Workflow satisfiability(WS)is an essential claim to access control(AC)policies from the view of resource allocation.So far

the related researches are concentrated on the decision problem of WS

which finds a single solution to show the correctness of an AC policy.However

to further verify its rationality under resource exception

and to count all the solutions will be more useful.In this paper

the counting problem of WS with exclusion and binding constraints is addressed.The problem is proved to be #P complete by constructing a polynomial time counting reduction from the well-known #P complete problem of #3SAT to it

and then gets a theoretical basis to be solved appropriately.