A characterisation of weightable quasi-metric generating functions

References

• M.A. Alghamdi, N. Shahzad, and O. Valero, Fixed point theorems in generalized metric spaces with applications to Computer Science, Fixed Point Theory and Applications 2013 (2013), 118.
   Google Scholar
• J. Borsík and J. Doboš, On a product of metric spaces, Math. Slovaca 31 (1981), 193–205.
   Google Scholar
• M.M. Deza and E. Deza, Encyclopedia of Distances, Springer, Berlin, 2009.
   Google Scholar
• L.M. García-Raffi, S. Romaguera, and E.A. Sánchez-Pérez, Sequence spaces and asymmetric norms in the theory of computational complexity, Mathematical and Computer Modeling 36 (2002), 1–11. doi: 10.1016/S0895-7177(02)00100-0
   Web of Science ®Google Scholar
• J. Goubault-Larrecq, Non-Hausdorff Topology and Domain Theory, Cambridge University Press, New York, 2013.
   Google Scholar
• J. Guerrero, J.J. Miñana, and O. Valero, On the Use of Fuzzy Preorders in Multi-robot Task Allocation Problem, In: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018, J. Medina et al. (eds.), Communications in Computer and Information Science, Vol. 853, pp. 195–206, Springer, Cham, 2018.
   Google Scholar
• P. Hitzler and A.K. Seda, Mathematical Aspects of Logic Programming Semantics, CRC Press, Boca Raton, 2010.
   Google Scholar
• H.-P.A. Künzi and V. Vajner, Weighted quasi-metrics, Annals of the New York Academy of Sciences 728 (2994), 64–77.
   Google Scholar
• J. Martín, G. Mayor, and O. Valero, On the symmetrization of quasi-metrics: an aggregation perspective, In: Aggregation Functions in Theory and in Practice. Advances in Intelligent Systems and Computing, H. Bustince et al. (eds.), Vol. 228, pp. 319-33, Springer, Berlin, 2013.
   Google Scholar
• S.G. Matthews, Partial metric topology, Annals of the New York Academy of Sciences 728 (1994), 183–197. doi: 10.1111/j.1749-6632.1994.tb44144.x
   Google Scholar
• S.G. Matthews, The cycle contraction mapping theorem, Theoretical Computer Science 151 (1995), 195–205. doi: 10.1016/0304-3975(95)00051-W
   Google Scholar
• J.J. Miñana and O. Valero, On Matthews’ relationship between quasi-metrics and partial metrics: an aggregation perspective, Results in Mathematics 5(2) (2020), 1–28.
   Google Scholar
• V. Pestov and A. Stojmirović, Indexing schemes for similarity search: an illustrated paradigm, Fundamenta Informaticae 70 (2006), 367–385.
   Web of Science ®Google Scholar
• V. Pestov and A. Stojmirović, Indexing schemes for similarity search in datasets of short protein fragments, Information Systems 32 (2007), 1145–1165. doi: 10.1016/j.is.2007.03.001
   Web of Science ®Google Scholar
• J. Rodríguez-López, S. Romaguera, and O. Valero, Denotational semantics for programming languages, balanced quasi-metrics and fixed points, International Journal of Computer Mathematics 85 (2008), 623–630. doi: 10.1080/00207160701210653
   Web of Science ®Google Scholar
• S. Romaguera, E.A. Sánchez-Pérez, and O. Valero, Computing complexity distances between algorithms, Kybernetika 39 (2003), 569–582.
