Abstract
Turing machine (TM) theory constitutes the theoretical basis for contemporary digital (von Neumann) computers. But it is problematic whether it could be an adequate theory of brain functions (computations) because, as it is widely accepted, the brain is a selectional device with blurred bounds between the areas responsible for data processing, control, and behavior. In this paper, by analogy with TMs, the optimal decoding algorithm of recent binary signal detection theory (BSDT) is presented in the form of a minimal onedimensional abstract selectional machine (ASM). The ASM's hypercomplexity is explicitly hypothesized, its optimal selectional and super-Turing computational performance is discussed. BSDT ASMs can contribute to a mathematically strict and biologically plausible theory of functional properties of the brain, mind/brain relations and super-Turing machines mimicking partially some cognitive abilities in animals and humans.
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