Верификация вычислительных решеток с особыми краевыми условиями бесконечными сетями Петри

A technique of the computing grid verification using invariants of infinite Petri nets was presented. Models of square grid structures in the form of parametric Petri nets for such edge conditions as connection of edges and truncated devices were constructed. Infinite systems of linear algebraic equations were composed on parametric Petri nets for calculating p-invariants; their parametric solutions were obtained. P-invariant Petri nets are structuraly conservative and bounded that together with liveness are the properties of ideal systems. Liveness investigation based on siphons and traps can be implemented by using p-invariants of modified nets.Представлена методика верификации вычислительных решеток с помощью нахождения инвариантов бесконечных сетей Петри. Построены модели структур квадратных решеток в форме параметрических сетей Петри для таких краевых условий, как соединение краев и усеченные устройства. По параметрическим сетям Петри построены бесконечные системы линейных алгебраических уравнений для вычисления p-инвариантов и получены их параметрические ре- шения. P-инвариантные сети Петри являются структурно консервативными и ограниченными, что, вместе с живостью, является свойствами моделей идеальных систем. Исследование живости модели на основе анализа сифонов и ловушек может быть выполнено с помощью p-инвариантов модифицированных сетей

Verifying Modal Workflow Specifications Using Constraint Solving

International audienceNowadaysworkflowsareextensivelyusedbycompaniestoimproveorganizationalefficiencyandproductivity.Thispaperfocusesontheverificationofmodalworkflowspecificationsusingconstraintsolvingasacomputationaltool.ItsmaincontributionconsistsindevelopinganinnovativeformalframeworkbasedonconstraintsystemstomodelexecutionsofworkflowPetrinetsandtheirstructuralproperties,aswellastoverifytheirmodalspecifications.Finally,animplementationandpromisingexperimentalresultsconstituteapracticalcontribution

Homogeneous Equations of Algebraic Petri Nets

Algebraic Petri nets are a formalism for modeling distributed systems and algorithms, describing control and data flow by combining Petri nets and algebraic specification. One way to specify correctness of an algebraic Petri net model "N" is to specify a linear equation "E" over the places of "N" based on term substitution, and coefficients from an abelian group "G". Then, "E" is valid in "N" iff "E" is valid in each reachable marking of "N". Due to the expressive power of Algebraic Petri nets, validity is generally undecidable. Stable linear equations form a class of linear equations for which validity is decidable. Place invariants yield a well-understood but incomplete characterization of all stable linear equations. In this paper, we provide a complete characterization of stability for the subclass of homogeneous linear equations, by restricting ourselves to the interpretation of terms over the Herbrand structure without considering further equality axioms. Based thereon, we show that stability is decidable for homogeneous linear equations if "G" is a cyclic group

On Enumerating Minimal Siphons in Petri nets using CLP and SAT solvers: Theoretical and Practical Complexity

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Process Petri Nets with Time Stamps and Their Using in Project Management

Process Petri nets with time stamps (PPNTS) are the newly introduced class of low-level Petri nets, whose definition and the properties are the main topic of this chapter; they generalize the properties of Petri net processes in the area of design, modeling and verification of generally parallel systems with the discrete time. Property-preserving Petri net process algebras (PPPAs) were originally designed for the specification and verification of manufacturing systems. PPPA does not need to verify composition of Petri net processes because all their algebraic operators preserve the specified set of the properties. These original PPPAs are generalized for the class of the PPNTSs in this chapter. The new COMP, SYNC and JOIN algebraic operators are defined for the class of PPNTS and their chosen properties are proved. With the support of these operators, the PPNTSs can be extended also to the areas of project management and the determination of the project critical path with the support of the critical path method (CPM). The new CPNET subclass of PPNTS class is defined in this chapter. It is specially designed for the generalization of the CPM activity charts and their properties. This fact is then demonstrated on the simple project example and its critical path and other property specifications