Abstract
Let C be a program written in a formal language in order to be executed by some kind of machinery. A statement about C might be true or false and has the form C:M. For the time being, just consider the statement C:M as a collection of data yielding information about the resources required to execute C; and if we know that C:M is true (or false), we know something useful when it comes to determine the computational complexity of C. Let Γ be a set of statements, and let Γ⊧C:M denote that C:M will be true if all the statements in Γ are true. (The statements in Γ might say something about the computational complexity of the subprograms of C.) If Γ = 0, we will simply write⊧C:M.
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References
Aho, A.V., Hopcroft, J.E., Jeffrey, D.: The design and analysis of computer algorithms. Addison-Wesley Publishing Co., Reading (1975)
Bellantoni, S.J., Cook, S.: A New Recursion-Theoretic Characterization of the Polytime Functions. Computational Complexity 2, 97–110 (1992)
Caseiro, V.H.: Equations for Defining Poly-time Functions. Ph.D. thesis, Dept. of informatics, Faculty of Mathematics and Natural Sciences University of Oslo (February 1997)
Frederiksen, C.C.: Automatic runtime analysis for first order functional programs. Master Thesis, Dep. of Computer Science, University of Copenhagen (2002)
Jones, N.D.: The expressive power of higher-order types or, life without CONS. J. Functional Programming 11, 55–94 (2001)
Jones, N.D.: LOGSPACE and PTIME characterized by programming languages. Theoretical Computer Science 228, 151–174 (1999)
Jones, N.D., Bohr, N.: Termination analysis of the untyped lambda-calculus. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 1–23. Springer, Heidelberg (2004)
Kristiansen, L.: Neat function algebraic characterizations of LOGSPACE and LINSPACE. Computational Complexity 14, 72–88 (2005)
Kristiansen, L., Niggl, K.-H.: On the computational complexity of imperative programming languages. Theoretical Computer Science 318, 139–161 (2004)
Kristiansen, L., Niggl, K.-H.: The Garland Measure and Computational Complexity of Stack Programs. Electronic Notes in Theoretical Computer Science, vol. 90. Elsevier, Amsterdam (2003)
Kristiansen, L., Voda, P.J.: Complexity classes and fragments of C. Information Processing Letters 88, 213–218 (2003)
Kristiansen, L., Voda, P.J.: Programming languages capturing complexity classes (submitted)
Lee, C.S., Jones, N., Ben-Amram, A.M.: The size-change principle for program termination. ACM Principles of Programming Languages, pp. 81–92. ACM Press, New York (2001)
Leivant, D.: Intrinsic theories and computational complexity. In: Leivant, D. (ed.) LCC 1994. LNCS, vol. 960, pp. 177–194. Springer, Heidelberg (1995)
Niggl, K.-H.: Control Structures in Programs and Computational Complexity. Annals of Pure and Applied Logic 133, 247–273 (2005)
Simmons, H.: The realm of primitive recursion. Arch. Math. Logic 27, 177–188 (1988)
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Kristiansen, L., Jones, N.D. (2005). The Flow of Data and the Complexity of Algorithms. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds) New Computational Paradigms. CiE 2005. Lecture Notes in Computer Science, vol 3526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494645_33
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DOI: https://doi.org/10.1007/11494645_33
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