Reachability Analysis of Time Basic Petri Nets: A Time Coverage Approach

Abstract

We introduce a technique for reachability analysis of Time-Basic (TB) Petri nets, a powerful formalism for realtime systems where time constraints are expressed as intervals, representing possible transition firing times, whose bounds are functions of marking's time description. The technique consists of building a symbolic reachability graph relying on a sort of time coverage, and overcomes the limitations of the only available analyzer for TB nets, based in turn on a time-bounded inspection of a (possibly infinite) reachability-tree. The graph construction algorithm has been automated by a tool-set, briefly described in the paper together with its main functionality and analysis capability. A running example is used throughout the paper to sketch the symbolic graph construction. A use case describing a small real system -that the running example is an excerpt from -has been employed to benchmark the technique and the tool-set. The main outcome of this test are also presented in the paper. Ongoing work, in the perspective of integrating with a model-checking engine, is shortly discussed.

Zone-based formal specification and timing analysis of real-time self-adaptive systems

“…The Time Reachability Graph (TRG) [32] is an abstract state-transition system which covers the infinite state space associated with a TB net model. The TRG construction, implemented by the Graphgen software tool [32,33], relies on the symbolic state notion and the symbolic firing mechanism.…”

“…The TRG construction, implemented by the Graphgen software tool [32,33], relies on the symbolic state notion and the symbolic firing mechanism. Let T S = {T i } i≥0 , be the set of time-stamp symbols.…”

“…Thus, they are replaced in the marking by T A symbols (i.e., anonymous time-stamps), then eliminated from the constraint [32,29].…”

“…This tool extends Graphgen [32], in order to support both the specification phase, through a graphic editor, and the verification phase, through the exploration of regions and adaptation sets of the TRG structure. The tool architecture (see Figure 14) includes different interconnected components that communicate by means of proper files.…”

“…The ZAFETY engine has been implemented on top of Graphgen [32], a Java software tool for the reachability analysis of TB nets. In fact, the TRG builder exploits the functionality of the Analysis and the DataLayer modules of Graphgen in order to create the reachable symbolic states of a TB net model.…”