Abstract
Let Σ1 be a subalphabet of Σ2. and let R1 and R2 be finite string-rewriting systems on Σ1 and Σ2, respectively. If the congruence \(\overset * \longleftrightarrow\)R1 and the congruence \(\overset * \longleftrightarrow\)R2 generated by R2 coincide on Σ1*, then R1 can be seen as representing the restriction of the system R2 to the subalphabet Σ1. Is this property decidable ? This question is investigated for several classes of finite canonical string-rewriting systems.
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