Abstract
Time Petri nets (TPN for short) are established as a powerful formalism for modeling and verifying systems with explicit soft and hard time constraints. However, their verification techniques run against the state explosion problem that is accentuated by the fact that the diamond property is difficult to meet, even for conflict-free transitions.
To deal with this limitation, the partial order reduction (POR) techniques of Petri nets (PN for short) are used in combination with the partially ordered sets (POSETs). Nevertheless, POSETs introduce extra selection conditions that may offset the benefits of the POR techniques.
This paper establishes a subclass of TPN for which the POR techniques of PN can be used without resorting to POSETs.
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Notes
- 1.
All and only all markings and firing sequences of the TPN are represented in the state space abstraction.
- 2.
A maximal firing sequence is either an infinite firable sequence or a finite firable sequence leading to a deadlock state.
- 3.
Two sequences of transitions \(\omega \) and \(\omega '\) are equivalent, denoted by \(\omega \equiv \omega '\) iff they are identical or each one can be obtained from the other by a series of permutations of transitions.
- 4.
\(LTL_{\{-X\}}\) is the classical linear temporal logic without the next-state operator X.
- 5.
The effect of a transition is the set of transitions disabled plus those newly enabled by its firing.
- 6.
All possible firing orders of the firable instances of the same transition are considered.
- 7.
A triangular atomic constraint is of the form \(x-y\prec c\), where x, y are real valued variables, c is a rational constant and \(\prec \in \{<,>,\le , \ge , =\}\).
- 8.
The effect of a transition t is the set of transitions disabled plus those newly enabled by firing t.
- 9.
A selective search w.r.t. D0, D1w and \(D2'\), from the initial state class of \(\mathcal {N}\), is a partial state space exploration, where the set of transitions selected to be fired, from the initial state class and each computed state class, satisfies D0, D1w and \(D2'\).
- 10.
A free-choice TPN is a safe TPN such that \(\forall t\in T, \forall t' \in CFS(t), pre(t) = pre(t') \wedge {\uparrow Is(t)}= {\uparrow Is(t')}\).
- 11.
A weighted comparable preset TPN is a safe TPN such that \(\forall t\in T, \forall t_j \in CFS(t_i), pre(t_i) \le pre(t_j) \vee pre(t_j) \le pre(t_i))\).
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Wang, K., Boucheneb, H., Barkaoui, K., Li, Z. (2020). Towards Efficient Partial Order Techniques for Time Petri Nets. In: Ben Hedia, B., Chen, YF., Liu, G., Yu, Z. (eds) Verification and Evaluation of Computer and Communication Systems. VECoS 2020. Lecture Notes in Computer Science(), vol 12519. Springer, Cham. https://doi.org/10.1007/978-3-030-65955-4_8
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