Related papers: Occam's Razor Applied to the Petri Net Coverabilit…
We study the synthesis of inductive half spaces (IHS). These are linear inequalities that form inductive invariants for Petri nets, capable of disproving reachability or coverability. IHS generalize classic notions of invariants like traps…
Petri nets are a popular formalism for modeling and analyzing distributed systems. Tokens in Petri net models can represent the control flow state or resources produced/consumed by transition firings. We define a resource as a part (a…
We provide a new representation-independent formulation of Occam's razor theorem, based on Kolmogorov complexity. This new formulation allows us to: (i) Obtain better sample complexity than both length-based and VC-based versions of Occam's…
Petri nets are a mathematical language for modeling and reasoning about distributed systems. In this paper we propose an approach to Petri nets for embedding reversibility, i.e., the ability of reversing an executed sequence of operations…
In recent years, low-rank tensor completion (LRTC) has received considerable attention due to its applications in image/video inpainting, hyperspectral data recovery, etc. With different notions of tensor rank (e.g., CP, Tucker, tensor…
We investigate classes of systems based on different interaction patterns with the aim of achieving distributability. As our system model we use Petri nets. In Petri nets, an inherent concept of simultaneity is built in, since when a…
A recent breakthrough by K\"unnemann, Mazowiecki, Sch\"utze, Sinclair-Banks, and Wegrzycki (ICALP, 2023) bounds the running time for the coverability problem in $d$-dimensional vector addition systems under unary encoding to $n^{2^{O(d)}}$,…
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…
Recent work by the authors equips Petri occurrence nets (PN) with probability distributions which fully replace nondeterminism. To avoid the so-called confusion problem, the construction imposes additional causal dependencies which restrict…
The formalism of the models with Petri networks provides a sound theoretical base, supported by powerful mathematical methods able to extract information necessary for the formalism and simulation of the real system that provides features…
We consider the Max Unique Coverage problem, including applications to the data stream model. The input is a universe of $n$ elements, a collection of $m$ subsets of this universe, and a cardinality constraint, $k$. The goal is to select a…
We present the framework of delta-complete analysis for bounded reachability problems of general hybrid systems. We perform bounded reachability checking through solving delta-decision problems over the reals. The techniques take into…
We study the problem of inferring the structure of a communication network based only on network measurements made from a set of hosts situated at the network periphery. Our novel approach called "OCCAM" is based on the principle of occam's…
The Minimum Vertex Cover problem, a classical NP-complete problem, presents significant challenges for exact solution on large graphs. Fixed-Parameter Tractability (FPT) offers a powerful paradigm to address such problems by exploiting a…
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…
Generative adversarial nets (GANs) have generated a lot of excitement. Despite their popularity, they exhibit a number of well-documented issues in practice, which apparently contradict theoretical guarantees. A number of enlightening…
Consider a Markovian Petri net with race policy. The marking process has a "product form" stationary distribution if the probability of viewing a given marking can be decomposed as the product over places of terms depending only on the…
Research on the vulnerability of electric networks with a complex network approach has produced significant results in the last decade, especially for transmission networks. These studies have shown that there are causal relations between…
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…
We consider approaches for causal semantics of Petri nets, explicitly representing dependencies between transition occurrences. For one-safe nets or condition/event-systems, the notion of process as defined by Carl Adam Petri provides a…