Component-Level Reduction Rules for Time Petri Nets with Application in C2 Systems 1 Jiacun Wang and Yi Deng School of Computer Science Florida International University Miami, FL33199 {wangji, deng}@cs.fiu.edu ABSTRACT In this paper, we propose a set of component-level reduction rules for TPN’s. Each of these reduction rules transforms a TPN component to a constant size of simple one while maintains the net’s external observable timing properties. Consequently, our method works at a coarser level than that works in individual transition level, and fewer applications of our rules are needed to reduce the size of the TPN under analysis. We illustrate the use and benefits of our reduction rules by modeling and analyzing the response time of a command and control system to its external arriving messages. 1. INTRODUCTION Time Petri nets (TPN’s) have been used for the modeling and verification of various time dependent systems [1,2,3,6,7,9]. The analysis of a TPN is normally based on the enumerative technique developed by Berthomieu et al. [1,2]. For a complex or even middle-sized TPN, however, it is difficult to enumerate its reachable states, which is commonly referred as state- explosion problem. Sloan et al. developed several reduction rules for TPN analysis, which work at individual transition level [8]. These reduction rules help to reduce the complexity of TPN analysis to some extent. However, it is not a trivial work to automatically search the preconditions of applying these reduction rules for a complex TPN. In this paper, we propose a set of component-level reduction rules for TPN’s (a component is a coarse grained subnet of a TPN). Each of our reduction rules transforms a TPN component to a constant size of simple one while maintains the net’s external observable timing properties. Consequently, our method works at a much coarser level than those developed by Sloan et al., and fewer applications of our rules are needed to reduce the size of the TPN under analysis. The rest of the paper is arranged as follows: Section 2 informally introduces the concept of compositional TPN models, Section 3 proposes a set of component-level reduction _____________________ 1. This work was supported in part by the NSF under Grant No. HDR- 9707076, by Air Force Office of Scientific Research under Grant No. F49620-96-1-0221, and by NASA under Grand No. NAGW-4080. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official polices or endorsements either expressed or implied by the above named Agencies rules, Section 4 addresses the analysis method for compositional TPN models, and Section 5 illustrates the use and benefits of our reduction rules by modeling and analyzing the response time of a command and control system to its external arriving message. 2. OVERVIEW OF COMPOSITIONAL TIME PETRI NETS The building blocks of a compositional TPN are components [6]. A component is a coarse grained subnet of a TPN. A compositional TPN model consists of two basic elements: component TPN models and inter-component connections (connections in brief). The component TPN models describe the real-time behavior and communication interface of the components; the connections specify how the components interact with each other and, in turn, form a composition model. All connections are defined using only communication interfaces, which gives us the flexibility to change the design of individual components without a need to void the analysis of the entire system. Figure 1 shows an example of a compositional TPN model. The model has three components – A, B, and C. Each component model has two parts: (1) communication ports (denoted graphically by half circles), including input ports (e.g., port6) and output ports (e.g., port7), and (2) a TPN that describes the time-dependent, operational behavior of the component, that is, it defines the semantics associated with the ports. The communication between a component and its environment is solely through the ports. A connection represents a channel of interaction between components. It is modeled by a simple TPN and defines the direction of message flow and delay in the channel. For example, components A and B have a request-reply relationship that is modeled by the bi-directional channel. The A B C Figure 1. Framework of compositional TPN model.