Abstract
The transition set semantics (Wang and Jiao, LNCS 6128:84–103, 2010) partitions the Petri net behaviors in a canonical way such that behaviors in an equivalence class have the same canonical transition set sequence. This article extends the semantics in two ways: firstly, the semantics is parameterized by the basic relation on the structural transitions to define different variants; secondly, the semantics for the infinite firing sequences of the net is defined. We prove that these extensions still preserve the well-definedness, soundness and completeness of the semantics. Furthermore, we show how to recognize some infinite sequences called back-loops in the view of this new semantics.
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