booleanfunctions have a fundamental role in neural networks and machine learning. Enumerating these functions and significant subclasses is a highly complex problem. Therefore, it is of interest to study subclasses t...
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booleanfunctions have a fundamental role in neural networks and machine learning. Enumerating these functions and significant subclasses is a highly complex problem. Therefore, it is of interest to study subclasses that escape this limitation and can be enumerated by means of sequences depending on the number of variables. In this article, we obtain seven new formulas corresponding to enumerations of some subclasses of booleanfunctions. The versatility of these functions does the problem interesting to several different fields as game theory, hypergraphs, reliability, cryptography or logic gates.
This paper considers inequivalent monotone booleanfunctions of an arbitrary number of variables, two monotone booleanfunctions are equivalent if one can be obtained from the other by permuting the variables. It focu...
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This paper considers inequivalent monotone booleanfunctions of an arbitrary number of variables, two monotone booleanfunctions are equivalent if one can be obtained from the other by permuting the variables. It focuses on some inequivalent monotone booleanfunctions with three and four types of equivalent variables, where the variables are either dominant or dominated. The paper provides closed formulas for their enumeration as a function of the number of variables. The problem we deal with is very versatile since inequivalent monotone booleanfunctions are monotonic simple games, structures that are used in many fields such as game theory, neural networks, artificial intelligence, reliability or multiple-criteria decision-making.
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