Genomic distance under gene substitutions

Languages under substitutions and balanced

= zu2(i + k) for all i E I,. If I = Z we call w a Z-word or a bi-infinite word. If I is finite we call x finite and its length Ixl is defined as The usual notation for a finite word of length n is x = xi ... zn where all xi E {a, &}. We write {a, b}* for the collection of finite words and {a, b~+ for the nonempty finite words. (The empty word will be denoted throughout by e). The concatena...

Distance Desert Automata and Star Height Substitutions

We introduce the notion of nested distance desert automata as a joint generalization and further development of distance automata and desert automata. We show that limitedness of nested distance desert automata is PSPACE-complete. As an application, we show that it is decidable in 22 O(n2) space whether the language accepted by an n-state non-deterministic automaton is of a star height less tha...

Syntactic Uni cation Problems under Constrained Substitutions

Some kind of practical problems such as security veri cation of cryptographic protocols can be described as a problem to accomplish a given purpose by using limited operations and limited materials only. To model such problems in a natural way, uni cation problems under constrained substitutions have been proposed. This paper is a collection of results on the decidability and the computational ...

Syntactic Uni cation Problem under Constrained Substitutions

Autocorrelation of gene frequencies under isolation by distance.

Spatial autocorrelation statistics are used for description of geographic variation of gene frequencies, but the relationship of these indices with the parameters describing the genetic structure of populations is not established. A simple relation is derived here between kinship coefficient and a measure of spatial autocorrelation, Moran's I. The autocorrelation coefficient of gene frequencies...