2021
DOI: 10.48550/arxiv.2112.10665
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On the Word Problem for Free Products of Semigroups and Monoids

Abstract: We study the language-theoretic aspects of the word problem, in the sense of Duncan & Gilman, of free products of semigroups and monoids. First, we provide algebraic tools for studying classes of languages known as super-AFLs, which generalise e.g. the context-free or the indexed languages. When C is a super-AFL closed under reversal, we prove that the semigroup (monoid) free product of two semigroups (resp. monoids) with word problem in C also has word problem in C. This recovers and generalises a recent resu… Show more

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Cited by 3 publications
(11 citation statements)
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“…Similarly general statements involving reversal-closed super-AFLs appear as the main results in previous work by the author[95,96,97].…”
supporting
confidence: 79%
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“…Similarly general statements involving reversal-closed super-AFLs appear as the main results in previous work by the author[95,96,97].…”
supporting
confidence: 79%
“…The terminology monadic ancestor property was introduced by the author in [96], and also appears in [95,97], but was treated implicitly already in [22,76], see especially [76,Lemma 3.4]. The idea of defining classes of languages via ancestry in rewriting systems is not new, and can be traced back at least to e.g.…”
Section: Rewriting Systemsmentioning
confidence: 99%
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“…We refer the reader to Nyberg-Brodda [61] for a full (rather straightforward) proof. Thus we have a combinatorial characterisation of super-AFLs in terms of rewriting systems.…”
Section: Proposition 11 Let C Be a Full Afl Then C Is A Super-afl If ...mentioning
confidence: 99%