H. G. Rice

Bio: H. G. Rice is an academic researcher. The author has contributed to research in topics: Decision problem & Undecidable problem. The author has an hindex of 1, co-authored 1 publications receiving 677 citations.

Classes of recursively enumerable sets and their decision problems

Abstract: 1. Introduction. In this paper we consider classes whose elements are re-cursively enumerable sets of non-negative integers. No discussion of recur-sively enumerable sets can avoid the use of such classes, so that it seems desirable to know some of their properties. We give our attention here to the properties of complete recursive enumerability and complete recursiveness (which may be intuitively interpreted as decidability). Perhaps our most interesting result (and the one which gives this paper its name) is the fact that no nontrivial class is completely recursive. We assume familiarity with a paper of Kleene [5](2), and with ideas which are well summarized in the first sections of a paper of Post Í7].

Recursively enumerable sets and degrees

Abstract: TABLE OF CONTENTS Introduction Chapter I. The relation of the structure of an r.e. set to its degree. 1. Post's program and simple sets. 2. Dominating functions and quotient lattices. 3. Maximal sets and high degrees. 4. Low degrees, atomless sets, and invariant degree classes. 5. Incompleteness and completeness for noninvariant properties. Chapter II. The structure, automorphisms, and elementary theory of the r.e. sets. 6. Basic facts and splitting theorems. 7. Hh-simple sets. 8. Major subsets and r-maximal sets. 9. Automorphisms of &. 10. The elementary theory of S. Chapter III. The structure of the r.e. degrees. 11. Basic facts. 12. The finite injury priority method. 13. The infinite injury priority method. 14. The minimal pair method and lattice embeddings in R. 15. Cupping and splitting r.e. degrees. 16. Automorphisms and decidability of R.

Inductive Logic Programming : Theory and Methods

Abstract: Inductive Logic Programming (ILP) is a new discipline which investigates the inductive construction of first-order clausal theories from examples and background knowledge. We survey the most important theories and methods of this new field. First, various problem specifications of ILP are formalized in semantic settings for ILP, yielding a “model-theory” for ILP. Second, a generic ILP algorithm is presented. Third, the inference rules and corresponding operators used in ILP are presented, resulting in a “proof-theory” for ILP. Fourth, since inductive inference does not produce statements which are assured to follow from what is given, inductive inferences require an alternative form of justification. This can take the form of either probabilistic support or logical constraints on the hypothesis language. Information compression techniques used within ILP are presented within a unifying Bayesian approach to confirmation and corroboration of hypotheses. Also, different ways to constrain the hypothesis language or specify the declarative bias are presented. Fifth, some advanced topics in ILP are addressed. These include aspects of computational learning theory as applied to ILP, and the issue of predicate invention. Finally, we survey some applications and implementations of ILP. ILP applications fall under two different categories: first, scientific discovery and knowledge acquisition, and second, programming assistants.

Dynamic Logic

Abstract: From the Publisher: Among the many approaches to formal reasoning about programs, Dynamic Logic enjoys the singular advantage of being strongly related to classical logic. Its variants constitute natural generalizations and extensions of classical formalisms. For example, Propositional Dynamic Logic (PDL) can be described as a blend of three complementary classical ingredients: propositional calculus, modal logic, and the algebra of regular events. In First-Order Dynamic Logic (DL), the propositional calculus is replaced by classical first-order predicate calculus. Dynamic Logic is a system of remarkable unity that is theoretically rich as well as of practical value. It can be used for formalizing correctness specifications and proving rigorously that those specifications are met by a particular program. Other uses include determining the equivalence of programs, comparing the expressive power of various programming constructs, and synthesizing programs from specifications. This book provides the first comprehensive introduction to Dynamic Logic. It is divided into three parts. The first part reviews the appropriate fundamental concepts of logic and computability theory and can stand alone as an introduction to these topics. The second part discusses PDL and its variants, and the third part discusses DL and its variants. Examples are provided throughout, and exercises and a short historical section are included at the end of each chapter.

Algorithmic Randomness and Complexity

Abstract: Preface- Acknowledgments- Introduction- I Background- Preliminaries- Computability Theory- Kolmogorov Complexity of Finite Strings- Relating Plain and Prefix-Free Complexity- Effective Reals- II Randomness of Sets- Martin-Lof Randomness- Other Notions of Effective Randomness- Algorithmic Randomness and Turing Reducibility- III Relative Randomness- Measures of Relative Randomness- The Quantity of K- and Other Degrees- Randomness-Theoretic Weakness- Lowness for Other Randomness Notions- Effective Hausdorff Dimension- IV Further Topics- Omega as an Operator- Complexity of CE Sets- References- Index

Abandoning objectives: Evolution through the search for novelty alone

Abstract: In evolutionary computation, the fitness function normally measures progress toward an objective in the search space, effectively acting as an objective function. Through deception, such objective functions may actually prevent the objective from being reached. While methods exist to mitigate deception, they leave the underlying pathology untreated: Objective functions themselves may actively misdirect search toward dead ends. This paper proposes an approach to circumventing deception that also yields a new perspective on open-ended evolution. Instead of either explicitly seeking an objective or modeling natural evolution to capture open-endedness, the idea is to simply search for behavioral novelty. Even in an objective-based problem, such novelty search ignores the objective. Because many points in the search space collapse to a single behavior, the search for novelty is often feasible. Furthermore, because there are only so many simple behaviors, the search for novelty leads to increasing complexity. By decoupling open-ended search from artificial life worlds, the search for novelty is applicable to real world problems. Counterintuitively, in the maze navigation and biped walking tasks in this paper, novelty search significantly outperforms objective-based search, suggesting the strange conclusion that some problems are best solved by methods that ignore the objective. The main lesson is the inherent limitation of the objective-based paradigm and the unexploited opportunity to guide search through other means.