Abstract
In [6], it is shown that four of its basic functional properties are enough to characterize plain Kolmogorov complexity, hence obtaining an axiomatic characterization of this notion. In this paper, we try to extend this work, both by looking at alternative axiomatic systems for plain complexity and by considering potential axiomatic systems for other types of complexity. First we show that the axiomatic system given by Shen cannot be weakened (at least in any natural way). We then give an analogue of Shen’s axiomatic system for conditional complexity. In the second part of the paper, we look at prefix-free complexity and try to construct an axiomatic system for it. We show however that the natural analogues of Shen’s axiomatic systems fail to characterize prefix-free complexity.
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Taveneaux, A. (2011). Towards an Axiomatic System for Kolmogorov Complexity. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds) Models of Computation in Context. CiE 2011. Lecture Notes in Computer Science, vol 6735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21875-0_30
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DOI: https://doi.org/10.1007/978-3-642-21875-0_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21874-3
Online ISBN: 978-3-642-21875-0
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