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A duality theoretic perspective on recognisable languages
Thesis (MSc)--Stellenbosch University, 2019.
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| Other Authors: | |
| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2019
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| _version_ | 1867613966776139776 |
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| access_status_str | Open Access |
| author | Rozanova, Julia |
| author2 | Rewitzky, I. M. |
| author_browse | Rewitzky, I. M. Rozanova, Julia |
| author_facet | Rewitzky, I. M. Rozanova, Julia |
| author_sort | Rozanova, Julia |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2019. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/105807 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:44:33.029Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2019 |
| publishDateRange | 2019 |
| publishDateSort | 2019 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/105807 A duality theoretic perspective on recognisable languages Rozanova, Julia Rewitzky, I. M. Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Mathematics. Boolean algebras Formal language theory Duality theory (Mathematics) Lattices Stone duality (Mathematics) UCTD Thesis (MSc)--Stellenbosch University, 2019. ENGLISH ABSTRACT : A connection between recognisable languages and profinite identities is established through the composition of two famous theorems: Eilenberg’s theorem and Reiterman’s theorem. In this work, we present a detailed account of the duality-theoretic approach by Gehrke et al. that has been shown to bridge the gap and demonstrate that Eilenberg’s varieties and profinite theories are directly linked: they are at opposite ends of an extended Stone-type duality, instantiating a Galois correspondence between subobjects and quotients and resulting in an equational theory of recognisable languages. We give an indepth overview of relevant components of algebraic language theory and the profinite equational theory of pseudovarieties in order to show how they are tied together by the duality-theoretic developments. Furthermore, we provide independent proofs of the key Galois connections at the heart of these bridging results. AFRIKAANSE OPSOMMING : Geen Afrikaanse opsomming geskikbaar nie 2019-02-18T09:50:19Z 2019-04-17T08:13:42Z 2019-02-18T09:50:19Z 2019-04-17T08:13:42Z 2019-04 Thesis http://hdl.handle.net/10019.1/105807 en_ZA Stellenbosch University vii, 78 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Boolean algebras Formal language theory Duality theory (Mathematics) Lattices Stone duality (Mathematics) UCTD Rozanova, Julia A duality theoretic perspective on recognisable languages |
| title | A duality theoretic perspective on recognisable languages |
| title_full | A duality theoretic perspective on recognisable languages |
| title_fullStr | A duality theoretic perspective on recognisable languages |
| title_full_unstemmed | A duality theoretic perspective on recognisable languages |
| title_short | A duality theoretic perspective on recognisable languages |
| title_sort | duality theoretic perspective on recognisable languages |
| topic | Boolean algebras Formal language theory Duality theory (Mathematics) Lattices Stone duality (Mathematics) UCTD |
| url | http://hdl.handle.net/10019.1/105807 |
| work_keys_str_mv | AT rozanovajulia adualitytheoreticperspectiveonrecognisablelanguages AT rozanovajulia dualitytheoreticperspectiveonrecognisablelanguages |