Some results on confluence: decision and what to do without

Florent Jacquemard 1, 2
1 Repmus - Représentations musicales
STMS - Sciences et Technologies de la Musique et du Son
2 MuTant - Synchronous Realtime Processing and Programming of Music Signals
UPMC - Université Pierre et Marie Curie - Paris 6, IRCAM, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : We recall first some decidability results on the confluence of TRS, and related properties about unicity of normal forms. In particular we put it in perspective old proofs of undecidability of confluence for the class of flat systems with more recent results, in order to discuss the importance of linearity wrt these decision problems. Second, we describe a case study on musical rhythm notation involving modeling rewrite systems which are not confluent. In this case, instead of applying rewrite rules directly, we enumerate the equivalence class of a given term using automata-based representations and dynamic programming.
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Florent Jacquemard. Some results on confluence: decision and what to do without. 5th International Workshop on Confluence, Beniamino Accattoli, Ashish Tiwari Sep 2016, Obergurgl, Austria. ⟨hal-01367535⟩

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