Finite-Memory Automata (Extended Abstract)

A model of computation dealing with infinite alphabets is proposed. This model is based on replacing the equality test by unijication. It appears to be a natural generalization of the classical Rabin-Scott finiteThe basic idea is to equip the automaton with a finite set of proper stam (like in the classic model), in which the “real computation” is done. In addition, the automaton is equipped with a finite set of regisrers, each state automata and possesses many of their properties. capable of being empty, or storing a symbol from the infinite alphabet. We refer to these registers as “windows”. The restricted power of the automaton is obtained by highly restricting its transition relation. Here, the novel idea is to replace the equality lest (of the next input symbol to some element of the finite alphabet), which underlies the classic model, by some (extended form of) unijication. What the automaton docs with the next input symbol is the following: If no window contains the input symbol, then it is copied into a specified window (depending on the state). Otherwise, the automaton “remembers” that the input symbol has been previously read. in which case the usual equality test applies. As it turns out, relating the next input symbol to many windows simultaneously. as well as initializing some windows to some constant letters from the infinite alphabet, lead to an easier development of the theory without seengthening the model.