On the structure of the space of complexity partial functions

References

• Romaguera , S. and Schellekens , M. 1999 . Quasi-metric properties of complexity spaces . Topology and its Applications , 98 : 311 – 322 .
   Web of Science ®Google Scholar
• Romaguera , S. and Schellekens , M. 2000 . The quasi-metric of complexity convergence . Quaestiones Mathematicae , 23 : 359 – 374 .
   Google Scholar
• Romaguera , S. and Schellekens , M. 2002 . Duality and quasi-normability for complexity spaces . Applied General Topology , 3 : 91 – 112 .
   Google Scholar
• García-Raffi , L. M. , Romaguera , S. and Sánchez-Pérez , E. A. 2002 . Sequences spaces and asymmetric norms in the theory of computational complexity . Mathematical and Computer Modelling , 36 : 1 – 11 .
   Web of Science ®Google Scholar
• García-Raffi , L. M. , Romaguera , S. and Sánchez-Pérez , E. A. 2003 . “ The supremum asymmetric norm on sequence algebras: a general framework to measure complexity distances ” . In Electronic Notes in Theoretical Computer Science Edited by: Flynn , S. , Hurley , T. , Mac an Airchinnigh , M. , Madden , N. , McGettrick , M. , Schellekens , M. and Seda , A. Vol. 74, pp. , 39 – 50 .
   Google Scholar
• García-Raffi , L. M. , Romaguera , S. and Sánchez-Pérez , E. A. 2004 . Weak topologies on asymmetric normed linear spaces and non-asymptotic criteria in the theory of complexity analysis of algorithms . Journal of Analysis and Applications , 2 : 125 – 138 .
   Google Scholar
• García-Raffi , L. M. , Romaguera , S. , Sánchez-Pérez , E. A. and Valero , O. 2003 . “ Normed semialgebras: a mathematical model for the complexity analysis of programs and algorithms ” . In Proceedings of the 7th World Multiconference on Systemics, Cybernetics and Informatics Vol. II , 55 – 58 .
   Google Scholar
• Rodríguez-López , J. , Romaguera , S. and Valero , O. 2006 . Asymptotic complexity of algorithms via the nonsymmetric Hausdorff distance . Computing Letters , 2 : 155 – 161 .
   Google Scholar
• Rodríguez-López , J. 2004 . A new approach to epiconvergence and some applications . Southeast Asian Bulletin of Mathematics , 28 : 685 – 701 .
   Google Scholar
• Romaguera , S. , Sánchez-Pérez , E. A. and Valero , O. 2003 . “ The complexity space of a valued linearly ordered set ” . In Electronic Notes in Theoretical Computer Science Edited by: Flynn , S. , Hurley , T. , Mac an Airchinnigh , M. , Madden , N. , McGettrick , M. , Schellekens , M. and Seda , A. Vol. 74 , 158 – 171 .
   Google Scholar
• Schellekens , M. 2004 . The correspondence between partial metrics and semivaluations . Theoretical Computer Science , 315 : 135 – 149 .
   Google Scholar
• Romaguera , S. and Schellekens , M. 2005 . Partial metric monoids and semivaluation spaces . Topology and its Applications , 153 : 948 – 962 .
   Web of Science ®Google Scholar
• Romaguera , S. , Sánchez-Pérez , E. A. and Valero , O. 2003 . Computing complexity distances between algorithms . Kybernetika , 39 : 569 – 582 .
   Web of Science ®Google Scholar
• Fletcher , P. and Lindgren , W. F. 1982 . Quasi-Uniform Spaces , New York : Marcel Dekker .
   Google Scholar
• Künzi , H. P.A. 2001 . “ Nonsymmetric distances and their associated topologies: about the origins of basic ideas in the area of asymmetric topology ” . In Handbook of the History of General Topology , Edited by: Aull , C. E. and Lowen , R. Vol. 3 , 853 – 968 . Dordrecht : Kluwer .
   Google Scholar
• Keimel , K. and Roth , W. 1992 . Ordered Cones and Approximation , Berlin : Springer-Verlag .
   Google Scholar
• Kopperman , R. D. 1982 . Lengths on semigroups and groups . Semigroup Forum , 25 : 345 – 360 .
   Google Scholar
• Gierz , G. , Hofmann , K. H. , Keimel , K. , Lawson , J. D. , Mislove , M. W. and Scott , D. S. 2003 . Continuous Lattices and Domains , Vol. 93 , Cambridge : Cambridge University Press . Encyclopedia of Mathematics and its Applications
   Google Scholar
• Davey , B. A. and Priestley , H. A. 1990 . Introduction to Lattices and Order , Cambridge : Cambridge University Press .
   Google Scholar
• Fuchssteiner , B. and Lusky , W. 1981 . Convex Cones , Amsterdam : North Holland .
   Google Scholar
• Schellekens , M. 1995 . “ The Smyth completion: a common foundation for denotational semantics and complexity analysis ” . In Electronic Notes in Theoretical Computer Science Edited by: Brookes , S. , Main , M. , Melton , A. and Mislove , M. Vol. 1 , 535 – 556 .
   Google Scholar
• Kahn , G. 1974 . “ The semantics of a simple language for parallel processing ” . In Information Processing 74 , Edited by: Rosenfield , J. L. 471 – 475 . Amsterdam : North-Holland .
   Google Scholar
• Perrin , D. and Pin , J. E. 2004 . Infinite Words: Automata, Semigroups, Logic and Games , Vol. 141 , Amsertdam : Elsevier . Pure Applied Mathematics series
   Google Scholar
• de Bakker , J. W. and de Vink , E. P. 1996 . Control Flow Semantics , Cambridge, Massachusetts : MIT Pres .
   Google Scholar
• de Bakker , J. W. and de Vink , E. P. 1996 . A metric approach to control flow semantics. In: Proceedings of the Eleventh Summer Conference on General Topology and Applications . Annals of the New York Academy of Sciences , 806 : 11 – 27 .
   Google Scholar
• de Bakker , J. W. and de Vink , E. P. 1998 . Denotational models for programming languages: applications of Banach's fixed point theorem . Topology Appl. , 85 : 35 – 52 .
   Web of Science ®Google Scholar
• Lecomte , P. and Rigo , M. 2002 . On the representation of real numbers using regular languages . Theory of Computing Systems , 35 : 13 – 38 .
   Web of Science ®Google Scholar