Let S = Sym(Ω) be the group of all permutations of an infinite set Ω. Extending an argument of Macpherson and Neumann, it is shown that if U is a generating set for S as a group, respectively as a monoid, then there exists a positive integer n such that every element of S may be written as a group word, respectively a monoid word, of length ≤ n in the elements of U. Some related questions are n...

We provide an extension of the perfect sampling algorithm of Fill (1998) to general chains, and describe how use of bounding processes can ease computational burden. Along the way, we unearth a simple connection between the Coupling From The Past (CFTP) algorithm originated by Propp and Wilson (1996) and our extension of Fill’s algorithm.

This work presents a faster method of simulating exactly from a distribution known as a Vervaat perpetuity. A parameter of the Vervaat perpetuity is β ∈ (0,∞). An earlier method for simulating from this distributon ran in time O((2.23β)β). This earlier method utilized dominated coupling from the past that bounded a stochastic process for perpetuities from above. By extending to non-Markovian up...

This research was conducted based on the phenomenon happened in school. The students had low ability grammar. They got difficulty constructing sentences by using some tenses. Therefore, this thesis discussed error analysis simple past tense writing recount text. purpose of to classify types errors made and find out sources which descriptive qualitative analysis. subjects were at first semester ...

Usually writing teachers feel commitment to provide their learners with corrective feedback (CF) to their linguistic errors. The study investigated whether two types of written corrective feedback, indirect focused corrective feedback and indirect unfocused corrective feedback, produced differential effects on the accurate use of grammatical forms by high intermediate EFL learners. In this stud...