Related papers: Improved Ackermannian lower bound for the Petri ne…
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…
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…
We prove several decidability and undecidability results for nu-PN, an extension of P/T nets with pure name creation and name management. We give a simple proof of undecidability of reachability, by reducing reachability in nets with…
In Petri net synthesis we ask whether a given transition system $A$ can be implemented by a Petri net $N$. Depending on the level of accuracy, there are three ways how $N$ can implement $A$: an embedding, the least accurate implementation,…
We propose a method for checking generalized reachability properties in Petri nets that takes advantage of structural reductions and that can be used, transparently, as a pre-processing step of existing model-checkers. Our approach is based…
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.
Ground Tree Rewrite Systems with State are known to have an undecidable control state reachability problem. Taking inspiration from the recent introduction of scope-bounded multi-stack pushdown systems, we define Senescent Ground Tree…
We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and conjunctive…
Real-world applications such as the internet of things, wireless sensor networks, smart grids, transportation networks, communication networks, social networks, and computer grid systems are typically modeled as network structures. Network…
Recently, Arjevani et al. [1] established a lower bound of iteration complexity for the first-order optimization under an $L$-smooth condition and a bounded noise variance assumption. However, a thorough review of existing literature on…
Dynamic networks of concurrent pushdown systems (DCPS) are a theoretical model for multi-threaded recursive programs with shared global state and dynamical creation of threads. The (global) state reachability problem for DCPS is undecidable…
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 crucial question in analyzing a concurrent system is to determine its long-run behaviour, and in particular, whether there are irreversible choices in its evolution, leading into parts of the reachability space from which there is no…
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…
We introduce {\omega}-Petri nets ({\omega}PN), an extension of plain Petri nets with {\omega}-labeled input and output arcs, that is well-suited to analyse parametric concurrent systems with dynamic thread creation. Most techniques (such as…
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…
The notion of Online State Complexity, introduced by Karp in 1967, quantifies the amount of states required to solve a given problem using an online algorithm, which is represented by a deterministic machine scanning the input from left to…
Despite recent progress which settled the complexity of the reachability problem for Vector Addition Systems with States (VASSes) as being Ackermann-complete we still lack much understanding for that problem. A striking example is the…
We define a new method for taking advantage of net reductions in combination with a SMT-based model checker. Our approach consists in transforming a reachability problem about some Petri net, into the verification of an updated reachability…
In a previous paper we introduced immediate observation Petri nets, a subclass of Petri nets with application domains in distributed protocols (population protocols) and theoretical chemistry (chemical reaction networks). IO nets enjoy many…