On the Boundedness Problem for Higher-Order Pushdown Vector Addition Systems

Vincent Penelle (1) , Sylvain Salvati (2) , Grégoire Sutre (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 LINKS - Linking Dynamic Data

Karp and Miller's algorithm is a well-known decision procedure that solves the termination and boundedness problems for vector addition systems with states (VASS), or equivalently Petri nets. This procedure was later extended to a general class of models, well-structured transition systems, and, more recently, to pushdown VASS. In this paper, we extend pushdown VASS to higher-order pushdown VASS (called HOPVASS), and we investigate whether an approach à la Karp and Miller can still be used to solve termination and boundedness. We provide a decidable characterisation of runs that can be iterated arbitrarily many times, which is the main ingredient of Karp and Miller's approach. However, the resulting Karp and Miller procedure only gives a semi-algorithm for HOPVASS. In fact, we show that coverability, termination and boundedness are all undecidable for HOPVASS, even in the restricted subcase of one counter and an order 2 stack. On the bright side, we prove that this semi-algorithm is in fact an algorithm for higher-order pushdown automata.

Mots clés: Higher-order pushdown automata; Vector addition systems; Boundedness problem; Termination problem; Coverability problem

Domaines: Théorie et langage formel [cs.FL]; Logique en informatique [cs.LO]

Vincent Penelle, Sylvain Salvati, Grégoire Sutre. On the Boundedness Problem for Higher-Order Pushdown Vector Addition Systems. FSTTCS 2018 - 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, Dec 2018, Ahmedabad, India. pp.44:1-44:20, ⟨10.4230/LIPIcs.FSTTCS.2018.44⟩. ⟨hal-01962407⟩