Finiteness results on rewriting systems
نویسندگان
چکیده
منابع مشابه
A Polygraphic Survey on Finiteness Conditions for Rewriting Systems
In 1987, Craig Squier proved that, if a monoid can be presented by a finite convergent string rewriting system, then it satisfies the homological finiteness condition left-FP3. Using this result, he has constructed finitely presented decidable monoids that cannot be presented by finite convergent rewriting systems. In 1994, Squier introduced the condition of finite derivation type, which is a h...
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String rewriting systems, also known as semi-Thue systems, consist of a set of rules l → r, specifying valid replacements of substrings of strings over a given alphabet. In the case of one single rule, it is an open problem whether there is a system that is neither terminating nor looping. Another open question is the decidability of termination. Difficulties arise especially for non-confluent ...
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Recently, Craig Squier introduced the notion of finite derivation type to show that some finitely presentable monoid has no presentation by means of a finite complete rewriting system. A similar result was already obtained by the same author using homology, but the new method is more direct and more powerful. Here, we present Squier’s argument with a bit of categorical machinery, making proofs ...
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Let R = ⊕ n∈N0 Rn be a Noetherian homogeneous ring with local base ring (R0,m0) and irrelevant ideal R+, let M be a finitely generated graded R− module. In this paper we show that if R0 is a local ring of dimension one, then H i R+(H 1 m0R (M)) is Artinian for each i ∈ N0. Let f be the least integer such that H i m0R(M) is not finitely generated graded R−module. In this case, we prove that ΓR+(...
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ژورنال
عنوان ژورنال: RAIRO. Informatique théorique
سال: 1981
ISSN: 0399-0540
DOI: 10.1051/ita/1981150403731