Step-Indexed Relational Reasoning for Countable Nondeterminism

Programming languages with countable nondeterministic choice are computationally interesting since countable nondeterminism arises when modeling fairness for concurrent systems. Because countable choice introduces non-continuous behaviour, it is well-known that developing semantic models for programming languages with countable nondeterminism is challenging. We present a step-indexed logical relations model of a higher-order functional programming language with countable nondeterminism and demonstrate how it can be used to reason about contextually defined may- and must-equivalence. In earlier step-indexed models, the indices have been drawn from {\omega}. Here the step-indexed relations for must-equivalence are indexed over an ordinal greater than {\omega}

An Incentive-Compatibility Approach to the Problem of Monitoring a Bureau

An incentive-compatibility framework for regulating a monopolist with unknown costs is applied to the sponsor’s problem of monitoring a bureau. Following Mueller (1989), the bureau does not make take-it-or-leave-it budget proposals to the sponsor. Rather, the bureau must announce a marginal cost per unit of output to the sponsor. Given that report, the sponsor chooses a price that it will pay to the bureau for each unit of output, and the sponsor chooses the level of output as well. The analysis reveals the price per unit of output that the sponsor must pay to the bureau to maximize social welfare.Bureaucracy; Administrative Processes in Public Organizations; Corruption; Asymmetric and Private Information; Incentive Compatibility; Monitoring

Classical causal models for Bell and Kochen-Specker inequality violations require fine-tuning

Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and are key resources for quantum advantage in information-processing tasks. Bell nonlocality is best understood as the incompatibility between quantum correlations and the classical theory of causality, applied to relativistic causal structure. Contextuality, on the other hand, is on a more controversial foundation. In this work, I provide a common conceptual ground between nonlocality and contextuality as violations of classical causality. First, I show that Bell inequalities can be derived solely from the assumptions of no-signalling and no-fine-tuning of the causal model. This removes two extra assumptions from a recent result from Wood and Spekkens, and remarkably, does not require any assumption related to independence of measurement settings -- unlike all other derivations of Bell inequalities. I then introduce a formalism to represent contextuality scenarios within causal models and show that all classical causal models for violations of a Kochen-Specker inequality require fine-tuning. Thus the quantum violation of classical causality goes beyond the case of space-like separated systems, and manifests already in scenarios involving single systems.Comment: 9 pages, 14 figures. Modified title, discussion and presentatio

Perspectives for Electronic Books in the World Wide Web Age

While the World Wide Web (WWW or Web) is steadily expanding, electronic books (e-books) remain a niche market. In this article, it is first postulated that specialized contents and device independence can make Web-based e-books compete with paper prints; and that adaptive features that can be implemented by client-side computing are relevant for e-books, while more complex forms of adaptation requiring server-side computations are not. Then, enhancements of the WWW standards (specifically of XML, XHTML, of the style-sheet languages CSS and XSL, and of the linking language XLink) are proposed for a better support of client-side adaptation and device independent content modeling. Finally, advanced browsing functionalities desirable for e-books as well as their implementation in the WWW context are described

Conservativity of embeddings in the lambda Pi calculus modulo rewriting (long version)

The lambda Pi calculus can be extended with rewrite rules to embed any functional pure type system. In this paper, we show that the embedding is conservative by proving a relative form of normalization, thus justifying the use of the lambda Pi calculus modulo rewriting as a logical framework for logics based on pure type systems. This result was previously only proved under the condition that the target system is normalizing. Our approach does not depend on this condition and therefore also works when the source system is not normalizing.Comment: Long version of TLCA 2015 pape

Stateless HOL

We present a version of the HOL Light system that supports undoing definitions in such a way that this does not compromise the soundness of the logic. In our system the code that keeps track of the constants that have been defined thus far has been moved out of the kernel. This means that the kernel now is purely functional. The changes to the system are small. All existing HOL Light developments can be run by the stateless system with only minor changes. The basic principle behind the system is not to name constants by strings, but by pairs consisting of a string and a definition. This means that the data structures for the terms are all merged into one big graph. OCaml - the implementation language of the system - can use pointer equality to establish equality of data structures fast. This allows the system to run at acceptable speeds. Our system runs at about 85% of the speed of the stateful version of HOL Light.Comment: In Proceedings TYPES 2009, arXiv:1103.311

