Symbolic Reachability Analysis of Higher-Order Context-Free Processes

TL;DR

This paper proves that the set of all predecessor configurations in higher-order context-free processes is regular and effectively computable, enabling symbolic reachability analysis and model checking for complex nested stack models.

Contribution

It extends the regularity and computability results from level 1 to higher-order context-free processes, facilitating advanced analysis techniques.

Findings

Predecessor sets are regular and effectively constructible for higher-order processes.

Enables symbolic reachability analysis for nested stack models.

Provides a model checking algorithm for a fragment of CTL logic.

Abstract

We consider the problem of symbolic reachability analysis of higher-order context-free processes. These models are generalizations of the context-free processes (also called BPA processes) where each process manipulates a data structure which can be seen as a nested stack of stacks. Our main result is that, for any higher-order context-free process, the set of all predecessors of a given regular set of configurations is regular and effectively constructible. This result generalizes the analogous result which is known for level 1 context-free processes. We show that this result holds also in the case of backward reachability analysis under a regular constraint on configurations. As a corollary, we obtain a symbolic model checking algorithm for the temporal logic E(U,X) with regular atomic predicates, i.e., the fragment of CTL restricted to the EU and EX modalities.