Mathematical methods for calculating invariants in Petri nets

Science of Computer Programming

Quilbeuf

et al. 2015

Using high level coordination primitives allows enhanced expressiveness of componentbased frameworks to cope with the inherent complexity of present-day systems designs. Nonetheless, their distributed implementation raises multiple issues, regarding both the correctness and the runtime performance of the final implementation. We propose a novel approach for distributed implementation of multiparty interactions subject to scheduling constraints expressed by priorities. We rely on a new composition operator named Restriction, whose semantics dynamically restricts the set of interactions allowed for execution, depending on the current state. We show that this operator provides a natural encoding for priorities. We provide a knowledge-based optimization that modifies the Restriction operator to avoid superfluous communication in the final implementation. We complete our framework through an enhanced conflict resolution protocol that natively implements Restriction. A prototype implementation allows us to compare performances of different optimizations.

Section: Invariants and Reachable Statesmentioning

confidence: 99%

Optimized distributed implementation of multiparty interactions with Restriction

Science of Computer Programming

Quilbeuf

et al. 2015

“…The work on algebraic methods for the generation of so called linear state-invariants for Petri net models is perhaps the most closest to ours. An introductory survey can be found in [13] while several extensions for invariant generation under particular constraints is available in [14]. These methods have been implemented since a long time and tools like CHARLIE [9] are widely known in the Petri net community.…”

Section: Verimag Research Report Nmentioning

confidence: 99%

Incremental Generation of Linear Invariants for Component-Based Systems

2013 13th International Conference on Application of Concurrency to System Design

Boyer

et al. 2013

Linear invariant generation has been intensively considered as an effective verification method for concurrent systems. However, none of the existing work on the topic strongly exploits the structure of the system and the algebra that defines the interactions between its components. This not only has an impact on the computation time, but also on the scalability of the method. In a series of recent work, we developed an incremental approach for generating boolean invariants for systems described in the BIP component framework. BIP is an expressive modeling formalism including a rich algebra to describe component interactions. The objective of this paper is to extend and propose new techniques dedicated to the computation of linear interactions invariants, i.e., invariants that are described by linear constraints and that relate states of several components in the system. In particular, we propose an incremental approach that allows to discover and reuse invariants that have already been computed on subparts of the model. Those new techniques have been implemented in DFINDER, a tool for checking deadlock freedom on BIP systems using invariants, and evaluated on several case studies. The experiments show that our approach outperforms classical techniques on a wide range of models.

“…For the example of Figure 1, at (on up ) + at (on) + at(dwn) = 1 is a linear invariant. Linear invariants are obtained using algebraic methods as described in [11].…”

Section: Invariants and Reachable Statesmentioning

confidence: 99%

Knowledge-Based Distributed Conflict Resolution for Multiparty Interactions and Priorities

Formal Techniques for Distributed Systems

Quilbeuf

et al. 2012

Abstract. Distributed decentralized implementation of systems of communicating processes raises non-trivial problems. Correct execution of multiparty interactions, subject to priority rules, requires sophisticated mechanisms for runtime conflict detection and resolution. We propose a method for detection of false conflicts which combines partial observation of the system's state and apriori knowledge extracted from invariants. We propose heuristics for determining optimal sets of observations leading to implementations with particular guarantees. We provide preliminary experimental results on an implementation of the method in the BIP framework.