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A web service is a software system that provides interaction between a service provider and its users. When developing web services, it is important to consider its security, one aspect of which is the absence of livelocks and deadlocks between its components. In this paper we consider the problem of synthesizing a safety web service server application that must interact with various client applications without livelocks.
It is assumed that the behavior of the web service and its known components is described by complete finite state machines (FSMs); the interaction of the web service components is described using the parallel composition operation. Thus, the problem of synthesizing a server application is reduced to solving the corresponding system of parallel FSM equations (inequalities), for which complete progressive solutions are of interest, since the use of such solutions for the synthesis of a server application guarantees the absence of livelocks and deadlocks in the work of a web service.
As is known, the largest (general) solution of a solvable system of equations is the intersection of the largest solutions of all equations of a system. The complexity of deriving the largest progressive solution is higher than the complexity of deriving the «usual» largest solution. In this regard, the problem of the possibility of reducing the solution of a system of FSM equations to the solution of a single equation is of interest. It is shown that, similarly to the case of finding the largest solution of the system, such a reduction is possible for two special cases when it is necessary to synthesize a safety server application that can: 1) work with different client applications and provide the same level of service, and in this case, the corresponding system of FSM equations is considered; 2) or work with one client application and provide different levels of service, and in this case, the corresponding system of FSM inequalities is considered.
Keywords:Web service, web service safety, finite state machine, parallel composition of finite state machines, finite state machine equation, system of finite state machine equations, progressive solution
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