This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Comments on 'Defining Software by Continuous Smooth Functions' by R.A. De Millo and R.J. Lipton
March 1993 (vol. 19 no. 3)
pp. 307-309

The commenter agrees with R.A. De Millo and R.S. Lipton's assertion in the above-titled work that continuous, smooth functions of comparable complexity can be used to represent Boolean functions computed by programs. The commenter reconciles this assertion with a referee's objection that the discontinuity of software resides in the large changes of behavior that results from small changes of code, which was countered by the authors by arguing that this notion of discontinuity is vague. It is suggested that this vagueness can be remedied if discontinuity is replaced by a more natural measure that nevertheless captures a similar intuition.

[1] R. A. De Millo and R. J. Lipton, "Defining software by continuous, smooth functions,"IEEE Trans. Software Eng., vol. 17, no. 4, pp. 383-384, Apr. 1991.
[2] A. N. Kolmogorov and S. V. Fomin,Elements of the Theory of Functions and Functional Analysis, vol. 1. Rochester NY: Graylock Press, 1957.
[3] J. E. Stoy,Denotational Semantics. Cambridge MA: MIT Press, 1981.
[4] A. V. Aho, J. E. Hopcroft, and J. D. Ullman,The Design and Analysis of Computer Algorithms. Menlo Park, CA: Addison-Wesley, 1974.
[5] I. Bratko,PROLOG: Programming for Artificial Intelligence. Reading, MA: Addison-Wesley, 1986.
[6] A. Naylor and M. Shademhr, "A linear approach to updating in logic-based models of manufacturing systems and other discrete-event systems," Tech. Rep. CSE-TRL-11-89, Dept. of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor.

Index Terms:
smooth functions; comparable complexity; Boolean functions; programs; natural measure; Boolean functions; computational complexity; software metrics
Citation:
N.Y. Foo, "Comments on 'Defining Software by Continuous Smooth Functions' by R.A. De Millo and R.J. Lipton," IEEE Transactions on Software Engineering, vol. 19, no. 3, pp. 307-309, March 1993, doi:10.1109/32.221140
Usage of this product signifies your acceptance of the Terms of Use.