Abstract
Formulas that make it possible to obtain guaranteed interval estimates of the execution frequency of code snippets of the sequential program are given based on asymptotic approximations obtained using the probability theory’s limit theorems. The selection method of appropriate approximation is described based on current estimates of the approximation accuracy of the binomial distribution by normal and Poisson distributions.
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References
A. V. Shalimov, “A method of determining the execution frequency of program basic blocks,” Modelir. Anal. Inform. Sist. 17 (2), 122–132 (2010).
Y. Wu and J. R. Larus, “Static branch frequency and program profile analysis,” in Proceedings of the 27th Annual International Symposium on Microarchitecture (San Jose, California USA, 1994), pp. 1–11.
T. Ball and J. R. Larus, “Optimally profiling and tracing programs,” ACM Trans. Program. Languages Syst. (TOPLAS) 16 (4), 1319–1360 (1994).
B. P. Pal’chun, “Method of software reliability testing,” in Functional Stability of Special Software of Automatic Systems (Moscow, 1989), pp. 111–117 [in Russian].
E. I. Parnov, On the Cross of Infinities (Atomizdat Moscow, 1967) [in Russian].
R. L. Smelianski and T. Alanko, “On the calculation of control transition probabilities in a program,” Inform. Proces. Lett., No. 3 (1984).
R. L. Smelyanskii, D. E. Gur’ev, and A. G. Bakhmurov, “On one mathematical model for program dynamical parameters calculation,” Programmirovanie, No. 6 (1986).
R. L. Smelyanskii, “On frequency analysis of sequential program code execution,” Program. Comp. Software 37, 153 (2011).
A. Shalimov and R. Smeliansky, “Program compaction for real-time applications,” in Proceedings of EUCAS Symposium (St.-Petersburg, 2013), pp. 479–496.
V. Yu. Korolev, Doctoral (Phys. Math.) Dissertation (Moscow State Univ. Moscow, 1994).
V. Yu. Korolev and I. A. Sokolov, Principles of Mathematical Theory of Modified System Reliability (IPI RAN Moscow, 2006) [in Russian].
S. Nagaev, V. Chebotarev, and K. Mikhailov, “On the Gaussian asymptotics of the binomial distributions,” in Proceedings of the 30th International Seminar on Stability Problems for Stochastic Models, Svetlogorsk, Russia, Sept. 24–30, 2012, pp 54–56.
V. Yu. Korolev, V. E. Bening, and S. Ya. Shorgin, Mathematical Foundations of Risk Theory (Fizmatlit Moscow, 2011) [in Russian].
I. G. Shevtsova, “On the absolute constants in the Berry-Esseen inequality and its structural and nonuniform improvements,” Inform. Primen. 7 (1), 124–125 (2013).
L. N. Bol’shev and N. V. Smirnov, Tables of Mathematical Statistics (Nauka Moscow, 1965) [in Russian].
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Original Russian Text © V.Yu. Korolev, R.L. Smelyanskii, T.R. Smelyanskii, A.V. Shalimov, 2015, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2015, No. 4, pp. 39–44.
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Korolev, V.Y., Smelyanskii, R.L., Smelyanskii, T.R. et al. On the estimation of the execution frequency of sequential program code snippets. J. Comput. Syst. Sci. Int. 54, 540–545 (2015). https://doi.org/10.1134/S1064230715040097
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DOI: https://doi.org/10.1134/S1064230715040097