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

LIPICS - Leibniz International Proceedings in Informatics, Nov 2018

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 � 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.

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Vincent Penelle, Sylvain Salvati, Gr\'egoire Sutre. On the Boundedness Problem for Higher-Order Pushdown Vector Addition Systems, LIPICS - Leibniz International Proceedings in Informatics, 2018, 44:1-44:20, DOI: 10.4230/LIPIcs.FSTTCS.2018.44