
TL;DR
This thesis develops a compositional operational semantics framework for networks modeled as $ ext{Q}$-nets and enriched graphs, unifying various network types through adjunctions and structured cospans.
Contribution
It introduces a categorical semantics for networks using adjunctions and structured cospans, enabling compositional analysis of diverse network models.
Findings
Constructed adjunctions for $ ext{Q}$-nets and $R$-matrices.
Developed double categories of open networks with input/output vertices.
Defined black-boxing that preserves composition for functional open networks.
Abstract
This thesis aims to develop a compositional theory for the operational semantics of networks. The networks considered are described by either internal or enriched graphs. In the internal case we focus on -nets, a generalization of Petri nets based on a Lawvere theory . -nets include many known variants of Petri nets including pre-nets, integer nets, elementary net systems, and bounded nets. In the enriched case we focus on graphs enriched in a quantale regarded as matrices with entries in . These -matrices represent distance networks, Markov processes, capacity networks, non-deterministic finite automata, simple graphs, and more. The operational semantics of -nets is constructed as an adjunction between -nets and categories internal to the category of models of . Similarly, the operational semantics of…
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Taxonomy
TopicsPetri Nets in System Modeling · Formal Methods in Verification · Distributed systems and fault tolerance
