The classical approach of computability theory is to consider models as operating on finite strings of symbols from a finite alphabet. Such strings may represent various discrete objects such as integers or algebraic expressions, but cannot represent general real, complex numbers (even when most mathematical models are based on the real number concept) or the complexity of input/output (I/O) systems of living beings. Such standard models have been captured by the Turing model [1], but some researchers have recently proposed some models more powerful than Turing machines, and others have studied alternative computational models that are Turing equivalent. There is an evident connection between the complexity of a model and its information complexity, spanning a hierarchy of computation from the finite automaton model to super Turing models.

In this paper, the authors consider models that more closely mimic the interaction between the device and the environment. The authors define a cognitive automaton (equivalent to a finite automaton, but with a different scenario than the standard) to try to create a model that reflects the adjustment and adaptation of living systems in their environments.

The authors make some remarkable suppositions: they say that their automatons “cannot be simulated by a standard Turing machine and in principle they may solve some non-computable tasks.” In this, they clearly are going against the Church-Turing thesis, even though they try to temper their comments with words like “standard,” “in principle,” and “tasks” (which is used instead of functions, languages, or sets). They claim also that mathematicians are able to prove “mechanically unprovable” theorems. I think there is a profound misunderstanding of what Gödel proved in his incompleteness theorems, and they are citing an argument of Penrose that has no solid foundation (the claim that the mind has super Turing capabilities, due to the quantum interactions involved) [2]. Of course their trick is to use “potentially” infinite sequences in cognitive automata.

It is evident that any property of those external sequences determines their computational power, and could be seen as a model containing different levels of complexity and amounts of information in its initial description, without separating it from the standard input. Of course, all of this depends on the complexity of the environment and the automaton’s dependence on this environment. The model has value as an original alternative model, but the authors present no remarkable results. The model could be used to investigate some properties of living systems and their environments, even when these relationships are evidently nonlinear or unknown in their intrinsic properties.