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

TL;DR

This paper revisits a game-semantic model of computation, demonstrating that a restricted class of automata can implement all PCF computations, revealing surprising computational capabilities beyond traditional automata.

Contribution

It shows that deterministic non-erasing pushdown automata with simple tape edges can simulate PCF, bridging game semantics and automata theory in a novel way.

Findings

Deterministic non-erasing pushdown automata can implement PCF computations.

Simple directed edges on the input tape restrict automata reading but do not limit computational power.

The automata model surpasses traditional automata capabilities, approaching Turing-complete computation.

Abstract

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.