Leafy Automata for Higher-Order Concurrency

TL;DR

This paper introduces leafy automata as a novel automata-theoretic model for representing the game semantics of FICA, enabling potential decidability results for higher-order concurrent programs.

Contribution

It proposes leafy automata as a new formalism for modeling FICA's game semantics, bridging automata theory and higher-order concurrency.

Findings

Leafy automata can represent FICA's game semantics.

A fragment of FICA can be verified via leafy automata.

Decidability of emptiness is achieved through Petri net reduction.

Abstract

Finitary Idealized Concurrent Algol (FICA) is a prototypical programming language combining functional, imperative, and concurrent computation. There exists a fully abstract game model of FICA, which in principle can be used to prove equivalence and safety of FICA 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 FICA. The automata use an infinite alphabet with a tree structure. We show that the game semantics of any FICA term can be represented by traces of a leafy automaton. Conversely, the traces of any leafy automaton can be represented by a FICA term. Because of the close match with FICA, 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 FICA 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.