This paper incorporates time constraints in the Horn logic model, and this extended model can verify Wide-Mouthed-Frog protocol
quickly. It discusses relations between the constraint system and Horn model, abstracts the constraint system, and gives the
proofs of some propositions and theorems. We also give the algorithm about how to compute the abstract constraint, and analyze
its complexity. As a case study we discuss the verification of Wide-Mouthed-Frog protocol whose attack can be found quickly
in new model. Therefore, the method in this paper is very effective in verification of time sensitive security protocols.
In the future, we will use this method to verify some complex protocols, such as Kerberos protocol etc.
Keywords time sensitive - security protocol - logic model - formal verification - constraint system
Supported by the National Natural Science Foundation of China under Grant No. 60473057, 90604007, 60703075, 90718017, the
National High Technology Research and Development Program of China No. 2007AA010301, and the Research Fund for the Doctoral
Program of Higher Education No. 20070006055.