  The Tsetlin Machine (TM) is a recent machine learning algorithm with several
distinct properties, such as interpretability, simplicity, and
hardware-friendliness. Although numerous empirical evaluations report on its
performance, the mathematical analysis of its convergence is still open. In
this article, we analyze the convergence of the TM with only one clause
involved for classification. More specifically, we examine two basic logical
operators, namely, the "IDENTITY"- and "NOT" operators. Our analysis reveals
that the TM, with just one clause, can converge correctly to the intended
logical operator, learning from training data over an infinite time horizon.
Besides, it can capture arbitrarily rare patterns and select the most accurate
one when two candidate patterns are incompatible, by configuring a granularity
parameter. The analysis of the convergence of the two basic operators lays the
foundation for analyzing other logical operators. These analyses altogether,
from a mathematical perspective, provide new insights on why TMs have obtained
state-of-the-art performance on several pattern recognition problems.
