TY - GEN A1 - Meer, Klaus A1 - Naif, Ameen T1 - Generalized finite automata over real and complex numbers T2 - Theoretical Computer Science N2 - In a recent work, Gandhi, Khoussainov, and Liu [7] introduced and studied a generalized model of finite automata able to work over arbitrary structures. As one relevant area of research for this model the authors identify studying such automata over particular structures such as real and algebraically closed fields. In this paper we start investigations into this direction. We prove several structural results about sets accepted by such automata, and analyze decidability as well as complexity of several classical questions about automata in the new framework. Our results show quite a diverse picture when compared to the well known results for finite automata over finite alphabets. KW - Generalized finite automata KW - Real and complex number computations KW - Decision problems for automata over uncountable structures Y1 - 2015 UR - http://www.sciencedirect.com/science/article/pii/S0304397515003928 U6 - https://doi.org/10.1016/j.tcs.2015.05.001 SN - 0304-3975 VL - Vol. 591 SP - 85 EP - 98 ER - TY - CHAP A1 - Meer, Klaus A1 - Naif, Ameen ED - Gopal, T. V. ED - Agrawal, Manindra ED - Li, Angsheng ED - Cooper, Stuart Barry T1 - Generalized Finite Automata over Real and Complex Numbers T2 - Theory and Applications of Models of Computation 11th Annual Conference, TAMC 2014, Chennai, India, April 11-13, 2014, Proceedings Y1 - 2014 UR - http://www.springer.com/us/book/9783319060880 SN - 978-3-319-06088-0 U6 - https://doi.org/10.1007/978-3-319-06089-7 SP - 168 EP - 187 PB - Springer International Publishing CY - Berlin [u.a.] ER - TY - CHAP A1 - Meer, Klaus A1 - Naif, Ameen ED - Dediu, Adrian-Horia ED - Janoušek, Jan ED - Martín-Vide, Carlos ED - Truthe, Bianca T1 - Periodic Generalized Automata over the Reals T2 - Language and Automata Theory and Applications 10th International Conference, LATA 2016, Prague, Czech Republic, March 14-18, 2016, Proceedings Y1 - 2016 UR - http://www.springer.com/de/book/9783319299990 SN - 978-3-319-29999-0 U6 - https://doi.org/10.1007/978-3-319-30000-9 SP - 168 EP - 180 PB - Springer International Publishing CY - Berlin [u.a.] ER -