Tau-Equivalences and Refinement for Petri Nets Based Design

The paper is devoted to the investigation of behavioral equivalences of concurrent systems modeled by Petri nets with silent transitions. Basic τ-equivalences and back-forth τ-bisimulation equivalences known from the literature are supplemented by new ones, giving rise to complete set of equivalence notions in interleaving / true concurrency and linear / branching time semantcis. Their interrelations are examined for the general class of nets as well as for their subclasses of nets without siltent transitions and sequential nets (nets without concurrent transitions). In addition, the preservation of all the equivalence notions by refinements (allowing one to consider the systems to be modeled on a lower abstraction levels) is investigated

An operations semantics for pure dataflow

We prove the equivalence between an operational and an extensional semantics for pure dataflow. The term pure dataflow refers to dataflow nets in which the nodes are functional (i.e. the output history is a function of the input history only) and the arcs are unbounded fifo queues. Gilles Kahn gave a method for the representation of a pure dataflow net as a set of equations; one equation for each arc in the net. We present a complete proof that the operational behaviour of a pure dataflow net is exactly described by the least fixed point solution to its associated set of equations. Our model is completely general since our nodes have the universality property, in that, for any continuous history function there exists a node that will compute it. Moreover since our nets are not built from a set of sequential primitive nodes the model is not in the communicating sequential processes framework. On the contrary our nets have the abstraction property in that any net can be collapsed into a node. The above proof gives complementary ways of viewing pure dataflow nets, that is, as either sets of equations or as graphs. It moreover gives rise to an elegant equational dataflow language. Pure dataflow then takes on an important role since it is a correct implementation for such a functional programming language; nodes being implementation of continuous history functions; arcs and datons being implementations of histories; and nets being mechanisms for computing the solutions to sets of equations

Modeling production configuration using nested colored object-oriented Petri-nets with changeable structures

Configuring production processes based on process platforms has been well recognized as an effective means for companies to provide product variety while maintaining mass production efficiency. The production processes of product families involve diverse variations in manufacturing and assembly processes resulted from a large variety of component parts and assemblies. This paper develops a multilevel system of nested colored object-oriented Petri nets with changeable structures to model the configuration of production processes. To capture the semantics associated with production configuration decisions, some unique modeling mechanisms are employed, including colored Petri nets, object-oriented Petri nets, changeable Petri net structures, and net nesting. The modeling formalism comprises resource nets, manufacturing nets, assembly nets and process nets. The paper demonstrates how these net definitions are applied to the specification of production process variants at different levels of abstraction. Also reported is a case study in an electronics company. The system model is further analyzed with focus on conflict prevention and deadlock detection

Observational Equivalence and Full Abstraction in the Symmetric Interaction Combinators

The symmetric interaction combinators are an equally expressive variant of Lafont's interaction combinators. They are a graph-rewriting model of deterministic computation. We define two notions of observational equivalence for them, analogous to normal form and head normal form equivalence in the lambda-calculus. Then, we prove a full abstraction result for each of the two equivalences. This is obtained by interpreting nets as certain subsets of the Cantor space, called edifices, which play the same role as Boehm trees in the theory of the lambda-calculus

Isotactics as a foundation for alignment and abstraction of behavioral models

There are many use cases in business process management that require the comparison of behavioral models. For instance, verifying equivalence is the basis for assessing whether a technical workflow correctly implements a business process, or whether a process realization conforms to a reference process. This paper proposes an equivalence relation for models that describe behaviors based on the concurrency semantics of net theory and for which an alignment relation has been defined. This equivalence, called isotactics, preserves the level of concurrency of aligned operations. Furthermore, we elaborate on the conditions under which an alignment relation can be classified as an abstraction. Finally, we show that alignment relations induced by structural refinements of behavioral models are indeed behavioral abstractions

A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets

Timed-arc Petri nets (TAPN) are a well-known time extension of the Petri net model and several translations to networks of timed automata have been proposed for this model. We present a direct, DBM-based algorithm for forward reachability analysis of bounded TAPNs extended with transport arcs, inhibitor arcs and age invariants. We also give a complete proof of its correctness, including reduction techniques based on symmetries and extrapolation. Finally, we augment the algorithm with a novel state-space reduction technique introducing a monotonic ordering on markings and prove its soundness even in the presence of monotonicity-breaking features like age invariants and inhibitor arcs. We implement the algorithm within the model-checker TAPAAL and the experimental results document an encouraging performance compared to verification approaches that translate TAPN models to UPPAAL timed automata.Comment: In Proceedings SSV 2012, arXiv:1211.587

Dimensional Confluence Algebra of Information Space Modulo Quotient Abstraction Relations in Automated Problem Solving Paradigm

Confluence in abstract parallel category systems is established for net class-rewriting in iterative closed multilevel quotient graph structures with uncountable node arities by multi-dimensional transducer operations in topological metrics defined by alphabetically abstracting net block homomorphism. We obtain minimum prerequisites for the comprehensive connector pairs in a multitude dimensional rewriting closure generating confluence in Participatory algebra for different horizontal and vertical level projections modulo abstraction relations constituting formal semantics for confluence in information space. Participatory algebra with formal automata syntax in its entirety representing automated problem solving paradigm generates rich variety of multitude confluence harmonizers under each fundamental abstraction relation set, horizontal structure mapping and vertical process iteration cardinality.Comment: The current work is an application as a continuation for my previous works in arXiv:1305.5637 and arXiv:1308.5321 using the key definitions of them sustaining consistency, consequently references being minimized. Readers are strongly advised to resort to the mentioned previous works for preliminaries. arXiv admin note: text overlap with arXiv:1408.137