Authors: Wojciech Czerwiński ; Piotr Hofman ; SŁawomir Lasota

This paper is about reachability analysis in a restricted subclass of multi-pushdown automata. We assume that the control states of an automaton are partially ordered, and all transitions of an automaton go downwards with respect to the order. We prove decidability of the reachability problem, and computability of the backward reachability set. As the main contribution, we identify relevant subclasses where the reachability problem becomes NP-complete. This matches the complexity of the same problem for communication-free vector addition systems, a special case of stateless multi-pushdown automata.

• 68Q17 - Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
• 68Q25 - Analysis of algorithms and problem complexity
• 68Q45 - Formal languages and automata