Leafy automata for higher-order concurrency

Finitary Idealized Concurrent Algol ([Formula: see text] ) is a prototypical programming language combining functional, imperative, and concurrent computation. There exists a fully abstract game model of [Formula: see text] , which in principle can be used to prove equivalence and safety of [Formula: see text] programs. Unfortunately, the problems are undecidable for the whole language, and only very rudimentary decidable sub-languages are known. We propose leafy automata as a dedicated automata-theoretic formalism for representing the game semantics of [Formula: see text] . The automata use an infinite alphabet with a tree structure. We show that the game semantics of any [Formula: see text] term can be represented by traces of a leafy automaton. Conversely, the traces of any leafy automaton can be represented by a [Formula: see text] term. Because of the close match with [Formula: see text] , we view leafy automata as a promising starting point for finding decidable subclasses of the language and, more generally, to provide a new perspective on models of higher-order concurrent computation. Moreover, we identify a fragment of [Formula: see text] that is amenable to verification by translation into a particular class of leafy automata. Using a locality property of the latter class, where communication between levels is restricted and every other level is bounded, we show that their emptiness problem is decidable by reduction to Petri net reachability.