Decision problems for linear recurrences involving arbitrary real numbers

We study the decidability of Skolem Problem, Positivity and Ultimate Problem for linear recurrences with real number initial values coefficients in bit-model computation. show that each problem there exists a correct partial algorithm which halts all instances answer is locally constant, thus establishing three problems are as close to decidable one can expect them be this setting. further algorithms halt on almost every instance respect usual Lebesgue measure Euclidean space. In comparison, analogous exact rational or algebraic known only fairly low order.