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Semantic Labelling

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AProVE Help SystemTechniquesTechniques working on SCCsSemantic Labelling

Description

The idea of Semantic Labelling on SCCs is based on the idea of Semantic Labelling on TRSs [Zan '95]. The difference is that instead of proving termination of a string rewrite system R, we want to prove absence of infinite P-chains over R. Let Σ# denote the signature of P minus the signature Σ of R.

If (M, φ) is a quasi-model of P ∪ R for >, then there are no infinite lab(P) ∪ Decr(Σ#,M,>)-chains over lab(R) ∪ Decr(Σ,M,>) if and only if there are no P-chains over R.

The Semantic Labelling in AProVE is used in conjunction with modular removal of rules (MRR), i.e. the quality of a model is assessed by the number of rules, dependency pairs or cycles that could be deleted by labeling P and R using the model, applying MRR and unlabeling the resulting SCCs.

Application and Configuration

You can select whether you want to return the labeled or the unlabeled SCC. Note that returning an unlabeled SCC does make sense, as some rules, dependency pairs or cycles will have been deleted in the process. Normally Semantic Labelling is restricted to string rewriting for efficiency reasons. This can be changed by selecting work on TRSs in addition to SRSs. The user can also define the size of the carrier set M (Model Size) and the range of the polynomials used for MRR in evaluating models (MRR Range).

Semantic Labelling increases the number of function symbols and rules significantly. As thus, it should only be applied when termination of the original term rewrite system R could not be shown using other techniques. As the search space explodes with the arities of functions symbols in R and the number of variables occurring in a rule, Semantic Labelling should normally only be applied to string rewrite systems or systems which are almost string rewrite systems.