Comparison With Abstract Rewriting Systems
As a mathematical object, an unlabeled state transition system is identical with an (unindexed) abstract rewriting system. If we consider the rewriting relation as an indexed set of relations, as some authors do, then a labeled state transition system is equivalent with an abstract rewriting system with the indices being the labels. The focus of the study and the terminology are different however. In a state transition system one is interested in interpreting the labels as actions, whereas in an abstract rewriting system the focus is on how objects may be transformed (rewritten) into others.
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