailey, K. Kurtz, D. Edwards, P. Hines, J. McDonnell Measuring category intuitiveness in unconstrained categorization tasks Cognition 121(1)  (2011) pp.83-100
  • Peter Hines, P. Scott}Categorical traces from single-photon linear optics,  in S. Abramsky, M. Mislove (ed.s), AMS Proceedings of Symposia in Applied Mathematics (vol. 71)  (2012) pp. 89-124
  • S. Stepney, V. Kendon, P. Hines, A. Sebald}A framework for Heterotic Computing 8th workshop on quantum physics and logic (QPL 2011), Nijmegen, Netherlands, ETPCS (95) (2012) pp. 263-273
  • Peter Hines A categorical analogue of the monoid semiring construction, Mathematical Structures in Computer Science 23(1)  (2013) pp. 55-94
  • Peter Hines Types and forgetfulness in categorical linguistics and quantum mechanics, in C. Heunen, M. Sadrzadeh, E. Grefenstette (ed.s), Quantum Physics and Linguistics: a compositional diagrammatic discourse, Oxford University Press (2013) pp. 1-34
  • Peter Hines Quantum speed-up and categorical distributivity, in B. Coecke, L. Ong, and P. Panangaden (Eds.) Computation, Logic, Games, and Quantum Foundations, LNCS 7860, pp. 122-138 (2013)
  • Peter Hines Modular Arithmetic Identities from Untyped Categorical Coherence, in G. Dueck, D. Miller (ed.s) Reversible Computation, Springer LNCS 7984 (2013) pp. 84-95
  • Peter Hines Classical Structures based on Unitaries, in B. Coecke, P. Panangaden (ed.s) Categories \& Types in Logic, Language, and Physics, Springer LNCS 8222  (2014) pp. 188-210
  • Peter Hines Coherence and strictification for self-similarity. Journal of Homotopy \& Related Structures (2016)
  • Peter Hines Information flow in pregroup models of natural language. {\em EPTCS} (2018)

Works under review

I have recently submitted the following papers, which are now under review:

  • Peter Hines Categorical coherence in cryptography: algebra, and number theory.
  • Peter Hines Girard's $!(\ )$ as a reversible fixed-point operator
  • Peter Hines Automata-theoretic models of free pregroups

Work in progress

The following works are in progress, or have recently been completed and I intend to submit them for publication shortly:

  • Picturing communication: graphical and categorical models of information flow
  • Notes on the category theory of Cantor Space  (Monograph)
  • Grigorchuk's group G via monoidal category theory

Manuscripts

The following manuscripts of mine, although unpublished, have been referenced by other authors. The majority of the material they contain has since appeared in my published work.

  • A one-object inverse compact closed category used in the Geometry of Interaction (1996)
  • A hierarchy of finite state machines and their algebraic models (2000)
  • Unitary computations of factorials (2004)
  • (joint work with P. Scott)  Conditional quantum iteration from categorical traces (2006)
  • A constructive decision procedure for commutativity of canonical diagrams (2012)