A Generalized Net for Machine Learning of the Process of Mathematical Problems Solving

The authors of the present paper prepared a series of research related to the ways of representation by Generalized nets (GNs, see [1] and the Appendix) the process of machine learning of different objects, e,g" neural networks, genetic algorithms, GNs, expert systems, systems (abstract, statical, dynamical, stohastical and others), etc. Working on their research [21, where they gave a counterexample of the 62-nd Smarandachejs problem (see [3]), they saw that the process of the machine learning of the process of the mathematical problems solving also can be described by a GN and by this reason the result form [2] was used as an example of the present research. After this, they saw that the process of solving of a lot of the Smarandache's problems can be represented by GNs in a similar way and this will be an object of next their research. The GN (see [IJ and the Appendix), which is described below have three types of tokens a-, 13and ,tokens. They interprete respectively the object which will be studied, its known property (properties) and the hypothesis, related to it) which must be checked. The tokens' initial characteristics correspond to these interpretations. The tokens enter the GN, respectively, through places • II with the initial characteristic "description of the object" (if we use the example from [2], this characteristic will be, e.g., "sequence of natural numbers"), • l2 with the initial characteristic "property (properties) of the object, described as an initial characteristic of a-token corresponding to the present j3-token" (in the case of the example mentioned above, it will be the following property "there are no three elements of the sequence, which are members of an arithmetic progression") and • L3 with the initial characteristic "description of an hypothesis about the object" (for the discussed example this characteristic will be, e.g., "the sum of the reciprocal values of the members of the sequence are smaller than 2"). We shall would like for the places' priorities to satisfy the following inequalities: