Abstract
There are several known ways to define a product automaton on the cartesian product of the state sets of two given automata. This paper introduces a new product called the cartesian composition and discusses how various properties of the product automaton depend on the corresponding properties of the factors. A main result is that any finite connected automaton has a unique representation as a cartesian composition of prime automata.
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Dörfler, W. The cartesian composition of automata. Math. Systems Theory 11, 239–257 (1977). https://doi.org/10.1007/BF01768479
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DOI: https://doi.org/10.1007/BF01768479