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pro vyhledávání: '"Rauzy, Emmanuel"'
To any family of languages LAN, let us associate the class, denoted $\pi(\text{LAN})$, of finitely generated groups that admit a group presentation whose set of relators forms a language in LAN. We show that the class of L-presented groups, as introd
Externí odkaz:
http://arxiv.org/abs/2402.01601
Autor:
Rauzy, Emmanuel
We revisit Dieter Spreen's notion of a representation associated to a numbered basis equipped with a strong inclusion relation. We show that by relaxing his requirements, we obtain different classically considered representations as subcases, includi
Externí odkaz:
http://arxiv.org/abs/2311.15861
Autor:
Rauzy, Emmanuel
In 1957, Lacombe initiated a systematic study of the different possible notions of "computable topological spaces". However, he interrupted this line of research, settling for the idea that "computably open sets should be computable unions of basic o
Externí odkaz:
http://arxiv.org/abs/2311.16340
Autor:
Rauzy, Emmanuel
Motivated by a theorem of Groves and Wilton, we propose the study of the lattice of numberings of isomorphism classes of marked groups as a rigorous and comprehensive framework to study global decision problems for finitely generated groups. We estab
Externí odkaz:
http://arxiv.org/abs/2111.01190
Autor:
Rauzy, Emmanuel
We investigate decision problems for finitely generated groups described by word problem algorithms. This is equivalent to studying groups described by computable labelled Cayley graphs. We relate these problems to the study of computable analysis on
Externí odkaz:
http://arxiv.org/abs/2111.01179
Autor:
Rauzy, Emmanuel
We prove that, for a finitely generated residually finite group, having solvable word problem is not a sufficient condition to be a subgroup of a finitely presented residually finite group. The obstruction is given by a residually finite group with s
Externí odkaz:
http://arxiv.org/abs/2002.02540
Autor:
Rauzy, Emmanuel
We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth function and solv
Externí odkaz:
http://arxiv.org/abs/2002.02541
Autor:
Rauzy, Emmanuel
We make the case that the so called "global decision problems" should not be investigated solely for groups described by finite presentations. We propose to use descriptions that be algorithms that perform some given tasks, and that encode the consid
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2842e42d06f20895777f889736952ae4
https://hal.archives-ouvertes.fr/hal-03410992/document
https://hal.archives-ouvertes.fr/hal-03410992/document
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