References

  1. S. Abramsky & B. Coecke (2004): A categorical semantics of quantum protocols. In: Logic in Computer Science. Proceedings of the 19th Annual IEEE Symposium, pp. 415–425, doi:10.1109/LICS.2004.1319636.
  2. Bob B. Coecke & B. Edwards (2011): Toy quantum categories. Electron. Notes Theor. Comput. Sci. 270(1), doi:10.1016/j.entcs.2011.01.004. Available at https://arxiv.org/abs/0808.1037.
  3. M. Backens (2016): Completeness and the ZX-calculus, doi:10.1109/LICS.2004.1319636. Available at https://arxiv.org/abs/1602.08954.
  4. J. Baez, B. Coya & F. Rebro (2017): Props in network theory. Available at https://arxiv.org/abs/1707.08321.
  5. J. Baez & B. Fong (2015): A compositional framework for passive linear networks. Available at https://arxiv.org/abs/1504.05625.
  6. J. Baez, B. Fong & B. Pollard (2016): A compositional framework for Markov processes. J. Math. Phys. 57, doi:10.1063/1.4941578.
  7. K. Bar, A. Kissinger & J. Vicary (2016): Globular: an online proof assistant for higher-dimensional rewriting. Available at http://globular.science.
  8. D. Cicala (2016): Spans of cospans. Available at https://arxiv.org/abs/1611.07886.
  9. D. Cicala & K. Courser (2017): Spans of cospans in a topos. Available at https://arxiv.org/abs/1707.02098.
  10. B. Coecke & R. Duncan (2008): Interacting quantum observables. In: Automata, languages and programming. Part II, Lecture Notes in Comput. Sci. 5126. Springer, Berlin, pp. 298–310, doi:10.1007/978-3-540-70583-3_25.
  11. B. Coecke & R. Duncan (2011): Interacting quantum observables: categorical algebra and diagrammatics. New J. Phys. 13, doi:10.1088/1367-2630/13/4/043016.
  12. B. Coecke & B. Edwards (2012): Spekkens's toy theory as a category of processes. In: Mathematical foundations of information flow, Proc. Sympos. Appl. Math. 71. Amer. Math. Soc., pp. 61–68, doi:10.1090/psapm/071/602.
  13. B. Coecke, B. Edwards & R. Spekkens (2011): Phase groups and the origin of non-locality for qubits. Electron. Notes Theor. Comput. Sci. 270(2), doi:10.1016/j.entcs.2011.01.021.
  14. B. Coecke & D. Pavlovic (2008): Quantum measurements without sums. In: Mathematics of quantum computation and quantum technology, Chapman & Hall CRC Appl. Math. Nonlinear Sci. Ser.. Chapman & Hall/CRC, Boca Raton, FL, pp. 559–596, doi:10.1201/9781584889007.ch16.
  15. B. Coecke, D. Pavlovic & J. Vicary (2013): A new description of orthogonal bases. Math. Structures Comput. Sci. 23(3), doi:10.1017/S0960129512000047.
  16. B. Coecke & S. Perdrix (2012): Environment and classical channels in categorical quantum mechanics. Log. Methods Comput. Sci. 8(4), doi:10.2168/LMCS-8(4:14)2012.
  17. A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel & M. Lowe (1997): Algebraic approaches to graph transformation. Basic concepts and double pushout approach. In: Handbook of graph grammars and computing by graph transformation, Vol. 1. World Sci. Publ., River Edge, NJ, doi:10.1142/9789812384720_0003.
  18. V. Danos, E. Kashefi & P. Panangaden (2007): The measurement calculus. J. ACM 54(2), doi:10.1145/1219092.1219096.
  19. L. Dixon, R. Duncan & A. Kissinger: Quantomatic. Available at https://sites.google.com/site/quantomatic/.
  20. R. Duncan & S. Perdrix (2009): Graph states and the necessity of Euler decomposition. In: Mathematical theory and computational practice, Lecture Notes in Comput. Sci. 5635. Springer, Berlin, pp. 167–177, doi:10.1007/978-3-642-03073-4_18.
