http://popups.lib.uliege.be/1373-5411/index.php?id=3871 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=4364 The formulations of the undecidability of the Halting Problem assume that the computing process being observed, the description of which is given on the input of the 'observing' Turing Machine, is the exact copy of the computing process running in the observing Turing Machine itself (Cantor's diagonal argument). By this way an analogue of stationary state in thermodynamic sense or an infinite cycle in computing sense is created, shielding now what is to be possibly discovered - the infinite cycle in the observed computing process for a 'normal' input. This shield is the real result of Cantor's diagonal argument which has been used for solving the Halting Problem. We believe that it is possible to recognize the infinite cycle, but with a time delay or staging in evaluating the trace of the observed computing process. Furthermore, the control unit of any Turing Machine is a finite automaton. Both these facts enable that the Pumping Lemma in the observing Turing Machine is usable and the general configuration types are constructed for the observed Turing Machine. This enables (in finite time) us (the observing Turing Machine) to recognize that the computing process in the observed Turing machine has entered into an infinite cycle. These ideas differ from Cantor's diagonal argument. Thu, 10 Oct 2024 10:04:15 +0200 Thu, 10 Oct 2024 10:05:23 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4364 http://popups.lib.uliege.be/1373-5411/index.php?id=3870 We consider the principle loss of the cell structure (information) caused by the normal cell duplication. This loss, known as aging by a 'tooth of time', can be measured by information entropy. Functionally, it can be described by a carnotized model of information transfer, by a direct heat cycle. The growth of the thermodynamic entropy in its environment is similar to the loss of the cell structure, measured, in biology, by the shortenning the length of the cell telomere [24] . The telomere is, said approximately, a box of chromozomes and its length is coding the age of the cell, or in other words, is coding the number of the cell's predecessors in the normal situation. During the pathological cell proliferation the opposite situation arises. Cells with a precise structure are generated, but of a type which is different from their normal type. This growth of cells' structure in a certain locality (within the whole organism) is 'paid for ' by the draining off energy from its environment. Again, this situation is describable by the thermodynamic model of information transfer, but in a reverse form this time. The decreasing value of the thermodynamic entropy, or increasing value of the information entropy is now evidenced (locally), but 'paid for' by the environment. In terms of cells, the growth of the cells structure is now measured by the lengthening of their telomeres [24] Mon, 30 Sep 2024 14:21:09 +0200 Mon, 30 Sep 2024 14:21:19 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3870