Comments on "Defining software by continuous smooth functions" by R.A. De Millo and R.J. Lipton

The commenter agrees with R.A. De Millo and R.S. Lipton's assertion in the above-titled work (see ibid., vol.17, no.4, p.383-4, 1991) 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.<
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