Abstract
In this paper, we present a method for state space reduction of dense-time Petri nets (TPNs) – an extension of Petri nets by adding a time interval to every transition for its firing. The time elapsing and memory operating policies define different semantics for TPNs. The decidability of many standard problems in the context of TPNs depends on the choice of their semantics. The state space of the TPN is infinite and non-discrete, in general, and, therefore, the analysis of its behavior is rather complicated. To cope with the problem, we elaborate a state space discretization technique and develop a partial order semantics for TPNs equipped with weak time elapsing and intermediate memory policies.
Highlights
Dense-Time Petri Nets (TPNs) are a well-established model to describe and study safety-critical systems that often require verification of real time characteristics, in addition to functional properties
It was shown that the marking reachability/coverability and boundedness problems are undecidable for time Petri nets with strong semantics and any memory policy, whereas the problems are decidable in the case of TPNs with weak intermediate semantics but not with weak atomic semantics
In the work [4], a transformation to the behavior with only integer time elapsings has been suggested for TPNs with strong semantics, while the discretization of the state space for weak semantics has hitherto not be treated in the literature, to the best of our knowledge
Summary
Dense-Time Petri Nets (TPNs) are a well-established model to describe and study safety-critical systems that often require verification of real time (quantitative) characteristics, in addition to functional (qualitative) properties. The presented in [6] approach to construct a partial order and non-deterministic representation of the behavior of safe TPNs with strong and clocks-on-tokens semantics consists in transforming time characteristics into net structure, i.e. representing them by additional places, transitions, and arcs. This allows for removing the restrictions of diverging time and of finite upper time bounds for transitions.
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