  21. R. Duncan & S. Perdrix (2010): Rewriting measurement-based quantum computations with generalised flow. Automata, Languages and Programming, doi:10.1007/978-3-642-14162-1_24.
  22. J. Evans, R. Duncan, A. Lang & P. Panangaden (2009): Classifying all mutually unbiased bases in Rel. Available at https://arxiv.org/abs/0909.4453.
  23. B. Fong (2016): The Algebra of Open and Interconnected Systems. Available at https://arxiv.org/abs/arXiv:1609.05382.
  24. A. Habel, J. Muller & D. Plump (2001): Double-pushout graph transformation revisited. Math. Structures Comput. Sci. 11(5), doi:10.1017/S0960129501003425.
  25. John J. Baez & B. Pollard (2017): A compositional framework for reaction networks. Rev. Math. Phys. 29(9), doi:10.1142/S0129055X17500283.
  26. A. Joyal & R. Street (1991): The geometry of tensor calculus. I. Adv. Math. 88(1), doi:10.1016/0001-8708(91)90003-P.
  27. A. Kissinger (2012): Pictures of processes: automated graph rewriting for monoidal categories and applications to quantum computing. Ph.D. Thesis, University of Oxford. Available at https://arxiv.org/abs/1203.0202.
  28. A. Kissinger & V. Zamdzhiev (2015): Quantomatic: a proof assistant for diagrammatic reasoning. In: Automated deduction—CADE 25, Lecture Notes in Comput. Sci. 9195. Springer, Cham, pp. 326–336, doi:10.1007/978-3-319-21401-6_22.
  29. Lucas L. Dixon, R. Duncan & A. Kissinger (2010). Electron. Proc. Theor. Comput. Sci. 26, doi:10.4204/EPTCS.26.16.
  30. S. MacLane & I. Moerdijk (2012): Sheaves in geometry and logic: A first introduction to topos theory. Springer Science & Business Media.
  31. A. Merry (2014): Reasoning with !-Graphs. CoRR abs/1403.7828. Available at http://arxiv.org/abs/1403.7828.
  32. M. Nielsen & I. Chuang (2010): Quantum computation and quantum information. Cambridge University Press, Cambridge, doi:10.1017/CBO9780511976667.
  33. D. Pavlovic (2009): Quantum and classical structures in nondeterministic computation. In: Quantum interaction, Lecture Notes in Comput. Sci. 5494. Springer, Berlin, pp. 143–157, doi:10.1007/978-3-642-00834-4_13.
  34. R. Penrose (1971): Applications of negative dimensional tensors. In: Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969). Academic Press, London, pp. 221–244. Available at http://homepages.math.uic.edu/~kauffman/Penrose.pdf.
  35. B. Pollard (2016): Open Markov Processes: A Compositional Perspective on Non-Equilibrium Steady States in Biology. Entropy 18(4), doi:10.3390/e18040140.
  36. P. Pstragowski (2014): On dualizable objects in monoidal bicategories, framed surfaces and the Cobordism Hypothesis. Available at https://arxiv.org/abs/1411.6691.
  37. V. Sassone & P. Sobocinski (2005): A congruence for Petri nets. Electronic Notes in Theoretical Computer Science 127(2), doi:10.1016/j.entcs.2005.02.008.
  38. P. Selinger (2011): A survey of graphical languages for monoidal categories. In: New structures for physics, Lecture Notes in Phys. 813. Springer, Heidelberg, pp. 289–355, doi:10.1007/978-3-642-12821-9_4.
  39. M. Shulman (2010): Constructing symmetric monoidal bicategories. Available at http://arxiv.org/abs/1004.0993.
  40. M. Stay (2016): Compact closed bicategories. Theory Appl. Categ. 31. Available at https://arxiv.org/abs/1301.1053.
Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org