Related papers: A Categorical Semantics for Bounded Petri Nets
The local analysis is an established approach to the study of singularities and mobility of linkages. Key result of such analyses is a local picture of the finite motion through a configuration. This reveals the finite mobility at that…
We generalise classical reconstruction results in algebra, using the language of monads, monoidal categories, module categories, as well as various notions of duality, such as closedness, Grothendieck--Verdier duality (also known as…
We introduce TopoNets, end-to-end probabilistic deep networks for modeling semantic maps with structure reflecting the topology of large-scale environments. TopoNets build a unified deep network spanning multiple levels of abstraction and…
Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, and have hand-tuned hyperparameters and reweighting methods. This paper…
We propose an automated procedure to prove polyhedral abstractions (also known as polyhedral reductions) for Petri nets. Polyhedral abstraction is a new type of state space equivalence, between Petri nets, based on the use of linear integer…
We outline a bicategorical syntax for the interaction between public and private information in classical information theory. We use this to give high-level graphical definitions of encrypted communication and secret sharing protocols,…
We analyze a model of quantum nets and show it has non-abelian topological order of doubled Fibonacci type. The ground state has the same topological behavior as that of the corresponding string-net model, but our Hamiltonian can be defined…
Place bisimilarity is a behavioral equivalence for finite Petri nets, proposed in \cite{ABS91} and proved decidable in \cite{Gor21}. In this paper we propose an extension to finite Petri nets with silent moves of the place bisimulation…
Systematically discovering semantic relationships in text is an important and extensively studied area in Natural Language Processing, with various tasks such as entailment, semantic similarity, etc. Decomposability of sentence-level scores…
The study of networks has grown into a substantial interdisciplinary endeavour that encompasses myriad disciplines in the natural, social, and information sciences. Here we introduce a framework for constructing taxonomies of networks based…
We investigate Petri nets with data, an extension of plain Petri nets where tokens carry values from an infinite data domain, and executability of transitions is conditioned by equalities between data values. We provide a decision procedure…
We identify and demonstrate a weakness of Petri Nets (PN) in specifying composite behavior of reactive systems. Specifically, we show how, when specifying multiple requirements in one PN model, modelers are obliged to specify mechanisms for…
In this paper, we extend some usual techniques of classification resulting from a large-scale data-mining and network approach. This new technology, which in particular is designed to be suitable to big data, is used to construct an open…
$\partial\mathbb{B}$ nets are differentiable neural networks that learn discrete boolean-valued functions by gradient descent. $\partial\mathbb{B}$ nets have two semantically equivalent aspects: a differentiable soft-net, with real weights,…
We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints…
Being able to find small Petri nets with the same behaviour as formal specifications of concurrent systems benefits both effective verification and practical implementation of such systems. This paper considers specifications given in the…
We provide bicategorical analogs of several aspects of the notion of geometry in the sense of the theory of spectrum. We first introduce a notion of local right biadjoint, and prove it to be equivalent to a notion of bistable pseudofunctor,…
Neural networks excel at pattern recognition but struggle with reliable logical reasoning, often violating basic logical principles during inference. We address this limitation by developing a categorical framework that systematically…
Petri Nets (PN) are widely used for modeling concurrent and distributed systems, but face challenges in modeling adaptive systems. To address this, we have formalized "rewritable" PT nets (RwPT) using Maude, a declarative language with…
Learning to construct text representations in end-to-end systems can be difficult, as natural languages are highly compositional and task-specific annotated datasets are often limited in size. Methods for directly supervising language…