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  1. Constructivity and Computability in Historical and Philosophical Perspective.Jacques Dubucs & Michel Bourdeau (eds.) - 2014 - Dordrecht, Netherland: Springer.
    Ranging from Alan Turing’s seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic, this comprehensive new work clarifies the relationship between computability on the one hand and constructivity on the other. The authors argue that even though constructivists have largely shed Brouwer’s solipsistic attitude to logic, there remain points of disagreement to this day. Focusing on the growing pains computability experienced as it was forced to address the demands of rapidly expanding applications, the content maps the (...)
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  • Program Size Complexity for Possibly Infinite Computations.Verónica Becher, Santiago Figueira, André Nies & Silvana Picchi - 2005 - Notre Dame Journal of Formal Logic 46 (1):51-64.
    We define a program size complexity function $H^\infty$ as a variant of the prefix-free Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in ${\{0,1\}}^\omega$ relative to the $H^\infty$ complexity. We prove that the classes of Martin-Löf random sequences and $H^\infty$-random sequences coincide and that the $H^\infty$-trivial sequences are exactly the recursive ones. We also study some properties of $H^\infty$ and compare it with other complexity functions. In particular, $H^\infty$ (...)
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