An exercise in transformational programming: Backtracking and Branch-and-Bound

We present a formal derivation of program schemes that are usually called Backtracking programs and Branch-and-Bound programs. The derivation consists of a series of transformation steps, specifically algebraic manipulations, on the initial specification until the desired programs are obtained. The well-known notions of linear recursion and tail recursion are extended, for structures, to elementwise linear recursion and elementwise tail recursion; and a transformation between them is derived too

Linearity and Scaling of a Statistical Model for the Species Abundance Distribution

We derive a linear recursion relation for the species abundance distribution in a statistical model of ecology and demonstrate the existence of a scaling solution

Binary sequence detector uses minimum number of decision elements

Detector of an n bit binary sequence code within a serial binary data system assigns states to memory elements of a code sequence detector by employing the same order of states for the sequence detector as that of the sequence generator when the linear recursion relationship employed by the sequence generator is given

One-dimensional linear recursions with Markov-dependent coefficients

For a class of stationary Markov-dependent sequences $(A_n,B_n)\in\mathbb{R}^2,$ we consider the random linear recursion $S_n=A_n+B_nS_{n-1},$ $n\in\mathbb{Z},$ and show that the distribution tail of its stationary solution has a power law decay.Comment: Published at http://dx.doi.org/10.1214/105051606000000844 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org