TRANSFINITE EQUATIONS IN TRANSFINITE STRINGS
Christian Choffrut, SÁNDOR HORVÁTH · International Journal of Algebra and Computation · 2000
Introduction Transfinite strings have long been introduced. Logicians were the first to study them with the pioneering works of Buchi on the decidability of the monadic second order logic on the ordinal ! 1 [3], followed by other investigations beyond ! 1 [19] or more specifically on the "automata" aspect of the theory [5]. In the area of theoretical computer science such objects can be viewed as modelling the behaviour of sequential processes consisting of infinite actions whose times define a convergent sequence, also known in the literature as Zeno strings. The vivid area of timed automata which takes the duration of transitions of finite automata into account makes explicit use of this notion see, e.g., [8]. In another, more algebraic direction, the classical approach of "rational languages" and its connection to the theory of "varieties" of algebraic structures developed by Eilenberg for finite strings [6, Chapter VII], was