Dynamic Slicing of Time Petri Net Based on MTL Property

Abstract

The time Petri net (TPN) is a powerful tool for modeling, simulating, and verifying real-time systems. Unfortunately, the state spaces of the time Petri net grow exponentially due to the complexity of real-time systems. The enormous size of the state spaces could also cause state explosion problems in model checking. This paper proposes an alternative dynamic slicing algorithm written as a metric temporal logic (MTL) formula to reduce the size of the time Petri net model by considering specific criteria. Our algorithm proposes an alternative dependency graph representing the global firing time interval of the transition to remove the transitions that are never fired and do not affect the state space. The dynamic slicing algorithm involves the initial marking and the properties of the target metric temporal logic formula. Unlike the unsliced time Petri net, the result preserves all necessary execution paths for the model checking of a particular metric temporal logic formula. Therefore, model checking can generate sufficient state space to conduct verification equivalent to the unsliced time Petri net but may take less time, including if the unsliced time Petri net causes state space explosion.

Symbolic Observation Graph-Based Generation of Test Paths

“…The entry points stack holds three couples, where (a 2 , {s 16 , s 17 , s 20 }) is on the top. After removing the pair from the stack, lines (10)(11) isolate the set of entry points and the aggregate. The former is stored in the target variable, and the latter in the agr variable.…”

“…Test inputs generation satisfying structural or behaviour coverage criteria suffers from the well known state space explosion problem [41]. Several approaches have offered solutions to cope with this problem such as symmetry reduction [17], live variable reduction [18], cone of influence [13], slicing [11], transition merging [50], partial order reduction [42], τ -confluence [33], and simultaneous reachability analysis [44]. Symbolic Observation Graph (SOG) [20,25] represents an efficient technique to reduce the state space graph based on the observation of the pertinent atomic propositions of a temporal formula to be verified.…”