Partial Order Reduction for Detecting Safety and Timing Failures of Timed Circuits

A more efficient time Petri net state space abstraction preserving linear properties

“…The test of condition (F implies t < t ) (step 6.3) is done in O(1) as follows D t t < 0. Recall that: The correctness and the completeness of this partial order are shown in [12,14] for one-safe and non zeno time Petri nets with no unbounded intervals. The non zenoness assumption guarantees that each enabled transition will eventually become firable unless it is disabled by another firing.…”

“…Several approaches have been developed that apply partial order reduction to model checking systems: the persistent set method [8], the ample set method [9], the stubborn set method [13], and the ready set method [11,12]. The common characteristic of all these methods is that they explore only a certain subset of execution paths from each state (state class).…”

“…Partial order reduction techniques take advantage of this by generating and exploring a graph with only a reduced set of firing sequences. At the same time, in order to preserve the truth value of the property to be verified, the reduced graph should contain, at least, one representative firing sequence from each class of equivalent firing sequences [5,6,8,9,10,11,12,13]. This paper proposes an efficient abstraction for time Petri nets which is both smaller and faster to compute than those proposed in the literature.…”

“…Many techniques have been developed to alleviate this problem. Among these techniques, we consider here the abstraction [1,2,3,4,7,10,11] and partial order techniques [5,6,8,9,11,12,13,14].…”