Related papers: Analysing cycloids using linear algebra
Cycloids are particular Petri nets for modelling processes of actions or events. They belong to the fundaments of Petri's general systems theory and have very different interpretations, ranging from Einstein's relativity theory and…
Cycloids are particular Petri nets for modelling processes of actions and events, belonging to the fundaments of Petri's general systems theory. Defined by four parameters they provide an algebraic formalism to describe strongly…
Cycloids are particular Petri nets for modelling processes of actions and events, belonging to the fundaments of Petri's general systems theory. Defined by four parameters they provide an algebraic formalism to describe strongly…
This paper describes a stand-alone, no-frills tool supporting the analysis of (labelled) place/transition Petri nets and the synthesis of labelled transition systems into Petri nets. It is implemented as a collection of independent,…
Petri nets are an established graphical formalism for modeling and analyzing the behavior of systems. An important consideration of the value of Petri nets is their use in describing both the syntax and semantics of modeling formalisms.…
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…
Leibniz algebras generated by one element, called cyclic, provide simple and illuminating examples of many basic concepts. It is the purpose of this paper to illustrate this fact.
We develop layered monoidal theories -- a generalisation of monoidal theories combining formal descriptions of a system at different levels of abstraction. Via their representation as string diagrams, monoidal theories provide a graphical…
The categorical modeling of Petri nets has received much attention recently. The Dialectica construction has also had its fair share of attention. We revisit the use of the Dialectica construction as a categorical model for Petri nets…
A matroid is a combinatorial structure that captures and generalizes the algebraic concept of linear independence under a broader and more abstract framework. Matroids are closely related with many other topics in discrete mathematics, such…
In this paper some reflections on the concept of transition are presented: groupoids are introduced as models for the construction of a ``generalized logic'' whose basic statements involve pairs of propositions which can be conditioned. In…
Networks are versatile representations of the interactions between entities in complex systems. Cycles on such networks represent feedback processes which play a central role in system dynamics. In this work, we introduce a measure of the…
Since Leibniz algebras were introduced by Loday as a generalization of Lie algebras, there has been a lot of interest in which results of the latter extend to the former. Cyclic algebras, those generated by one element, are a useful tool…
Process algebra has been successful in many ways; but we don't yet see the lineaments of a fundamental theory. Some fleeting glimpses are sought from Petri Nets, physics and geometry.
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
Clifford algebras are used for definition of spinors. Because of using spin-1/2 systems as an adequate model of quantum bit, a relation of the algebras with quantum information science has physical reasons. But there are simple mathematical…
Cycle polytopes of matroids have been introduced in combinatorial optimization as a generalization of important classes of polyhedral objects like cut polytopes and Eulerian subgraph polytopes associated to graphs. Here we start an…
In recent work, the author and others have studied compositional algebras of Petri nets. Here we consider mathematical aspects of the pure linking algebras that underly them. We characterise composition of nets without places as the…
We investigate the construction and properties of Clifford algebras by a similar manner as our previous construction of the octonions, namely as a twisting of group algebras of Z_2^n by a cocycle. Our approach is more general than the usual…
In this paper we introduce the notion of spread net. Spread nets are (safe) Petri nets equipped with vector clocks on places and with ticking functions on transitions, and are such that vector clocks are consistent with the ticking of…