159 research outputs found
Separators in Continuous Petri Nets
Leroux has proved that unreachability in Petri nets can be witnessed by a
Presburger separator, i.e. if a marking cannot reach a
marking , then there is a formula of Presburger
arithmetic such that: holds; is forward
invariant, i.e., and imply
); and holds. While these
separators could be used as explanations and as formal certificates of
unreachability, this has not yet been the case due to their
(super-)Ackermannian worst-case size and the (super-)exponential complexity of
checking that a formula is a separator.
We show that, in continuous Petri nets, these two problems can be overcome.
We introduce locally closed separators, and prove that: (a) unreachability can
be witnessed by a locally closed separator computable in polynomial time; (b)
checking whether a formula is a locally closed separator is in NC (so, simpler
than unreachablity, which is P-complete).
We further consider the more general problem of (existential) set-to-set
reachability, where two sets of markings are given as convex polytopes. We show
that, while our approach does not extend directly, we can still efficiently
certify unreachability via an altered Petri.Comment: Submitted to LMCS as an extension of the FoSSaCS'22 conference
versio
Measures induced by units
The half-open real unit interval (0,1] is closed under the ordinary
multiplication and its residuum. The corresponding infinite-valued
propositional logic has as its equivalent algebraic semantics the equational
class of cancellative hoops. Fixing a strong unit in a cancellative hoop
-equivalently, in the enveloping lattice-ordered abelian group- amounts to
fixing a gauge scale for falsity. In this paper we show that any strong unit in
a finitely presented cancellative hoop H induces naturally (i.e., in a
representation-independent way) an automorphism-invariant positive normalized
linear functional on H. Since H is representable as a uniformly dense set of
continuous functions on its maximal spectrum, such functionals -in this context
usually called states- amount to automorphism-invariant finite Borel measures
on the spectrum. Different choices for the unit may be algebraically unrelated
(e.g., they may lie in different orbits under the automorphism group of H), but
our second main result shows that the corresponding measures are always
absolutely continuous w.r.t. each other, and provides an explicit expression
for the reciprocal density.Comment: 24 pages, 1 figure. Revised version according to the referee's
suggestions. Examples added, proof of Lemma 2.6 simplified, Section 7
expanded. To appear in the Journal of Symbolic Logi
Presentation of the 9th Edition of the Model Checking Contest.
International audience; The Model Checking Contest (MCC) is an annual competition of software tools for model checking. Tools must process an increasing benchmark gathered from the whole community and may participate in various examinations: state space generation, computation of global properties, computation of some upper bounds in the model, evaluation of reachability formulas, evaluation of CTL formulas, and evaluation of LTL formulas.For each examination and each model instance, participating tools are provided with up to 3600 s and 16 gigabyte of memory. Then, tool answers are analyzed and confronted to the results produced by other competing tools to detect diverging answers (which are quite rare at this stage of the competition, and lead to penalties).For each examination, golden, silver, and bronze medals are attributed to the three best tools. CPU usage and memory consumption are reported, which is also valuable information for tool developers
On Minimum-time Control of Continuous Petri nets: Centralized and Decentralized Perspectives
Muchos sistemas artificiales, como los sistemas de manufactura, de logística, de telecomunicaciones o de tráfico, pueden ser vistos "de manera natural" como Sistemas Dinámicos de Eventos Discretos (DEDS). Desafortunadamente, cuando tienen grandes poblaciones, estos sistemas pueden sufrir del clásico problema de la explosión de estados. Con la intención de evitar este problema, se pueden aplicar técnicas de fluidificación, obteniendo una relajación fluida del modelo original discreto. Las redes de Petri continuas (CPNs) son una aproximación fluida de las redes de Petri discretas, un conocido formalismo para los DEDS. Una ventaja clave del empleo de las CPNs es que, a menudo, llevan a una substancial reducción del coste computacional. Esta tesis se centra en el control de Redes de Petri continuas temporizadas (TCPNs), donde las transiciones tienen una interpretación temporal asociada. Se asume que los sistemas siguen una semántica de servidores infinitos (velocidad variable) y que las acciones de control aplicables son la disminución de la velocidad del disparo de las transiciones. Se consideran dos interesantes problemas de control en esta tesis: 1) control del marcado objetivo, donde el objetivo es conducir el sistema (tan rápido como sea posible) desde un estado inicial a un estado final deseado, y es similar al problema de control set-point para cualquier sistema de estado continuo; 2) control del flujo óptimo, donde el objetivo es conducir el sistema a un flujo óptimo sin conocimiento a priori del estado final. En particular, estamos interesados en alcanzar el flujo máximo tan rápido como sea posible, lo cual suele ser deseable en la mayoría de sistemas prácticos. El problema de control del marcado objetivo se considera desde las perspectivas centralizada y descentralizada. Proponemos varios controladores centralizados en tiempo mínimo, y todos ellos están basados en una estrategia ON/OFF. Para algunas subclases, como las redes Choice-Free (CF), se garantiza la evolución en tiempo mínimo; mientras que para redes generales, los controladores propuestos son heurísticos. Respecto del problema de control descentralizado, proponemos en primer lugar un controlador descentralizado en tiempo mínimo para redes CF. Para redes generales, proponemos una aproximación distribuida del método Model Predictive Control (MPC); sin embargo en este método no se considera evolución en tiempo mínimo. El problema de control de flujo óptimo (en nuestro caso, flujo máximo) en tiempo mínimo se considera para redes CF. Proponemos un algoritmo heurístico en el que calculamos los "mejores" firing count vectors que llevan al sistema al flujo máximo, y aplicamos una estrategia de disparo ON/OFF. También demostramos que, debido a que las redes CF son persistentes, podemos reducir el tiempo que tarda en alcanzar el flujo máximo con algunos disparos adicionales. Los métodos de control propuestos se han implementado e integrado en una herramienta para Redes de Petri híbridas basada en Matlab, llamada SimHPN
Hybrid Petri nets with multiple stochastic transition firings
This paper introduces an algorithm for the efficient computation of transient measures of interest in Hybrid Petri nets in which the stochastic transitions are allowed to fire an arbitrary but finite number of times. Each firing increases the dimensionality of the underlying discrete/continuous state space. The algorithm evolves around a partitioning of the multi-dimensional state-space into regions, making use of advanced algorithms (and libraries) for computational geometry. To bound the number of stochastic transition firings the notion of control tokens is newly introduced. While the new partitioning algorithm is general, the implementation is currently limited to only two stochastic firings. The feasibility and usefulness of the new algorithm is illustrated in a case study of a water refinery plant with cascading failures
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