The correlation space of Gaussian latent tree models and model selection without fitting

We provide a complete description of possible covariance matrices consistent with a Gaussian latent tree model for any tree. We then present techniques for utilising these constraints to assess whether observed data is compatible with that Gaussian latent tree model. Our method does not require us first to fit such a tree. We demonstrate the usefulness of the inverse-Wishart distribution for performing preliminary assessments of tree-compatibility using semialgebraic constraints. Using results from Drton et al. (2008) we then provide the appropriate moments required for test statistics for assessing adherence to these equality constraints. These are shown to be effective even for small sample sizes and can be easily adjusted to test either the entire model or only certain macrostructures hypothesized within the tree. We illustrate our exploratory tetrad analysis using a linguistic application and our confirmatory tetrad analysis using a biological application.Comment: 15 page

The Sheaf-Theoretic Structure Of Non-Locality and Contextuality

We use the mathematical language of sheaf theory to give a unified treatment of non-locality and contextuality, in a setting which generalizes the familiar probability tables used in non-locality theory to arbitrary measurement covers; this includes Kochen-Specker configurations and more. We show that contextuality, and non-locality as a special case, correspond exactly to obstructions to the existence of global sections. We describe a linear algebraic approach to computing these obstructions, which allows a systematic treatment of arguments for non-locality and contextuality. We distinguish a proper hierarchy of strengths of no-go theorems, and show that three leading examples --- due to Bell, Hardy, and Greenberger, Horne and Zeilinger, respectively --- occupy successively higher levels of this hierarchy. A general correspondence is shown between the existence of local hidden-variable realizations using negative probabilities, and no-signalling; this is based on a result showing that the linear subspaces generated by the non-contextual and no-signalling models, over an arbitrary measurement cover, coincide. Maximal non-locality is generalized to maximal contextuality, and characterized in purely qualitative terms, as the non-existence of global sections in the support. A general setting is developed for Kochen-Specker type results, as generic, model-independent proofs of maximal contextuality, and a new combinatorial condition is given, which generalizes the `parity proofs' commonly found in the literature. We also show how our abstract setting can be represented in quantum mechanics. This leads to a strengthening of the usual no-signalling theorem, which shows that quantum mechanics obeys no-signalling for arbitrary families of commuting observables, not just those represented on different factors of a tensor product.Comment: 33 pages. Extensively revised, new results included. Published in New Journal of Physic

Exploration and exploitation in the presence of network externalities

This paper examines the conditions under which exploration of a new, incompatible technologyis conducive to firm growth in the presence of network externalities. In particular, this studyis motivated bythe divergent evolutions of the PC and the workstation markets in response to a new technology: reduced instruction set computing (RISC). In the PC market, Intel has developed new microprocessors bymaintaining compatibilitywith the established architecture, whereas it was radicallyr eplaced byRISC in the workstation market. History indicates that unlike the PC market, the workstation market consisted of a large number of power users, who are less sensitive to compatibilitythan ordinaryusers. Our numerical analysis indicates that the exploration of a new, incompatible technologyis more likelyto increase the chance of firm growth when there are a substantial number of power users or when a new technologyis introduced before an established technologytakes off. (; ; ;

SIC-POVMs and Compatibility among Quantum States

An unexpected connection exists between compatibility criteria for quantum states and symmetric informationally complete POVMs. Beginning with Caves, Fuchs and Schack's "Conditions for compatibility of quantum state assignments" [Phys. Rev. A 66 (2002), 062111], I show that a qutrit SIC-POVM studied in other contexts enjoys additional interesting properties. Compatibility criteria provide a new way to understand the relationship between SIC-POVMs and mutually unbiased bases, as calculations in the SIC representation of quantum states make clear. This, in turn, illuminates the resources necessary for magic-state quantum computation, and why hidden-variable models fail to capture the vitality of quantum mechanics.Comment: 15 pages, 4 MUBs, 2 errata for CFS (2002), 1 graph with chromatic number 4. v4: journal versio