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An extension of the dual complexity space and an application to computer science. (English) Zbl 1198.68153
Summary: In 1999, Romaguera and Schellekens introduced the theory of dual complexity spaces as a part of the development of a mathematical (topological) foundation for the complexity analysis of programs and algorithms [S. Romaguera and M. Schellekens, “Quasi-metric properties of complexity spaces”, Topology Appl. 98, No. 1–3, 311–322 (1999; Zbl 0941.54028)]. In this work we extend the theory of dual complexity spaces to the case that the complexity functions are valued on an ordered normed monoid. We show that the complexity space of an ordered normed monoid inherits the ordered normed structure. Moreover, the order structure allows us to prove some topological and quasi-metric properties of the new dual complexity spaces. In particular, we show that these complexity spaces are, under certain conditions, Hausdorff and satisfy a kind of completeness. Finally, we develop a connection of our new approach with Interval Analysis.
MSC:
68Q25Analysis of algorithms and problem complexity
54E50Complete metric spaces
54F05Linearly, generalized, and partial ordered topological spaces
References:
[1]Acióly, B. M.; Bedregal, R. C.: A quasi-metric topology compatible with inclusion monotonicity on interval space, Reliab. comput. 3, 305-313 (1997) · Zbl 0889.65051 · doi:10.1023/A:1009935210180
[2]Edalat, A.; Lieutier, A.; Pattinson, D.: A computational model for multi-variable differential calculus, Lecture notes in comput. Sci. 3441, 505-519 (2005) · Zbl 1119.03062 · doi:10.1007/b106850
[3]Edalat, A.; Pattinson, D.: A domain theoretic account of Euler’s method for solving initial value problems, Lecture notes in comput. Sci. 3732, 112-121 (2006)
[4]Edalat, A.; Pattinson, D.: A domain theoretic account of Picard’s theorem, Lecture notes in comput. Sci. 3142, 494-505 (2004) · Zbl 1098.65078 · doi:10.1007/b99859
[5]Edalat, A.; Krznaric, M.; Lieutier, A.: Domain-theoretic solution of differential equations (Scalar fields), Electron. notes theor. Comput. sci. 83 (2004)
[6]Edalat, A.; Lieutier, A.: Domain theory and differential calculus (Functions of one variable), Math. structures comput. Sci. 14, 771-802 (2004) · Zbl 1062.03037 · doi:10.1017/S0960129504004359
[7]Escardó, M. H.: PCF extended with real numbers, Theoret. comput. Sci. 162, 79-115 (1996) · Zbl 0871.68034 · doi:10.1016/0304-3975(95)00250-2
[8]Escardó, M. H.; Streicher, T.: Induction and recursion on the partial real line with applications to real PCF, Theoret. comput. Sci. 210, 121-157 (1999) · Zbl 0912.68123 · doi:10.1016/S0304-3975(98)00099-1
[9]Fletcher, P.; Lindgren, W. F.: Quasi-uniform spaces, Lect. notes pure appl. Math. 77 (1982) · Zbl 0501.54018
[10]Künzi, H. P. A.: Nonsymmetric topology, Colloq. math. Soc. jános bolyai math. Stud. 4, 303-338 (1995)
[11]Künzi, H. P. A.; Romaguera, S.: Spaces of continuous functions and quasi-uniform convergence, Acta math. Hungar. 75, 287-298 (1997) · Zbl 0921.54011 · doi:10.1023/A:1006593505036
[12]Künzi, H. P. A.; Ryser, C.: The bourbaki quasi-uniformity, Topology proc. 20, 161-183 (1995) · Zbl 0876.54022 · doi:http://at.yorku.ca/b/a/a/a/20.htm
[13]Fuchssteiner, B.; Lusky, W.: Convex cones, (1981)
[14]Martin, K.: Powerdomains and zero finding, Electron. notes theor. Comput. sci. 59, 173-184 (2002)
[15]Martin, K.: The measurement process in domain theory, Lecture notes in comput. Sci. 1853, 116-126 (2000) · Zbl 0973.68131
[16]Moore, R. E.: Methods and applications of interval analysis, SIAM stud. Appl. math. (1979)
[17]Romaguera, S.; Sánchez-Pérez, E. A.; Valero, O.: Computing complexity distances between algorithms, Kybernetika 39, 569-582 (2003)
[18]Romaguera, S.; Sánchez-Pérez, E. A.; Valero, O.: Quasi-normed monoids and quasi-metrics, Publ. math. Debrecen 62, 53-69 (2003) · Zbl 1026.54027
[19]Romaguera, S.; Schellekens, M. P.: Quasi-metric properties of complexity spaces, Topology appl. 98, 311-322 (1999) · Zbl 0941.54028 · doi:10.1016/S0166-8641(98)00102-3
[20]Romaguera, S.; Schellekens, M. P.: Duality and quasi-normability for complexity spaces, Appl. gen. Topol. 3, 91-112 (2002) · Zbl 1022.54018
[21]Schellekens, M. P.: Extendible spaces, Appl. gen. Topol. 3, 169-184 (2002) · Zbl 1038.68078
[22]Schellekens, M. P.: The smyth completion: A common foundation for the denotational semantics and complexity analysis, Electron. notes theor. Comput. sci. 1, 211-232 (1995) · Zbl 0910.68135 · doi:http://www.elsevier.com/cas/tree/store/tcs/free/noncas/pc/volume1.htm#schellekens
[23]Scott, D.: Lattice theory, data types and semantics, , 66-106 (1972) · Zbl 0279.68042
[24]Kandasamy, W. F. Vasantha: Bialgebraic structures and smarandache bialgebraic structures, (2003)