We consider the time Petri nets (an extension of Petri nets), where every transition has its time interval. The policies of time-elapsing and the memory policies define different semantics for time Petri nets. The decidability of many standard problems with an infinite discrete structure depends on the choice of semantics. The state space of the time Petri nets is infinite and non-discrete. It is known that there is a reduction of the state space to discrete one for the time Petri nets with strong semantics. In this paper, we prove that a state space reduction can be applied to weak time Petri nets equipped with intermediate and atomic memory policies.