Raimundo Barreto,  Marília Neves,  Eduardo Tavares,  Paulo Maciel. 

Finding a hard real-time feasible schedule is not trivial since this problem is NP-hard in its general form. There are two general approaches for scheduling tasks: runtime and pre-runtime scheduling. For many cases, runtime methods do not find a feasible schedule even if such a schedule exists. Such situations often occurs when the design model imposes intertask relations, such as precedence and exclusion relations. The method proposed in this work finds a pre-runtime scheduling, provided that one exists, using state space exploration. The main problem with such methods is the space size, which can grow exponentially. This paper applies minimization methods on the state space, and presents a depth-first search method on a timed labeled transition system derived from the time Petri net model. This model is a compact and precise representation of tasks, their relations and constraints.

http://www.lbd.dcc.ufmg.br/colecoes/wso/2004/010.pdf

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