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Seminal results establish that the coverability problem for Vector Addition Systems with States (VASS) is in EXPSPACE (Rackoff, '78) and is EXPSPACE-hard already under unary encodings (Lipton, '76). More precisely, Rosier and Yen later…
We show that the regular separability problem of VASS reachability languages is decidable and $\mathbf{F}_{\omega}$-complete. At the heart of our decision procedure are doubly-marked graph transition sequences, a new proof object that…
Does the trace language of a given vector addition system (VAS) intersect with a given context-free language? This question lies at the heart of several verification questions involving recursive programs with integer parameters. In…
Multi-pushdown systems are a standard model for concurrent recursive programs, but they have an undecidable reachability problem. Therefore, there have been several proposals to underapproximate their sets of runs so that reachability in…
We consider history-determinism, a restricted form of non-determinism, for Vector Addition Systems with States (VASS) when used as acceptors to recognise languages of finite words. History-determinism requires that the non-deterministic…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
Well-structured transition systems (WSTS) are an abstract family of systems that encompasses a vast landscape of infinite-state systems. By requiring a well-quasi-ordering (wqo) on the set of states, a WSTS enables generic algorithms for…
In this work, we extend undecidability of language equivalence for two-dimensional Vector Addition System with States (VASS) accepting by coverability condition. We show that the problem is undecidable even when one of the two-dimensional…
The geometric dimension of a Vector Addition System with States (VASS), emerged in Leroux and Schmitz (2019) and formalized by Fu, Yang, and Zheng (2024), quantifies the dimension of the vector space spanned by cycle effects in the system.…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over discrete time. We analyse this problem with respect to the allowable control sets, which in general are assumed to be defined by…
A complete characterization of the complexity of the reachability problem for vector addition system has been open for a long time. The problem is shown to be Tower complete.
We study the language universality problem for One-Counter Nets, also known as 1-dimensional Vector Addition Systems with States (1-VASS), parameterized either with an initial counter value, or with an upper bound on the allowed counter…
We introduce the well structured problem as the question of whether a model (here a counter machine) is well structured (here for the usual ordering on integers). We show that it is undecidable for most of the (Presburger-defined) counter…
The aim of this paper is to deliver broad understanding of a class of languages of boundedly-ambiguous VASS, that is k-ambiguous VASS for some natural k. These are languages of Vector Addition Systems with States with the acceptance…
Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…
Reachability for piecewise affine systems is known to be undecidable, starting from dimension $2$. In this paper we investigate the exact complexity of several decidable variants of reachability and control questions for piecewise affine…
In many kinds of infinite-state systems, the coverability problem has significantly lower complexity than the reachability problem. In order to delineate the border of computational hardness between coverability and reachability, we propose…
The reachability problem in vector addition systems is a central question, not only for the static verification of these systems, but also for many inter-reducible decision problems occurring in various fields. The currently best known…
Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with…
Multi-stack pushdown systems are a well-studied model of concurrent computation using threads with first-order procedure calls. While, in general, reachability is undecidable, there are numerous restrictions on stack behaviour that lead to…