Abstract
Extended colored logic Petri nets (ECLPNs) are extensions of logic Petri nets (LPNs) and colored logic Petri nets (CLPNs). They are equivalent to LPNs and CLPNs, which can describe the batch processing and indeterminacy functions of resources in cooperative systems. The advantage of ECLPNs is that their net structures are much simpler than their equivalent CLPNs, and therefore, ECLPNs can be easily used to model and analyze cooperative systems. For systems containing several subsystems with the same function and structure, we can describe them by a single ECLPN. Then we propose a composition method of ECLPNs. We define the robustness of a system based on ECLPN which reflects the validity of the collaboration of subsystems. We define a strict conservativeness that guarantees data security. The robustness and strict conservativeness of composed ECLPNs are analyzed. An E-commerce example is presented to illustrate the modeling capacity and the advantage of ECLPNs.
Highlights
E-commerce systems are becoming more and more complicated, and their compatibility analysis is a co-NP-hardness problem [1]
Definition 3 [11]: A Logic Petri Net is described as a sixtuple logic Petri nets (LPNs) = (P, T, F, I, O, M ), where P is a finite set of places; T = TD ∪ TI ∪ TO is a finite set of transitions; F is a set of directed arcs; I is a mapping function such that ∀t ∈ TI, I (t) is a logical input expression denoted by fI ; O is a mapping function such that ∀t ∈ TO, O(t) is a logical output expression denoted by fO; and M is a marking function, which defines the number of tokens in each place
In this paper, we give the method of the composition of Extended colored logic Petri nets (ECLPNs) and analyze its properties
Summary
E-commerce systems are becoming more and more complicated, and their compatibility analysis is a co-NP-hardness problem [1]. PNs with inhibitor arcs [10] cannot describe batch processing functions and passing value indeterminacy as clearly and concisely as logic Petri nets (LPNs) [11] do. An LPN can describe passing value indeterminacy in cooperative systems Z. Wang et al.: Composition and Application of ECLPNs to E-Commerce Systems transition, they control which place tokens should flow into after the transition has fired. Colored logic Petri nets (CLPNs) proposed in [27] guarantee that output logic transitions can correctly output tokens by checking their colors and logical expressions. We propose a composition method of ECLPNs to model E-commerce systems in this paper.
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