ABSTRACT We classify functions in recursive graph theory in terms of how many queries to K (or ∅ or ∅) are required to compute them. We show that (1) binary search is optimal (in terms of the number of queries to K) for finding the chromatic number of a recursive graph and that no set of Turing degree less than 0 will suffice, (2) determining if a recursive graph has a finite chromatic number i...

Higher-order recursive schemes offer an interesting method of approximating program semantics. The semantics of a scheme is an infinite tree labeled with built-in constants. This tree represents the meaning of the program up to the meaning of built-in constants. It is much easier to reason about properties of such trees than properties of interpreted programs. Moreover some interesting properti...

Although Turing did not know it at the time, he was not the first to prove that the Entscheidungsproblem had no algorithmic solution. The first such proof is implicit in the work of Kurt Gödel; in lectures on his incompleteness theorems2 at Princeton in 1934, Gödel described a model of general recursive functions, which he largely credited to Jacques Herbrand.3 Gödel’s incompleteness theorem ca...

The problem of two-dimensional recursive digital filtering of large images by the sectioning (or block-mode) technique has been considered. It has been stated that, if the impulse-response sequence of the recursive digital filter dies down relatively sharply, by a suitable truncation, the available sectioning techniques can be used to perform the filtering operation, as with nonrecursive filter...

Recently, we have shown that the differential properties of the surfaces represented by 3D volumic images can be recovered using their partial derivatives. For instance, the crest lines can be characterized by the first, second and third partial derivatives of the grey levrl function I(x,y,z) . This paper deals with the following points : the computation of the partial derivatives of an image c...

In this paper, the 1-D real-valued discrete Gabor transform (RDGT) proposed in our previous work and its relationship with the complex-valued discrete Gabor transform (CDGT) are briefly reviewed. Block time-recursive RDGT algorithms for the efficient and fast computation of the 1-D RDGT coefficients and for the fast reconstruction of the original signal from the coefficients are then developed ...

In this paper, a recursive computation method is developed to derive the multiple reflections of nonuniform transmission lines. The true impedance profiles of the nonuniform transmission lines are then reconstructed with the help of this method. This method is more efficient than other algorithm. To validate this method, two nonuniform microstrip lines are designed and measured using Agilent ve...

A new recursive algorithm for fast computation of twodimensional discrete cosine transforms (2-D DCT) is derived by converting the 2-D data matrices into 1-D vectors and then using different partition methods for the time and frequency indices. The algorithm first computes the 2-D complex DCT (2-D CCT) and then produces two 2-D DCT outputs simultaneously through a post-addition step. The decomp...

In this thesis we provide a characterization of probabilistic computation in itself, from a recursion-theoretical perspective, without reducing it to deterministic computation. More specifically, we show that probabilistic computable functions, i.e., those functions which are computed by Probabilistic Turing Machines (PTM), can be characterized by a natural generalization of Kleene’s partial re...

A new runtime environment for the execution of recursive matrix algorithms on a supercomputer with distributed memory is proposed. It designed both dense and sparse matrices. The ensures decentralized control computation process. As an example block algorithm, Cholesky factorization symmetric positive definite in form dichotomous algorithm described. results experiments different numbers cores ...