We provide machine-independent characterizations of some complexity classes, over an arbitrary structure, in the model of computation proposed by L. Blum, M. Shub and S. Smale. We show that the levels of the polynomial hierarchy correspond to safe recursion with predicative minimization. The levels of the digital polynomial hierarchy correspond to safe recursion with digital predicative minimiz...

The focus of this paper is the technique of recur8\on analysis. Recursion analysis is used by the Boyer-Moore Theorem Prover to choose an appropriate induct ion schema and variable to prove theorems by mathematical induct ion. A rat ional reconstruction of recursion analysis is out l ined, using the technique of proof plans. This rat ional reconstruction suggests an extension of recursion analy...

Much is already known about when a conjugate gradient method can be implemented with short recursions for the direction vectors. The work done in 1984 by Faber and Manteuuel 3] gave necessary and suucient conditions on the iteration matrix A, in order for a conjugate gradient method to be implemented with a single recursion of a certain form. However, this form does not take into account all po...

In a recent paper, Launchbury, Lewis, and Cook observe that some Haskell applications could bene t from a combinator m x for expressing recursion over monadic types. We investigate three possible de nitions of m x and implement them in Haskell. Like traditional xpoint operators, there are two approaches to the de nition of m x: an unfolding one based on mathematical semantics, and an updating o...

Connectionist models have used general principles to model phenomena across many mental domains. Thus, they seem promising for uniting diverse syntactic phenomena (e.g., language, music, action). A challenge has been understanding how recursion can work in neurons. Headway has been made in training Recurrent Neural Networks (RNNs) to process languages which can be handled by the use of one or m...

Guarded recursion is a form of recursion where recursive calls are guarded by delay modalities. Previous work has shown how guarded recursion is useful for constructing logics for reasoning about programming languages with advanced features, as well as for constructing and reasoning about elements of coinductive types. In this paper we investigate how type theory with guarded recursion can be u...

This paper presents recursion unrolling, a technique for improving the performance of recursive computations. Conceptually, recursion unrolling inlines recursive calls to reduce control flow overhead and increase the size of the basic blocks in the computation, which in turn increases the effectiveness of standard compiler optimizations such as register allocation and instruction scheduling. We...

In this work we generalize primitive recursion in order to construct a hierarchy of terminating total recursive operators which we refer to as leveled primitive recursion of order i(PRi). Primitive recursion is equivalent to leveled primitive recursion of order 1 (PR1). The functions constructable from the basic functions make up PR0. Interestingly, we show that PR2 is a conservative extension ...

A celebrated contribution of Bellantoni and Cook was a function algebra to capture FPTIME. This algebra uses recursion on notation. Later, Oitavem showed that including primitive recursion, an algebra is obtained which captures FPSPACE. The main results of this paper concern variants of the latter algebra. First, we show that iteration can replace primitive recursion. Then, we consider the resu...

An algorithm for the symbolic computation of recursion operators for systems of nonlinear differential-difference equations (DDEs) is presented. Recursion operators allow one to generate an infinite sequence of generalized symmetries. The existence of a recursion operator therefore guarantees the complete integrability of the DDE. The algorithm is based in part on the concept of dilation invari...