An ACCL which is not a CRCL
Colm \'O D\'unlaing
TL;DR
This paper demonstrates the existence of an almost-confluent congruential language (ACCL) that is not a Church-Rosser congruential language (CRCL), addressing an open question in formal language theory.
Contribution
It provides the first known example of an ACCL that is not a CRCL, advancing understanding of language classifications.
Findings
Established the existence of an ACCL not equivalent to any CRCL
Clarified the relationship between ACCL and CRCL classes
Contributed to the theoretical foundations of formal language classification
Abstract
It is fairly easy to show that every regular set is an almost-confluent congruential language (ACCL), and it is known that every regular set is a Church-Rosser congruential language (CRCL). Whether there exists an ACCL, which is not a CRCL, seems to remain an open question. In this note we present one such ACCL.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Natural Language Processing Techniques