We extend a classical result in ordinary recursion theory to higher recursion theory, namely that every recursively enumerable set can be represented in any model A by some Horn theory, where A can be any model of a higher recursion theory, like primitive set recursion, αrecursion, or β -recursion. We also prove that, under suitable conditions, a set defined through a Horn theory in a set A is ...

Portfolio credit risk models as well as models for operational risk can often be treated analogously to the collective risk model coming from insurance. Applying the classical Panjer recursion in the collective risk model can lead to numerical instabilities, for instance if the claim number distribution is extended negative binomial or extended logarithmic. We present a generalization of Panjer...

This article discusses how to use queue to make non-recursion algorithm of binary link tree. As for a general binary tree, if we adopt sequence storage, firstly we should extend it first into a complete binary tree, secondly we store it to a temporary queue according to the sequence of up-down and left-right. On the basis of the properties of the complete binary tree and the queue, if we can co...

Although HTN planning is in general undecidable, there are many syntactically identifiable sub-classes of HTN problems that can be decided. For these sub-classes, the decision procedures provide upper complexity bounds. Lower bounds were often not investigated in more detail, however. We generalize a propositional HTN formalization to one that is based upon a function-free first-order logic and...

Nonlinear recursion is one of the most challenging classes of logic programs for eecient evaluation in logic programming systems. We identify one popular class of nonlinear recur-sion, regular nonlinear recursion, and investigate its eecient implementation by a deductive database approach. The approach performs a detailed query binding analysis based on query information, constraint information...