Integer Vector Addition Systems with States

• Published in: Reachability Problems pp. 112 - 124
• Main Authors: Haase, Christoph, Halfon, Simon
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Inclusion Problem; Linear Diophantine Equation; Partial Word; Presburger Arithmetic; Register Machine
• ISBN: 9783319114385; 3319114387
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-11439-2_9

This paper studies reachability, coverability and inclusion problems for Integer Vector Addition Systems with States (ℤ-VASS) and extensions and restrictions thereof. A ℤ-VASS comprises a finite-state controller with a finite number of counters ranging over the integers. Although it is folklore that reachability in ℤ-VASS is NP-complete, it turns out that despite their naturalness, from a complexity point of view this class has received little attention in the literature. We fill this gap by providing an in-depth analysis of the computational complexity of the aforementioned decision problems. Most interestingly, it turns out that while the addition of reset operations to ordinary VASS leads to undecidability and Ackermann-hardness of reachability and coverability, respectively, they can be added to ℤ-VASS while retaining NP-completeness of both coverability and reachability.