Publication: Verificación de extensiones de Redes de Petri con precios, tiempo y múltiples instancias
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2016-07-01
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Universidad Complutense de Madrid
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Abstract
Las redes de Petri son un lenguaje formal muy adecuado para la modelizacíon, ańalisis y verificacíon de sistemas concurrentes con infinitos estados. En particular, son muy apropiadas para estudiar las propiedades de seguridad de dichos sistemas, dadas sus buenas propiedades de decidibilidad. Sin embargo, en muchas ocasiones las redes de Petri carecen de la expresividad necesaria para representar algunas caracteŕısticas fundamentales de los sistemas que se manejan hoy en d́ıa, como el manejo de tiempo real, costes reales, o la presencia de varios procesos con un ńumero no acotado de estados ejecut́andose en paralelo. En la literatura se han definido y estudiado algunas extensiones de las redes de Petri para la representaci ́on de las caracteŕısticas anteriores. Por ejemplo, las “Redes de Petri Temporizadas” [83, 10](TPN) incluyen el manejo de tiempo real y las ν-redes de Petri [78](ν-PN) son capaces de representar un ńumero no acotado de procesos con infinitos estados ejecut́andose concurrentemente. En esta tesis definimos varias extensiones que réunen estas dos caracteŕısticas y estudiamos sus propiedades de decidibilidad. En primer lugar definimos las “ν-Redes de Petri Temporizadas”, que réunen las caracteŕısticas expresivas de las TPN y las ν-PN. Este nuevo modelo es capaz de representar sistemas con un ńumero no acotado de procesos o instancias, donde cada proceso es representado por un nombre diferente, y tiene un ńumero no acotado de relojes reales. En este modelo un reloj de una instancia debe satisfacer ciertas condiciones (pertenecer a un intervalo dado) para formar parte en el disparo de una transicíon. Desafortunadamente, demostramos que la verificacíon de propiedades de seguridad es indecidible para este modelo...
The model of Petri nets is a formal modeling language which is very suitable for the analysis and verification of infinite-state concurrent systems. In particular, due to its good decidability properties, it is very appropriate to study safety properties over such systems. However, Petri nets frequently lack the expressiveness to represent several essential characteristics of nowadays systems such as real time, real costs, or the managing of several parallel processes, each with an unbounded number of states. Several extensions of Petri nets have been defined and studied in the literature to fix these shortcomings. For example, Timed Petri nets [83, 10] deal with real time and ν-Petri nets [78] are able to represent an unbounded number of different infinite-state processes running concurrently. In this thesis we define new extensions which encompass these two characteristics, and study their decidability properties. First, we define Timed ν-Petri nets by joining together Timed Petri nets and ν-Petri nets. The new model represents systems in which each process (also called instance) is represented by a different pure name, and it is endowed with an unbounded number of clocks. Then, a clock of an instance must satisfy certain given conditions (belonging to a given interval) in order to take part in the firing of a transition. Unfortunately, we prove that the verification of safety properties is undecidable for this model. In fact, it is undecidable even if we only consider two clocks per process. We restrict this model and define Locally-Synchronous ν-Petri nets by considering only one clock per instance, and successfully prove the decidability of safety properties for this model. Moreover, we study the expressiveness of Locally-Synchronous ν-Petri nets and prove that it is the most expressive non Turing-complete extension of Petri nets with respect to the languages they accept...
The model of Petri nets is a formal modeling language which is very suitable for the analysis and verification of infinite-state concurrent systems. In particular, due to its good decidability properties, it is very appropriate to study safety properties over such systems. However, Petri nets frequently lack the expressiveness to represent several essential characteristics of nowadays systems such as real time, real costs, or the managing of several parallel processes, each with an unbounded number of states. Several extensions of Petri nets have been defined and studied in the literature to fix these shortcomings. For example, Timed Petri nets [83, 10] deal with real time and ν-Petri nets [78] are able to represent an unbounded number of different infinite-state processes running concurrently. In this thesis we define new extensions which encompass these two characteristics, and study their decidability properties. First, we define Timed ν-Petri nets by joining together Timed Petri nets and ν-Petri nets. The new model represents systems in which each process (also called instance) is represented by a different pure name, and it is endowed with an unbounded number of clocks. Then, a clock of an instance must satisfy certain given conditions (belonging to a given interval) in order to take part in the firing of a transition. Unfortunately, we prove that the verification of safety properties is undecidable for this model. In fact, it is undecidable even if we only consider two clocks per process. We restrict this model and define Locally-Synchronous ν-Petri nets by considering only one clock per instance, and successfully prove the decidability of safety properties for this model. Moreover, we study the expressiveness of Locally-Synchronous ν-Petri nets and prove that it is the most expressive non Turing-complete extension of Petri nets with respect to the languages they accept...
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Tesis inédita de la Universidad Complutense de Madrid, Facultad de Informática, Departamento de Sistemas Informáticos y Computación, leída el 25-01-2016