Petri net language is a powerful tool for describing dynamic behaviors of physical systems. However, it is not easy to obtain the language expression for a given Petri net especially a structure-complex net. In this p...Petri net language is a powerful tool for describing dynamic behaviors of physical systems. However, it is not easy to obtain the language expression for a given Petri net especially a structure-complex net. In this paper, we first analyze the behaviors of S-nets, which are structure-simple. With the decomposition method based on a given index function on the place set, a given structure-complex Petri net can be decomposed into a set of structure-simple S-nets. With the language relationships between the original system and the decomposed subnets, an algorithm to obtain the language expression of a given structure-complex net system is presented, which benefits the analysis of physical systems based on the Petri net language.展开更多
Cyber nets are also known as self modifying nets. Though proposed anddefined some 20 years ago, they have never been under thorough study eversince. The reason for this is simple: the nonlinear nature of such nets kee...Cyber nets are also known as self modifying nets. Though proposed anddefined some 20 years ago, they have never been under thorough study eversince. The reason for this is simple: the nonlinear nature of such nets keeps themaway from applications of well developed methods known to the whole Petri NetSociety in the world. This paper attempts to make a start of studying cybernets in depth by proposing a way to define and to verify S-invariants and T-invariants in such nets. These invariants reflect important dynamic propertiesof cyber nets. Invariants in cyber nets play a role similar to loop invariantsproposed and studied by E.W. Dijkstra and D. Gries when cyber nets are usedfor program specification.展开更多
基金This work was supported by the National Natural Science Foundation of China(No.60173053&No.60274063)the Excellent Young Scientist Foundation of Shandong Province of China(No.02BS069).
文摘Petri net language is a powerful tool for describing dynamic behaviors of physical systems. However, it is not easy to obtain the language expression for a given Petri net especially a structure-complex net. In this paper, we first analyze the behaviors of S-nets, which are structure-simple. With the decomposition method based on a given index function on the place set, a given structure-complex Petri net can be decomposed into a set of structure-simple S-nets. With the language relationships between the original system and the decomposed subnets, an algorithm to obtain the language expression of a given structure-complex net system is presented, which benefits the analysis of physical systems based on the Petri net language.
文摘Cyber nets are also known as self modifying nets. Though proposed anddefined some 20 years ago, they have never been under thorough study eversince. The reason for this is simple: the nonlinear nature of such nets keeps themaway from applications of well developed methods known to the whole Petri NetSociety in the world. This paper attempts to make a start of studying cybernets in depth by proposing a way to define and to verify S-invariants and T-invariants in such nets. These invariants reflect important dynamic propertiesof cyber nets. Invariants in cyber nets play a role similar to loop invariantsproposed and studied by E.W. Dijkstra and D. Gries when cyber nets are usedfor program specification.
