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 - 2016 UR - https://opus4.kobv.de/opus4-UBICO/frontdoor/index/index/docId/15624 UR - http://www.sciencedirect.com/science/article/pii/S0304397515003928 SN - 0304-3975 VL - Vol. 591 SP - 85 EP - 98 ER -