A Characterisation of Deterministic Context-Free Languages by Means of Right-Congruences

We study here a kind of rewriting systems called controlled rewriting systems (c-systems for short) which generalise the notion of regular semi-Thue systems. We show that the deterministic context-free languages are exactly the sets of the form [R]↔⋅s, where R is a rational set and ↔⋅S is the right-congruence generated by a c-system of S of a restricted type (S is basic and confluent).

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