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Language classes associated with automata over matrix groups.

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Title: Language classes associated with automata over matrix groups.
Authors: Bordihn, Henning, Nagy, Benedek, Vaszil, György, Salehi, Özlem1 ozlem.salehi@boun.edu.tr, D'Alessandro, Flavio2,3, Say, A.C. Cem1
Source: RAIRO - Theoretical Informatics & Applications. Apr-Dec2018, Vol. 52 Issue 2-4, p253-268. 16p. 4 Diagrams.
Subjects: Matrix groups, Finite state machines, Complexity (Philosophy), Abelian groups, Combinatorics
Abstract: We investigate the language classes recognized by group automata over matrix groups. For the case of 2 × 2 matrices, we prove that the corresponding group automata for rational matrix groups are more powerful than the corresponding group automata for integer matrix groups. Finite automata over some special matrix groups, such as the discrete Heisenberg group and the Baumslag-Solitar group are also examined. We also introduce the notion of time complexity for group automata and demonstrate some separations among related classes. The case of linear-time bounds is examined in detail throughout our repertory of matrix group automata. [ABSTRACT FROM AUTHOR]
Copyright of RAIRO - Theoretical Informatics & Applications is the property of EDP Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22RAIRO+-+Theoretical+Informatics+%26+Applications%22">RAIRO - Theoretical Informatics & Applications</searchLink>. Apr-Dec2018, Vol. 52 Issue 2-4, p253-268. 16p. 4 Diagrams.
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  Data: <searchLink fieldCode="DE" term="%22Matrix+groups%22">Matrix groups</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+state+machines%22">Finite state machines</searchLink><br /><searchLink fieldCode="DE" term="%22Complexity+%28Philosophy%29%22">Complexity (Philosophy)</searchLink><br /><searchLink fieldCode="DE" term="%22Abelian+groups%22">Abelian groups</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorics%22">Combinatorics</searchLink>
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  Data: We investigate the language classes recognized by group automata over matrix groups. For the case of 2 × 2 matrices, we prove that the corresponding group automata for rational matrix groups are more powerful than the corresponding group automata for integer matrix groups. Finite automata over some special matrix groups, such as the discrete Heisenberg group and the Baumslag-Solitar group are also examined. We also introduce the notion of time complexity for group automata and demonstrate some separations among related classes. The case of linear-time bounds is examined in detail throughout our repertory of matrix group automata. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of RAIRO - Theoretical Informatics & Applications is the property of EDP Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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