   Web of Science ®Google Scholar
• S. Romaguera and M.P. Schellekens, Quasi-metric properties of complexity spaces, Topology and its Applications 98 (1999), 311–322. doi: 10.1016/S0166-8641(98)00102-3
   Web of Science ®Google Scholar
• S. Romaguera and M.P. Schellekens, The quasi-metric of complexity convergence, Quaestiones Mathematicae 23 (2000), 359–374. doi: 10.2989/16073600009485983
   Google Scholar
• S. Romaguera, M. Schellekens, and O. Valero, The complexity space of partial functions: a connection between complexity analysis and denotational semantics, International Journal of Computer Mathematics 88 (2011), 1819–1829. doi: 10.1080/00207161003631885
   Web of Science ®Google Scholar
• S. Romaguera, P. Tirado, and O. Valero, Complete partial metric spaces have partially metrizable computational models, International Journal of Computer Mathematics 89 (2012), 284–290. doi: 10.1080/00207160.2011.559229
   Web of Science ®Google Scholar
• S. Romaguera, P. Tirado, and O. Valero, New results on mathematical foundations of asymptotic complexity analysis of algorithms via complexity space, International Journal of Computer Mathematics 89 (2012), 1728–1741. doi: 10.1080/00207160.2012.659246
   Web of Science ®Google Scholar
• S. Romaguera and O. Valero, A quantitative computational model for complete partial metric spaces via formal balls, Mathematical Structures in Computer Science 19 (2009), 541–563. doi: 10.1017/S0960129509007671
   Web of Science ®Google Scholar
• S. Romaguera and O. Valero, Domain theoretic characterizations of quasi-metric completeness in terms of formal balls, Mathematical Structures in Computer Science 20 (2010), 453–472. doi: 10.1017/S0960129510000010
   Web of Science ®Google Scholar
• S. Romaguera and O. Valero, Asymptotic complexity analysis and denotational semantics for recursive programs based on complexity spaces, In: Semantics-Advances in Theories and Mathematical Models, M. Afzal (ed.), Vol. 1, pp. 99–120, InTech Open Science, London, 2012.
   Google Scholar
• J.J.M.M. Rutten, Elements of generalized ultrametric domain theory, Theoretical Computer Science 170 (1996), 349–381. doi: 10.1016/S0304-3975(96)80711-0
   Web of Science ®Google Scholar
• M. Schellekens, The Smyth completion: a common foundation for denotational semantics and complexity analysis, Electronic Notes in Theoretical Computer Science 1 (1995), 211–232. doi: 10.1016/S1571-0661(04)00029-5
   Google Scholar
• M.P. Schellekens, On upper weightable spaces, Annals of the New York Academy of Sciences 806 (1996), 348–363. doi: 10.1111/j.1749-6632.1996.tb49180.x
   Web of Science ®Google Scholar
• M.P. Schellekens, A characterization of partial metrizability: domains are quantifiable, Electronic Notes in Theoretical Computer Science 305 (2003), 409–432. doi: 10.1016/S0304-3975(02)00705-3
   Google Scholar
• M.P. Schellekens, The correspondence between partial metrics and semi-valuations, Theoretical Computer Science 315 (2004), 135–149. doi: 10.1016/j.tcs.2003.11.016
   Web of Science ®Google Scholar
• A.K. Seda, Quasi-metrics and the semantics of logic programs, Fundamenta Informaticae 29 (1997), 97–117. doi: 10.3233/FI-1997-291205
   Google Scholar
• A.K. Seda, Some issues concerning fixed points in computational logic: quasi-metrics, multivalued mappings and the Knaster-Tarski theorem, Topology Proceedings 24 (1999), 223–250.
   Google Scholar
• N. Shahzad and O. Valero, On 0-complete partial metric spaces and quantitative fixed point techniques in Denotational Semantics, Abstract and Applied Analysis 2013 (2013), Article ID 985095. doi: 10.1155/2013/985095
   Google Scholar
• N. Shahzad, O. Valero, M.A. Alghamdi, and M.A. Alghamdi, A fixed point theorem in partial quasi-metric spaces and an application to software engineering, Applied Mathematics and Computation 268 (2015), 1292–1301. doi: 10.1016/j.amc.2015.06.074
   Web of Science ®Google Scholar
• M.B. Smyth, Quasi-uniformities: reconciling domains with metric spaces, Lecture Notes in Computer Science 298 (1988), 236–253. doi: 10.1007/3-540-19020-1_12
   Google Scholar
• M.B. Smyth, Totally bounded spaces and compact ordered spaces as domain of computation, In: Topology and Category Theory in Computer Science, G.M. Reed, et al. (eds.), pp. 207–229, Oxford University Press, New York, 1991.
   Google Scholar
• P. Vitolo, The representation of weighted quas-metric spaces, Rendiconti dell’Istituto di Matematica dell’Università di Trieste 31 (1999), 95–100.
   Google Scholar
• W.A. Wilson, On quasi-metric spaces, American Journal of Mathematics (JSTOR) 53(3) (1931), 675–684. doi: 10.2307/2371174
   Google Scholar