A Game-Semantic Model of Computation, Revisited: an Automata-Theoretic Perspective

In the previous work, we have given a novel, game-semantic model of computation in an intrinsic, non-inductive and non-axiomatic manner, which is similar to Turing machines but beyond computation on natural numbers, e.g., higher-order computation. As the main theorem of the work, it has been shown that the game-semantic model may execute all the computation of the programming language PCF. The present paper revisits this result from an automata-theoretic perspective: It shows that deterministic non-erasing pushdown automata whose input tape is equipped with simple directed edges between cells can implement all the game-semantic PCF-computation, where the edges rather restrict the cells of the tape which the automata may read off. This is a mathematically highly-surprising phenomenon because it is well-known that the more powerful non-deterministic erasing pushdown automata are strictly weaker than Turing machines (in the Chomsky hierarchy), let alone than PCF.