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Defining Software by Continuous, Smooth Functions
April 1991 (vol. 17 no. 4)
pp. 383-384

A simple proof is given, showing that for every operational description of a software system expressed as a discrete state transition function on a virtual machine, there is a continuous smooth function on the reals that agrees with the state transition function on all legal states and has exactly the same complexity. It is suggested that an implication of this result is that there is no reason, in principle, that the methods of classical analysis cannot be used in software engineering.

[1] R. A. DeMillo, R. J. Lipton, and A. J. Perlis, "Social processes and proofs of theorems and programs,"Commun. ACM, vol. 22, no. 5, pp. 271-280, 1979.
[2] D. L. Parnas, "Why software is unreliable," Univ. Victoria, Rep. DCS- 47-IR, July 1985; this paper was later merged with others and published under the title "Software aspects nf strategic defense systems,"Amer. Scientist, vol. 73, no. 5, pp. 432-440, Sept.-Oct. 1985.
[3] M. Stone, "A generalized weierstrass approximation theorem," inStudies in Modern Analysis, vol. 1, R. C. Buck, Ed. MAA, 1962.
[4] P. R. Halmos,Lectures on Boolean AlgebraNew York: Van Nostrand, 1967.
[5] H. Rasiowa and R. Sikorski,Mathematics of Metamathematics. Polish Scientific, 1970.

Index Terms:
software system; discrete state transition function; virtual machine; continuous smooth function; legal states; complexity; classical analysis; software engineering; computational complexity; software engineering
R.A. DeMillo, R.J. Lipton, "Defining Software by Continuous, Smooth Functions," IEEE Transactions on Software Engineering, vol. 17, no. 4, pp. 383-384, April 1991, doi:10.1109/32.90437
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