Open Petri nets: Non-deterministic processes and compositionality

2019

2009

Abstract. We present an encoding for (bound) processes of the asynchronous CCS with replication into open Petri nets: ordinary Petri nets equipped with a distinguished set of open places. The standard token game of nets models the reduction semantics of the calculus; the exchange of tokens on open places models the interactions between processes and their environment.

Computer Simulation [Working Title], 2019

This chapter is dedicated to several structure features of Petri nets. There is detailed description of appropriate access in Petri nets and reachable tree mechanism construction. There is an algorithm that describes the minimum sequence of possible transitions. The algorithm developed by us finds the shortest possible sequence for the network promotion state, which transfers the mentioned network state to the coverage state. The corresponding theorem is proven, which states that due to the describing algorithm, the number of transitions in the covering state is minimal. This chapter studies the interrelation of languages of colored Petri nets and traditional formal languages. The Venn diagram, modified by the author, is presented, which shows the relationship between the languages of the colored Petri nets and some traditional languages. As a result, it is shown that the language class of colored Petri nets includes an entire class of context-free languages and some other classes. The results obtained show that it is not possible to model the Patil problem using the well-known semaphores P and V or classical Petri nets, so the mentioned systems have limited properties.

Programming and Computer …, 2001

In the paper, a formal model based on Petri nets is proposed in the context of a compositional approach to the development and analysis of complex concurrent and distributed systems. Mutlilabels of Petri nets are introduced allowing labeling a transition not only with a single symbol, but also with a multiset of symbols. Operations on multilabeled Petri nets-parallel composition and restriction-are defined. A definition of a Petri net entity is given based on the notion of multilabels. A Petri net entity is a Petri net with a set of multilabels, where each multilabel is regarded as an access point of the entity. The operation of entity composition is introduced. Equivalence of entities is defined based on bisimulation equivalence of Petri nets. It is shown that the equivalence relation is congruent with respect to entity composition. It is also demonstrated that the composition operation is commutative and associative.

CONCUR 2010-Concurrency Theory, 2011

We introduce a novel compositional algebra of Petri nets, as well as a stateful extension of the calculus of connectors. These two formalisms are shown to have the same expressive power.

2003

This paper deals with the study of behavioral equivalences between labeled (placeltransitwn) Petri nets preserving the causal relationship among transition firings. This is achieved by d e m g a very slight modification in the conventional Petri net formalism, leading to associating an additional ir$ormation to each tokm of the net. Following this approach, bisimulation equivalences are defined within a partial order framework, in a way similar to P a r r s notion of bisimilarity originally d e w d for interleaving based models.

Advanced Computer Systems, 2002

Petri nets, a popular discrete automaton model, are convenient for describing some parallel operations. A net used for such purpose cannot be a closed system but has to contain input and output places. Such a model is defined here as an operational Petri net. Analysis of Petri nets is a difficult task. In the paper the method of analysis is suggested, based on the original approach to decomposition and oriented for the considered class of nets. Applying the approach to the cyclic nets is also considered. Some experimental results are presented.

Lecture Notes in Computer Science, 1980

A relational model for non-deterministic programs is presented. Several predicate transformers are introduced and it is shown that one of them satisfies all the healthiness criteria indicated by Dijkstra for a useful total correctness predicate transformer.

2006

A Petri net is confluent if its firing relation is confluent, i.e., for any two reachable markings there exists a marking reachable from both of them. We prove that confluence is a decidable property for Petri nets and it is preserved by asynchronous parallel composition. Applications to Petri net structural transformations and term rewriting systems are then pointed out.

arXiv (Cornell University), 2023

We classify all additive invariants of open Petri nets: these are ℕ-valued invariants which are additive with respect to sequential and parallel composition of open Petri nets. In particular, we prove two classification theorems: one for open Petri nets and one for monically open Petri nets (i.e. open Petri nets whose interfaces are specified by monic maps). Our results can be summarized as follows. The additive invariants of open Petri nets are completely determined by their values on a particular class of single-transition Petri nets. However, for monically open Petri nets, the additive invariants are determined by their values on transitionless Petri nets and all single-transition Petri nets. Our results confirm a conjecture of John Baez (stated during the AMS' 2022 Mathematical Research Communities workshop).