An Introduction to Signed Petri Net

In this paper, the notion of a signed graph and Petri net (PN) is combined to introduce a new concept of Signed Petri net (SiPN). The balancedness in the signed graph, formulated by Harary and Cartwright, can be used to study and analyze social networks. This notion of balancedness is extended to Petri net via SiPN as such a concept has not been defined for already existing Petri nets. A balanced SiPN has been defined and its characterization is given. An illustrative example is provided which utilizes the newly introduced concept of assignment of sign to places of SiPN to determine whether an online transaction initiated by a bank customer is denied or approved by the bank. Lastly, applications of SiPN in the message transmission system and production unit are discussed. These concepts clearly demonstrate the advantages of the proposed approach of SiPN.