Effective Translation of Algebraic PNs with Active Tokens in Maude: A Model for Adaptive Systems

Reisig's Algebraic Petri nets (APN), also known as SPEC-inscribed Petri nets, are regarded as some of the most powerful and expressive high-level Petri net formalisms ever established. Despite this, there exists only a limited number of comprehensive implementations for this foundational model, and none are situated within a purely algebraic framework. Here, we introduce an efficient translation of APN using Maude, a declarative programming language that operates with rewriting semantics. By exploring two distinct definitions, we address the nuanced modeling challenges arising from Maude's operational semantics based on pattern-matching. We further demonstrate the advantage of using rewritable terms as active tokens, which is naturally supported by Maude. The paper presents simple examples throughout, with an advanced example of adaptive Multilevel Feedback Queue scheduling