Arithmetic logical Irreversibility and the Turing's Halt Problem

A new approach to the halting problem of the Turing machine using different interpretations of the Shannon measure of the information on the computational process represented as a distribution of events and defining a new concept of arithmetic logical irreversibility and memory erasure that generate uncertainty and computational improbability due to loss of information during computation. Different computational steps (input) can give the same result (next step, output) introducing thus information entropy in the computing process and uncertainty about the original step (cause). This means that the same output is produced by different inputs. Global indeterminism of computation as distribution but determinism of the computation as current process because the outputs are the same but the information not. The program or Turing machine as macro description of the computational states as micro description that they may be several and different but give the same result when they work .Comment: Irreversibility and undecidability are not one and the same. There are models of computation for which the halting problem is trivially decidable, such as primitive recursion. Conversely, there are reversible models for which it remains undecidable, like the model of reversible Turing machine