Real time counter machines

An automaton called the balloon automaton is defined. The balloon automaton comes in four varieties, depending on whether the device is deterministic or nondeterministic, and whether the input head can move in one or two directions. Subsets of the balloon automata of each variety, called closed classes are defined. Almost all the known types of automata are equivalent to some closed class of balloon automata. Properties of closed classes are given. For example, whatever the variety, the languages accepted by a closed class are closed under intersection with a regular set. For a given organization of storage, closed classes of the four varieties can be defined. These four classes are said to form a family. A class may be recursive or not, and the emptiness problem may be solvable or unsolvable. Some surprising relationships exist between the recursiveness and solvability of emptiness for the classes in a family.