相关论文: Small Polynomial Time Universal Petri Nets

We discuss the complexity of path enumeration and counting in weighted temporal graphs. In a weighted temporal graph, each edge has an availability time, a traversal time and some real cost. We introduce two bicriteria temporal min-cost…

Boolean Petri nets equipped with nop allow places and transitions to be independent by being related by nop. We characterize for any fixed natural number g the computational complexity of synthesizing nop-equipped Boolean Petri nets from…

Homology groups of labelled asynchronous transition systems and Petri nets are introduced. Examples of computing the homology groups are given. It is proved that if labelled asynchronous transition systems are bisimulation equivalent, then…

We consider the problem of assigning radii to a given set of points in the plane, such that the resulting set of circles is connected, and the sum of radii is minimized. We show that the problem is polynomially solvable if a connectivity…

Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…

Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business…

We show that the EXPSPACE-hardness result for structural liveness of Petri nets [Jancar and Purser, 2019] holds even for a simple subclass of conservative nets. As our main result, we prove that for structurally live conservative nets, the…

Petri nets and their variants are often considered through their interleaved semantics, i.e. considering executions where, at each step, a single transition fires. This is clearly a miss, as Petri nets are a true concurrency model. This…

Computing steady-state distributions in infinite-state stochastic systems is in general a very dificult task. Product-form Petri nets are those Petri nets for which the steady-state distribution can be described as a natural product…

The celebrated result of Kabanets and Impagliazzo (Computational Complexity, 2004) showed that PIT algorithms imply circuit lower bounds, and vice versa. Since then it has been a major challenge to understand the precise connections between…

Tensor networks (TNs) enable compact representations of large tensors through shared parameters. Their use in probabilistic modeling is particularly appealing, as probabilistic tensor networks (PTNs) allow for tractable computation of…

In process mining, alignments quantify the degree of deviation between an observed event trace and a business process model and constitute the most important conformance checking technique. We study the algorithmic complexity of computing…

Multivariate Time Series (MTS) forecasting involves modeling temporal dependencies within historical records. Transformers have demonstrated remarkable performance in MTS forecasting due to their capability to capture long-term…

In this paper we investigate the intrinsic sequential time complexity of universal elimination procedures for arbitrary continuous data structures encoding input and output objects of elimination theory (i.e. polynomial equation systems)…

Solutions proposed for the longstanding problem of automatic decomposition of Petri nets into concurrent processes, as well as methods developed in Grenoble for the automatic conversion of safe Petri nets to NUPNs (Nested-Unit Petri Nets),…

The coverability and boundedness problems for Petri nets are known to be Expspace-complete. Given a Petri net, we associate a graph with it. With the vertex cover number k of this graph and the maximum arc weight W as parameters, we show…

Optical neural networks (ONNs), implemented on an array of cascaded Mach-Zehnder interferometers (MZIs), have recently been proposed as a possible replacement for conventional deep learning hardware. They potentially offer higher energy…

We bring together the semiclassical approximation, matrix integrals and the theory of symmetric polynomials in order to solve a long standing problem in the field of quantum chaos: to compute transport moments when tunnel barriers are…

A Petri net is structurally cyclic if every configuration is reachable from itself in one or more steps. We show that structural cyclicity is decidable in deterministic polynomial time. For this, we adapt the Kosaraju's approach for the…

Bayesian online algorithms for Sum-Product Networks (SPNs) need to update their posterior distribution after seeing one single additional instance. To do so, they must compute moments of the model parameters under this distribution. The…