RAIRO-Theor. Inf. Appl.
Volume 52, Number 2-3-4, April–December 2018
8th Workshop on Non-classical Models of Automata and Applications (NCMA 2016)
|Page(s)||253 - 268|
|Published online||24 January 2019|
Language classes associated with automata over matrix groups★,★★,★★★
Department of Computer Engineering, Boğaziçi University,
2 Department of Mathematics, Boğaziçi University, Bebek 34342, İstanbul, Turkey.
3 Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185 Roma, Italy.
* Corresponding author: email@example.com
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.
Mathematics Subject Classification: 68Q45 / 68Q05
Key words: Group automata / time complexity
This work was supported by Boğaziçi University Research Fund under grant number 11760. A preliminary version of this work was presented at the 8th Workshop on Non-Classical Models of Automata and Applications (NCMA), Debrecen, Hungary, August 29–30, 2016.
Özlem Salehi was partially supported by TÜBİTAK (Scientific and Technological Research Council of Turkey).
© EDP Sciences, 2019
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