Related papers: On Affine Reachability Problems
Neural networks (NN) have been successfully applied to approximate various types of complex control laws, resulting in low-complexity NN-based controllers that are fast to evaluate. However, when approximating control laws using NN,…
This paper discusses the computational resolution and presents numerical results for solving affine combinations of Heaviside composite optimization problems (abbreviated as A-HSCOPs) by a progressive integer programming (abbreviated as…
Vector Addition Systems and equivalent Petri nets are a well established models of concurrency. The central algorithmic problem for Vector Addition Systems with a long research history is the reachability problem asking whether there exists…
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…
We study the complexity of algorithmic problems for matrices that are represented by multi-terminal decision diagrams (MTDD). These are a variant of ordered decision diagrams, where the terminal nodes are labeled with arbitrary elements of…
Chip-firing and rotor-routing are two well-studied examples of abelian networks. We study the complexity of their respective reachability problems. We show that the rotor-routing reachability problem is decidable in polynomial time, and we…
We study the computational complexity of constrained nonnegative Gram feasibility. Given a partially specified symmetric matrix together with affine relations among selected entries, the problem asks whether there exists a nonnegative…
Parametric timed automata (PTA) are an extension of timed automata in which clocks can be compared against parameters. The reachability problem asks for the existence of an assignment of the parameters to the non-negative integers such that…
In this paper we propose two new subclasses of Petri nets with resets, for which the reachability and coverability problems become tractable. Namely, we add an acyclicity condition that only applies to the consumptions and productions, not…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
We study programs with integer data, procedure calls and arbitrary call graphs. We show that, whenever the guards and updates are given by octagonal relations, the reachability problem along control flow paths within some language w1* ...…
The problem of finding the maximal dimension of linear or affine subspaces of matrices whose rank is constant, or bounded below, or bounded above, has attracted many mathematicians from the sixties to the present day. The problem has caught…
Vector addition systems with states (VASS), also known as Petri nets, are a popular model of concurrent systems. Many problems from many areas reduce to the reachability problem for VASS, which consists of deciding whether a target…
A central decision problem in Petri net theory is reachability asking whether a given marking can be reached from the initial marking. Related is the covering problem (or sub-marking reachbility), which decides whether there is a reachable…
The reachability problem in 3-dimensional vector addition systems with states (3-VASS) is known to be PSpace-hard, and to belong to Tower. We significantly narrow down the complexity gap by proving the problem to be solvable in…
We present solutions to the matrix completion problems proposed by the Alignment Research Center that have a polynomial dependence on the precision $\varepsilon$. The motivation for these problems is to enable efficient computation of…
In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance:…
A recent result of Haase et al. has shown that reachability in two-clock timed automata is log-space equivalent to reachability in bounded one-counter automata. We show that reachability in bounded one-counter automata is PSPACE-complete.
We construct an automaton group with a PSPACE-complete word problem, proving a conjecture due to Steinberg. Additionally, the constructed group has a provably more difficult, namely EXPSPACE-complete, compressed word problem and acts over a…
Recently a strong connection has been shown between the tractability of integer programming (IP) with bounded coefficients on the one side and the structure of its constraint matrix on the other side. To that end, integer linear programming…