Slime Mould Games Based on Rough Set Theory

Abramsky, S. and Jagadeesan, R. (1994). Games and full completeness for multiplicative linear logic, The Journal of Symbolic Logic 59(2): 543-574.10.2307/2275407Search in Google Scholar

Abramsky, S. and Mellies, P.-A. (1999). Concurrent games and full completeness, Proceedings of the 14th Symposium on Logic in Computer Science, Trento, Italy, pp. 431-442.Search in Google Scholar

Aczel, P. (1988). Non-Well-Founded Sets, Cambridge University Press, Cambridge.Search in Google Scholar

Adamatzky, A. (2007a). Physarum machine: Implementation of a Kolmogorov-Uspensky machine on a biological substrate, Parallel Processing Letters 17(04): 455-467.10.1142/S0129626407003150Search in Google Scholar

Adamatzky, A. (2007b). Physarum machines: Encapsulating reaction-diffusion to compute spanning tree, Die Naturwissenschaften 94(12): 975-980.10.1007/s00114-007-0276-517603779Search in Google Scholar

Adamatzky, A. (2010). Physarum Machines: Computers from Slime Mould, World Scientific, Singapore.10.1142/7968Search in Google Scholar

Baillot, P., Danos, V., Ehrhard, T. and Regnier, L. (1997). Believe it or not, AJM’s games is a model of classical linear logic, Proceedings of the 12th Symposium on Logic in Computer Science, Warsaw, Poland, pp. 68-75.Search in Google Scholar

Bouyer, P., Brenguier, R., Markey, N. and Ummels, M. (2011). Nash equilibria in concurrent games with B¨uchi objectives, Proceedings of the IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, Mumbai, India, pp. 375-386.Search in Google Scholar

Bouyer, P., Brenguier, R., Markey, N. and Ummels, M. (2012). Concurrent games with ordered objectives, in L. Birkedal (Ed.), Foundations of Software Science and Computational Structures, Springer, Berlin, pp. 301-315.10.1007/978-3-642-28729-9_20Search in Google Scholar

Brenguier, R. (2013). PRALINE: A tool for computing Nash equilibria in concurrent games, in N. Sharygina and H. Veith (Eds.), Computer Aided Verification, Springer, Berlin, pp. 890-895.10.1007/978-3-642-39799-8_63Search in Google Scholar

Clempner, J. (2006). Modeling shortest path games with Petri nets: A Lyapunov based theory, International Journal of Applied Mathematics and Computer Science 16(3): 387-397.Search in Google Scholar

Henzinger, T.A., Manna, Z. and Pnueli, A. (1992). Timed transition systems, in J.W. de Bakker et al. (Eds.), REX 1991, Lecture Notes in Computer Science, Vol. 600, Springer, Berlin/Heidelberg, pp. 226-251.10.1007/BFb0031995Search in Google Scholar

Khrennikov, A. and Schumann, A. (2014). Quantum non-objectivity from performativity of quantum phenomena, Physica Scripta 2014(T163): 014-020.10.1088/0031-8949/2014/T163/014020Search in Google Scholar

Kim, J. and Jeong, S. (1994). Learn to Play Go, Good Move Press, New York, NY.Search in Google Scholar

Nakagaki, T., Yamada, H. and Toth, A. (2000). Maze-solving by an amoeboid organism, Nature 407(6803): 470-470.10.1038/3503515911028990Search in Google Scholar

Neubert, H., Nowotny, W., Baumann, K. and Marx, H. (1995). Die Myxomyceten Deutschlands und des angrenzenden Alpenraumes unter besonderer Berucksichtigung Österreichs. Band 2: Physarales, Karlheinz Baumann Verlag, Gomaringen.Search in Google Scholar

Pancerz, K. and Schumann, A. (2015). Rough set models of Physarum machines, International Journal of General Systems 44(3): 314-325.10.1080/03081079.2014.997529Search in Google Scholar

Pancerz, K. and Schumann, A. (2017). Rough set description of strategy games on Physarum machines, in A. Adamatzky (Ed.), Advances in Unconventional Computing, Volume 2: Prototypes, Models and Algorithms, Emergence, Complexity and Computation, Vol. 23, Springer, Cham, pp. 615-636.10.1007/978-3-319-33921-4_23Search in Google Scholar

Pawlak, Z. (1991). Rough Sets. Theoretical Aspects of Reasoning about Data, Kluwer, Dordrecht.10.1007/978-94-011-3534-4Search in Google Scholar

Petri, R.J. (1887). Eine kleine modification des Koch’schen Plattenverfahrens, Centralblatt f¨ur Bakteriologie und Parasitenkunde 1: 279-280.Search in Google Scholar

Saipara, P. and Kumam, P. (2016). Fuzzy games for a general Bayesian abstract fuzzy economy model of product measurable spaces, Mathematical Methods in the Applied Sciences 39(16): 4810-4819.10.1002/mma.3809Search in Google Scholar

Schumann, A. (2014). Payoff cellular automata and reflexive games, Journal of Cellular Automata 9(4): 287-313.Search in Google Scholar

Schumann, A. (2016). Syllogistic versions of Go games on Physarum, in A. Adamatzky (Ed.), Advances in Physarum Machines: Sensing and Computing with Slime Mould, Emergence, Complexity and Computation, Vol. 21, Springer, Cham, pp. 651-685.10.1007/978-3-319-26662-6_30Search in Google Scholar

Schumann, A. and Pancerz, K. (2015). A rough set version of the Go game on Physarum machines, Proceedings of the 9th EAI International Conference on Bio-inspired Information and Communications Technologies, New York, NY, USA, pp. 446-452.10.4108/eai.3-12-2015.2262488Search in Google Scholar

Schumann, A., Pancerz, K., Adamatzky, A. and Grube, M. (2014). Bio-inspired game theory: The case of Physarum polycephalum, Proceedings of the 8th International Conference on Bio-inspired Information and Communications Technologies, Boston, MA, USA, pp. 9-16.10.4108/icst.bict.2014.257869Search in Google Scholar

Trejo, K., Clempner, J. and Poznyak, A. (2015). Computing the Stackelberg/Nash equilibria using the extraproximal method: Convergence analysis and implementation details forMarkov chains games, International Journal of Applied Mathematics and Computer Science 25(2): 337-351, DOI: 10.1515/amcs-2015-0026.10.1515/amcs-2015-0026Open DOISearch in Google Scholar

Winskel, G. and Nielsen, M. (1995). Models for concurrency, in S. Abramsky et al. (Eds.), Handbook of Logic in Computer Science, Vol. 4, Oxford University Press, Oxford, pp. 1-148.Search in Google Scholar

Yao, Y. and Lin, T. (1996). Generalization of rough sets using modal logics, Intelligent Automation and Soft Computing 2(2): 103-120.10.1080/10798587.1996.10750660Search in Google Scholar

Yao, Y.Y., Wong, S.K.M. and Lin, T.Y. (1997). A review of rough set models, in T.Y. Lin and N. Cercone (Eds.), Rough Sets and Data Mining: Analysis of Imprecise Data, Kluwer, Dordrecht, pp. 47-75.10.1007/978-1-4613-1461-5_3Search in Google Scholar

Ziarko, W. (1993). Variable precision rough set model, Journal of Computer and System Sciences 46(1): 39-59.10.1016/0022-0000(93)90048-2Search in Google Scholar