Related papers: Reachability is Tower Complete
We introduce a novel technique for checking reachability in Petri nets that relies on a recently introduced compositional algebra of nets. We prove that the technique is correct, and discuss our implementation. We report promising…
One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…
We study several decision problems for counter systems with guards defined by convex polyhedra and updates defined by affine transformations. In general, the reachability problem is undecidable for such systems. Decidability can be achieved…
Petri nets are a classical model of concurrency widely used and studied in formal verification with many applications in modeling and analyzing hardware and software, data bases, and reactive systems. The reachability problem is central…
Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamilton-Jacobi approaches, suffer from the curse of…
Reachability logic has been applied to $\mathbb{K}$ rewrite-rule-based language definitions as a language-generic logic of programs. To be able to verify not just code but also distributed system designs, a new rewrite-theory-generic…
This study focuses on reachability problems in differential games. An improved level set method for computing reachable tubes is proposed in this paper. The reachable tube is described as a sublevel set of a value function, which is the…
The reachability analysis of recursive programs that communicate asynchronously over reliable FIFO channels calls for restrictions to ensure decidability. Our first result characterizes communication topologies with a decidable reachability…
Motivated by the controllability/reachability problems for switched linear control systems and some classes of nonlinear (mechanical) control systems we address a related problem of existence of a cyclic vector for an associative (matrix)…
Reachability and other path-based measures on temporal graphs can be used to understand spread of infection, information, and people in modelled systems. Due to delays and errors in reporting, temporal graphs derived from data are unlikely…
Detectability describes the property of a system to uniquely determine, after a finite number of observations, the current and subsequent states. In this paper, to reduce the complexity of checking the detectability properties in the…
In this paper we introduce a new network reachability problem where the goal is to find the most reliable path between two nodes in a network, represented as a directed acyclic graph. Individual edges within this network may fail according…
A turn sequence of left and right turns is realized as a simple rectilinear chain of integral segments whose turns at its bends are the same as the turn sequence. The chain starts from the origin and ends at some point which we call a…
This paper proves the NP-completeness of the reachability problem for the class of flat counter machines with difference bounds and, more generally, octagonal relations, labeling the transitions on the loops. The proof is based on the fact…
A vector addition system (VAS) with an initial and a final marking and transition labels induces a language. In part because the reachability problem in VAS remains far from being well-understood, it is difficult to devise decision…
This note is a product of digestion of the famous proof of decidability of the reachability problem for vector addition systems with states (VASS), as first established by Mayr in 1981 and then simplified by Kosaraju in 1982. The note is…
We provide an Ackermannian complexity lower bound for the reachability problem for checking programs, a model equivalent to Petri nets. Moreover in fixed dimension $2d+4$, we show that the problem is $\mathbb{F}_d$-hard. As a direct…
We study linear-time temporal logics interpreted over data words with multiple attributes. We restrict the atomic formulas to equalities of attribute values in successive positions and to repetitions of attribute values in the future or…
Vector addition systems (VAS), also known as Petri nets, are a popular model of concurrent systems. Many problems from many areas reduce to the reachability problem for VAS, which consists of deciding whether a target configuration of a VAS…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…