What is "x-machine"

The X-machine (XM) is a theoretical model of computation introduced by Samuel Eilenberg in 1974.S. Eilenberg (1974)

Automata, Languages and Machines, Vol. A.
Academic Press, London.

The X in "X-machine" represents the fundamental data type on which the machine operates; for example, a machine that operates on databases (objects of type database) would be a database-machine. The X-machine model is structurally the same as the finite state machine, except that the symbols used to label the machine's transitions denote relations of type X→X. Crossing a transition is equivalent to applying the relation that labels it (computing a set of changes to the data type X), and traversing a path in the machine corresponds to applying all the associated relations, one after the other.