On Monoids Presented by Rewriting Systems and Automatic Structures for Their Submonoids
نویسندگان
چکیده
Generalizing results of Otto & Ruškuc, this paper shows that every finitely generated submonoid of a monoid presented by a confluent finite special rewriting system admits an automatic structure that is simultaneously rr-, `r-, r`-, and ``-automatic; and that every finitely generated submonoid of a monoid presented by a confluent regular monadic rewriting system admits an automatic structure that is simultaneously rrand ``-automatic. An algorithm is given to decide whether the monoid presented by a confluent monadic finite rewriting system is `ror r`-automatic. Should such a monoid be `ror r`-automatic, the rewriting system’s language of normal form words forms part of such an automatic structure. These results are applied to yield answers to some hitherto open questions and to recover and generalize established results.
منابع مشابه
Monoids Presented by Rewriting Systems and Automatic Structures for their Submonoids
This paper studies rr-, lr-, rl-, and ll-automatic structures for finitely generated submonoids of monoids presented by confluent rewriting system that are either finite and special or regular andmonadic. A new technique is developed that uses an automaton to ‘translate’ betweenwords in the original rewriting system andwords over the generators for the submonoid. This is applied to show that th...
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