Abstract
In this paper we prove that plain complexity induces the weakest form of randomness for all Blum Universal Static Complexity Spaces [11]. As a consequence, there is all infinite sequences have an infinite number of non-random prefixes with respect to any given Blum Universal Static Complexity Space. This is a generalization of the result obtained by Solovay [27] and Calude [7] for plain complexity, and also of the result obtained by Câmpeanu [10], and independently, later on, by Bienvenu and Downey in [1] for prefix-free complexity.
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Câmpeanu, C. (2012). Randomness Behaviour in Blum Universal Static Complexity Spaces. In: Kutrib, M., Moreira, N., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2012. Lecture Notes in Computer Science, vol 7386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31623-4_10
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DOI: https://doi.org/10.1007/978-3-642-31623-4_10
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