Dynamic Data Structures for Document Collections and Graphs

In the dynamic indexing problem, we must maintain a changing collection of text documents so that we can efficiently support insertions, deletions, and pattern matching queries. We are especially interested in developing efficient data structures that store and query the documents in compressed form. All previous compressed solutions to this problem rely on answering rank and select queries on a dynamic sequence of symbols. Because of the lower bound in [Fredman and Saks, 1989], answering rank queries presents a bottleneck in compressed dynamic indexing. In this paper we show how this lower bound can be circumvented using our new framework. We demonstrate that the gap between static and dynamic variants of the indexing problem can be almost closed. Our method is based on a novel framework for adding dynamism to static compressed data structures. Our framework also applies more generally to dynamizing other problems. We show, for example, how our framework can be applied to develop compressed representations of dynamic graphs and binary relations

On Formalism Freeness : Implementing Gödel's 1946 Princeton Bicentennial Lecture

Peer reviewe

The Ontological Ground of the Alethic Modality

This paper is concerned with the wholly metaphysical question of whether necessity and possibility rest on nonmodal foundations—whether the truth conditions for modal statements are, in the final analysis, nonmodal. It is argued that Lewis’s modal realism is either arbitrary and stipulative or else it is circular. Even if there were Lewisean possible worlds, they could not provide the grounds for modality. D. M. Armstrong’s combinatorial approach to possibility suffers from similar defects. Since more traditional reductions to cognitive or linguistic facts suffer similar fates, the conclusion that the alethic modality is primitive and incapable of reduction is offered

Uniform Diagonalization Theorem for Complexity Classes of Promise Problems including Randomized and Quantum Classes

Diagonalization in the spirit of Cantor's diagonal arguments is a widely used tool in theoretical computer sciences to obtain structural results about computational problems and complexity classes by indirect proofs. The Uniform Diagonalization Theorem allows the construction of problems outside complexity classes while still being reducible to a specific decision problem. This paper provides a generalization of the Uniform Diagonalization Theorem by extending it to promise problems and the complexity classes they form, e.g. randomized and quantum complexity classes. The theorem requires from the underlying computing model not only the decidability of its acceptance and rejection behaviour but also of its promise-contradicting indifferent behaviour - a property that we will introduce as "total decidability" of promise problems. Implications of the Uniform Diagonalization Theorem are mainly of two kinds: 1. Existence of intermediate problems (e.g. between BQP and QMA) - also known as Ladner's Theorem - and 2. Undecidability if a problem of a complexity class is contained in a subclass (e.g. membership of a QMA-problem in BQP). Like the original Uniform Diagonalization Theorem the extension applies besides BQP and QMA to a large variety of complexity class pairs, including combinations from deterministic, randomized and quantum classes.Comment: 15 page

Interpretation-driven mapping: A framework for conducting search and re-representation in parallel for computational analogy in design

This paper presents a framework for the interactions between the processes of mapping and rerepresentation within analogy making. Analogical reasoning systems for use in design tasks require representations that are open to being reinterpreted. The framework, interpretation-driven mapping, casts the process of constructing an analogical relationship as requiring iterative, parallel interactions between mapping and interpreting. This paper argues that this interpretation-driven approach focuses research on a fundamental problem in analogy making: how do the representations that make new mappings possible emerge during the mapping process? The framework is useful for both describing existing analogy-making models and designing future ones. The paper presents a computational model informed by the framework Idiom, which learns ways to reinterpret the representations of objects as it maps between them. The results of an implementation in the domain of visual analogy are presented to demonstrate its feasibility. Analogies constructed by the system are presented as examples. The interpretation-driven mapping framework is then used to compare representational change in Idiom to that in three previously published systems

Outline of a new approach to the nature of mind

I propose a new approach to the constitutive problem of psychology ‘what is mind?’ The first section introduces modifications of the received scope, methodology, and evaluation criteria of unified theories of cognition in accordance with the requirements of evolutionary compatibility and of a mature science. The second section outlines the proposed theory. Its first part provides empirically verifiable conditions delineating the class of meaningful neural formations and modifies accordingly the traditional conceptions of meaning, concept and thinking. This analysis is part of a theory of communication in terms of inter-level systems of primitives that proposes the communication-understanding principle as a psychological invariance. It unifies a substantial amount of research by systematizing the notions of meaning, thinking, concept, belief, communication, and understanding and leads to a minimum vocabulary for this core system of mental phenomena. Its second part argues that written human language is the key characteristic of the artificially natural human mind. Overall, the theory both supports Darwin’s continuity hypothesis and proposes that the mental gap is within our own species