We present a high-level parallel calculus for nested sequences, NSC, ooered as a possible theoretical \core" of an entire class of collection-oriented parallel languages. NSC is based on while-loops as opposed to general recursion. A formal, machine independent deenition of the parallel time complexity and the work complexity of programs in NSC is given. Our main results are: (1) We give a tran...

In 1] Buchholz presented a method to build notation systems for innnite sequent-style derivations, analogous to well-known systems of notation for ordinals. The essential feature is that from a notation one can read oo by a primitive (not "0-) recursive function its n-th predecessor and e.g. the last rule applied. Here we extend the method to the more general setting of innnite (typed) terms, i...

This thesis is concerned with analysing the impact of nesting (restricted) control structures in programs, such as primitive recursion or loop statements, on the running time or computational complexity. The method obtained gives insight as to why some nesting of control structures may cause a blow up in computational complexity, while others do not. The method is demonstrated for three types o...

We propose a sound, complete, and automatic method for pairwise reachability analysis of higher-order concurrent programs with recursion, nested locks, joins, and dynamic thread creation. The method is based on a reduction to higher-order model checking (i.e., model checking of trees generated by higher-order recursion schemes). It can be considered an extension of Gawlitz et al.’s work on the ...

In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...