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arXiv · 1805.05845

On the complexity of the correctness problem for non-zeroness test instruction sequences

J. A. Bergstra·C. A. Middelburg
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Abstract

This paper concerns the question to what extent it can be efficiently determined whether an arbitrary program correctly solves a given problem. This question is investigated with programs of a very simple form, namely instruction sequences, and a very simple problem, namely the non-zeroness test on natural numbers. The instruction sequences concerned are of a kind by which, for each $n > 0$, each function from $\{0,1\}^n$ to $\{0,1\}$ can be computed. The established results include the time complexities of the problem of determining whether an arbitrary instruction sequence correctly implements the restriction to $\{0,1\}^n$ of the function from $\{0,1\}^*$ to $\{0,1\}$ that models the non-zeroness test function, for $n > 0$, under several restrictions on the arbitrary instruction sequence.

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J. A. Bergstra, C. A. Middelburg. 2018-05-15. On the complexity of the correctness problem for non-zeroness test instruction sequences. https://doi.org/10.1016/j.tcs.2019.03.040

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