We improve several upper bounds to the complexity of the membership problem for languages deened by iterated morphisms (D0L systems). The complexity bounds are expressed in terms of DLOGT IME-uniform circuit families. We prove: 1) For polynomially growing D0L systems the membership problem is contained in AC 0. 2) For arbitrary D0L systems the membership problem is contained in NC 1. 3) The lat...

Numeration Systems Definition An abstract numeration system is a triple S = (L,Σ, <) where L is a regular language over a totally ordered alphabet (Σ, <). Enumerating the words of L with respect to the genealogical ordering induced by < gives a one-to-one correspondence repS : N → L valS = rep −1 S : L → N. Example L = a∗, Σ = {a} n 0 1 2 3 4 · · · rep (n) ε a aa aaa aaaa · · · Abstract Numerat...

Rudolf Freund studied the splicing systems on graphs and strings. In this paper, with the definition of semigraph folding for the spliced DNA molecule, we characterized the morphic and antimorphic evolution for the alphabet for the folding of spliced semigraph. Also we obtain the set of all properly δlimit words is a totally ordered set with < δ for an antimorphic evolution.

* Correspondence: [email protected] LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China Full list of author information is available at the end of the article Abstract We consider the differential equation f’’ + Af’ + Bf = 0 where A(z) and B(z) ≢ 0 are mero-morphic functions. Assume that A(z) belongs to the Edrei-Fuchs class and B(z) has a deficient valu...

Higher-order functions pose a challenge for both static program analyses and optimizing compilers. To simplify the analysis compilation of languages with higher-order functions, rich body prior work has proposed variety defunctionalization techniques, which can eliminate from by transforming to semantically-equivalent first-order representation. Several modern take this step further, specializi...

Given a quasi-projective complex variety X and a projective variety Y , one may endow the set of morphisms, Mor(X, Y ), from X to Y with the natural structure of a topological space. We introduce a convenient technique (namely, the notion of a functor on the category of “smooth curves”) for studying these function complexes and for forming continuous pairings of such. Building on this technique...