A method of generating instructions to be executed by a plurality of execution engines that shares a resource is provided. The method comprises, in a first generation step: reading a first engine logical timestamp vector of a first execution engine of the execution engines, the logical timestamp representing a history of access operations for the resource; determining whether the first engine logical timestamp vector includes a most-up-to-date logical timestamp of the resource in the first generation step; based on the first engine logical timestamp vector including the most-up-to-date logical timestamp of the resource in the first generation step, generating an access instruction to be executed by the first execution engine to access the resource; and scheduling the first execution engine to execute the access instruction.