A graph-based program specification specifies at least a partial ordering among a plurality of tasks represented by its nodes. Executing a specified program includes: executing a first subroutine corresponding to a first task, including a first task section for performing the first task; storing state information indicating a state of the first task selected from a set of possible states that includes: a pending state in which the first task section is waiting to perform the first task, and a suppressed state in which the first task section has been prevented from performing the first task; and executing a second subroutine corresponding to a second task, including a second task section for performing the second task, and a control section that controls execution of the second task section based at least in part on the state of the first task indicated by the stored state information.