We study data nets, a generalisation of Petri nets in which tokens carry data from linearlyordered infinite domains and in which whole-place operations such as resets and transfers are possible. Data nets subsume several known classes of infinite-state systems, including multiset rewriting systems and polymorphic systems with arrays.

We show that coverability and termination are decidable for arbitrary data nets, and that boundedness is decidable for data nets in which whole-place operations are restricted to transfers. By providing an encoding of lossy channel systems into data nets without whole-place operations, we establish that coverability, termination and boundedness for the latter class have non-primitive recursive complexity. The main result of the paper is that, even for unordered data domains (i.e., with only the equality predicate), each of the three verification problems for data nets without whole-place operations has non-elementary complexity.

/pdf/nets-with-tokens-which-carry-data-9kquqwjnyi.pdf

Nets with Tokens which Carry Data

Decidability and complexity of Petri nets with unordered data

Information systems have to support more and more complex organizations and the cooperation between organizations. The functionality of these systems is divided in components: each component has its own dedicated set of functionality. Whereas in past years, design and verification mostly focused on the internal aspects of a component, like the data aspect and behavioral aspect, the focus nowadays shifts more and more to the design and verification of the interaction between systems. Different organizations provide systems that need to communicate. Specifically, an organization may allow its components to be used by systems of other organizations. This way, an inter organizational network of communicating components is formed. One of the main aspects of such a network is that organizations do not want to share with whom they are communicating. This way, the individual systems form a, possibly unknown, large scale ecosystem: a dynamic network of communicating components. These systems communicate via messages: a component requests a service from another component, which in turn eventually sends its answer. Hence, communication between the components is asynchronous by nature. Verification of asynchronously communicating systems is known to be a hard problem. In this thesis, we develop a framework to design large scale component-based information systems in which components communicate asynchronously. The framework allows for verification of local conditions for termination of the complete system. The formal foundation of the framework is Petri nets, in which communication is asynchronous by nature. Classical Petri nets can be used both for modeling the internal activities of a component, as well as for the interaction between components. We focus on soundness of systems: a system should always have a possibility to terminate. We propose sufficient criteria for compositional verification of soundness: if each component in the system is sound, and each pair of asynchronously communicating components satisfies some condition, the whole system is sound. The framework provides methods to design components that are sound by construction. The method uses soundness preserving refinements of Petri net places in different components by pairs of sound subcomponents. Data can be used to enrich the behavioral aspect, the control flow, of an information system, and data is used to store and present information to the users of the system. Classical Petri nets only focus on the ordering of activities. To integrate the data aspect and behavioral aspect of components, we define a sub class of coloured Petri nets, which is on the one hand expressive enough to model the flow and correlation of objects and messages, and on the other hand the possibility of verification remains. All techniques are combined in a design approach for the development of component based information systems. The approach uses the framework to develop a formal specification from user requirements. The developed specification is directly usable as a prototype, as it has execution semantics. The tool "Yasper" is developed to support the approach. Process mining techniques can be used to support the design process of component based information systems, by extracting internal aspects of a component, like data, resources and control flow. In the thesis, we present a process discovery algorithm based on integer linear programming, which can be used for this purpose, as it can handle negative instances that describe undesired behavior.

/pdf/compositional-design-and-verification-of-component-based-3fa2suxlho.pdf

Compositional design and verification of component-based information systems

Processes are a key application area for formal models of concurrency. The core concepts of Petri nets have been adopted in research and industrial practice to describe and analyze the behavior of processes where each instance is executed in isolation. Unaddressed challenges arise when instances of processes may interact with each other in a one-to-many or many-to-many fashion. So far, behavioral models for describing such behavior either also include an explicit data model of the processes to describe many-to-many interactions, or cannot provide precise operational semantics.

Describing Behavior of Processes with Many-to-Many Interactions

We study the relationship between name creation and replication in a setting of infinite-state communicating automata. By name creation we mean the capacity of dynamically producing pure names, with no relation between them other than equality or inequality. By replication we understand the ability of systems of creating new parallel identical threads, that can synchronize with each other. We have developed our study in the framework of Petri nets, by considering several extensions of P/T nets. In particular, we prove that in this setting name creation and replication are equivalent, but only when a garbage collection mechanism is added for idle threads. However, when simultaneously considering both extensions the obtained model is, a bit surprisingly, Turing complete and therefore, more expressive than when considered separately.

http://antares.sip.ucm.es/frosa/docs/fi08.pdf

Name creation vs. replication in Petri net systems

http://antares.sip.ucm.es/~frosa/docs/secco05.pdf

On the Expressiveness of Mobile Synchronizing Petri Nets

http://antares.sip.ucm.es/~frosa/docs/mtcoord05.pdf

Mobile Synchronizing Petri Nets: A Choreographic Approach for Coordination in Ubiquitous Systems

In this paper we extend our basic model of Ubiquitous Nets, by adding a replication operator that creates new copies of the net firing the replicating transition. We prove that the location attribute and thus the mobility feature are not essential characteristics of the obtained model, since it is equivalent to the particular case of Centralized Systems, where all components are stationary and co-located in a single location. This allows us to restrict ourselves to Centralized Systems when studying the decidability of reachability and coverability properties. In this way, we prove that both reachability and coverability remain decidable. Finally, we introduce an alternative version that includes a garbage collection mechanism that allows us to remove empty nets from the state of the system. We show that in this case coverability remains decidable.

Replicated ubiquitous nets

Replicated Ubiquitous Nets

In this paper we propose a progressive technique for teaching recursion with the aim of making easier the understanding of this concept by students of other areas than computer science. Since knowledge is intended to be actively constructed by the students and not passively absorbed from textbooks and lecturers, the adopted teaching technique is derived from constructivism. This paper presents a study of the results obtained in 2005 by two groups of students from Mathematics and Statistics degrees.

/pdf/platyhelminthes-are-re-constructed-recursively-2uhne5frx9.pdf

Olga Marroquín-Alonso

Papers

On the Expressiveness of Mobile Synchronizing Petri Nets

Mobile Synchronizing Petri Nets: A Choreographic Approach for Coordination in Ubiquitous Systems

Replicated ubiquitous nets

Replicated Ubiquitous Nets

Platyhelminthes are [re]constructed recursively