Ordered Tree-Pushdown Systems

TL;DR

This paper introduces a novel class of pushdown systems with tree-structured stacks and limited lookahead, demonstrating decidable reachability and encoding various advanced formalisms, with tight complexity results.

Contribution

It defines a new ordered tree-pushdown system model with decidable reachability and shows its applicability to multiple existing formal systems.

Findings

Decidable reachability for the new class of systems.

Encoding of several formalisms within the new model.

Tight complexity bounds for each formalism.

Abstract

We define a new class of pushdown systems where the pushdown is a tree instead of a word. We allow a limited form of lookahead on the pushdown conforming to a certain ordering restriction, and we show that the resulting class enjoys a decidable reachability problem. This follows from a preservation of recognizability result for the backward reachability relation of such systems. As an application, we show that our simple model can encode several formalisms generalizing pushdown systems, such as ordered multi-pushdown systems, annotated higher-order pushdown systems, the Krivine machine, and ordered annotated multi-pushdown systems. In each case, our procedure yields tight complexity.