Reconciling Shannon and Scott with a Lattice of Computable Information

This paper proposes a reconciliation of two different theories of information. The first, originally proposed in a lesser-known work by Claude Shannon (some five years after the publication of his celebrated quantitative theory of communication), describes how the information content of channels can be described qualitatively, but still abstractly, in terms of information elements, where information elements can be viewed as equivalence relations over the data source domain. Shannon showed that these elements have a partial ordering, expressing when one information element is more informative than another, and that these partially ordered information elements form a complete lattice. In the context of security and information flow this structure has been independently rediscovered several times, and used as a foundation for understanding and reasoning about information flow. The second theory of information is Dana Scott\u27s domain theory, a mathematical framework for giving meaning to programs as continuous functions over a particular topology. Scott\u27s partial ordering also represents when one element is more informative than another, but in the sense of computational progress - i.e. when one element is a more defined or evolved version of another. To give a satisfactory account of information flow in computer programs it is necessary to consider both theories together, in order to understand not only what information is conveyed by a program (viewed as a channel, \ue0 la Shannon) but also how the precision with which that information can be observed is determined by the definedness of its encoding (\ue0 la Scott). To this end we show how these theories can be fruitfully combined, by defining the Lattice of Computable Information (LoCI), a lattice of preorders rather than equivalence relations. LoCI retains the rich lattice structure of Shannon\u27s theory, filters out elements that do not make computational sense, and refines the remaining information elements to reflect how Scott\u27s ordering captures possible varieties in the way that information is presented. We show how the new theory facilitates the first general definition of termination-insensitive information flow properties, a weakened form of information flow property commonly targeted by static program analyses

Decidability of strong equivalence for subschemas of a class of linear, free, near-liberal program schemas

The article attached is a preprint version of the final published article which can be accessed at the link below. The article title has been changed. For referencing purposes please use the published details. Copyright © 2010 Elsevier B.V. All rights reserved.A program schema defines a class of programs, all of which have identical statement structure, but whose functions and predicates may differ. A schema thus defines an entire class of programs according to how its symbols are interpreted. Two schemas are strongly equivalent if they always define the same function from initial states to final states for every interpretation. A subschema of a schema is obtained from a schema by deleting some of its statements. A schema S is liberal if there exists an initial state in the Herbrand domain such that the same term is not generated more than once along any executable path through S. In this paper, we introduce near-liberal schemas, in which this non-repeating condition applies only to terms not having the form g() for a constant function symbol g. Given a schema S that is linear (no function or predicate symbol occurs more than once in S) and a variable v, we compute a set of function and predicate symbols in S which is a subset of those defined by Weiser's slicing algorithm and prove that if for every while predicate q in S and every constant assignment w:=g(); lying in the body of q, no other assignment to w also lies in the body of q, our smaller symbol set defines a correct subschema of S with respect to the final value of v after execution. We also prove that if S is also free (every path through S is executable) and near-liberal, it is decidable which of its subschemas are strongly equivalent to S. For the class of pairs of schemas in which one schema is a subschema of the other, this generalises a recent result in which S was required to be linear, free and liberal.This work was supported by a grant from the Engineering and Physical Sciences Research Council, Grant EP/E002919/1

Characterizing minimal semantics-preserving slices of predicate-linear, free, liberal program schemas

This is a preprint version of the article - Copyright @ 2011 ElsevierA program schema defines a class of programs, all of which have identical statement structure, but whose functions and predicates may differ. A schema thus defines an entire class of programs according to how its symbols are interpreted. A subschema of a schema is obtained from a schema by deleting some of its statements. We prove that given a schema S which is predicate-linear, free and liberal, such that the true and false parts of every if predicate satisfy a simple additional condition, and a slicing criterion defined by the final value of a given variable after execution of any program defined by S, the minimal subschema of S which respects this slicing criterion contains all the function and predicate symbols ‘needed’ by the variable according to the data dependence and control dependence relations used in program slicing, which is the symbol set given by Weiser’s static slicing algorithm. Thus this algorithm gives predicate-minimal slices for classes of programs represented by schemas satisfying our set of conditions. We also give an example to show that the corresponding result with respect to the slicing criterion defined by termination behaviour is incorrect. This complements a result by the authors in which S was required to be function-linear, instead of predicate-linear.This work was supported by a grant from the Engineering and Physical Sciences Research Council, Grant EP/E002919/1

Proving Differential Privacy with Shadow Execution

Recent work on formal verification of differential privacy shows a trend toward usability and expressiveness -- generating a correctness proof of sophisticated algorithm while minimizing the annotation burden on programmers. Sometimes, combining those two requires substantial changes to program logics: one recent paper is able to verify Report Noisy Max automatically, but it involves a complex verification system using customized program logics and verifiers. In this paper, we propose a new proof technique, called shadow execution, and embed it into a language called ShadowDP. ShadowDP uses shadow execution to generate proofs of differential privacy with very few programmer annotations and without relying on customized logics and verifiers. In addition to verifying Report Noisy Max, we show that it can verify a new variant of Sparse Vector that reports the gap between some noisy query answers and the noisy threshold. Moreover, ShadowDP reduces the complexity of verification: for all of the algorithms we have evaluated, type checking and verification in total takes at most 3 seconds, while prior work takes minutes on the same algorithms.Comment: 23 pages, 12 figures, PLDI'1

Detection of Orbital Fluctuations Above the Structural Transition Temperature in the Iron-Pnictides and Chalcogenides

We use point contact spectroscopy to probe $\rm{AEFe_2As_2}$ ($\rm{AE=Ca, Sr, Ba}$) and $\rm{Fe_{1+y}Te}$. For $\rm{AE=Sr, Ba}$ we detect orbital fluctuations above $T_S$ while for AE=Ca these fluctuations start below $T_S$. Co doping preserves the orbital fluctuations while K doping suppresses it. The fluctuations are only seen at those dopings and temperatures where an in-plane resistive anisotropy is known to exist. We predict an in-plane resistive anisotropy of $\rm{Fe_{1+y}Te}$ above $T_S$. Our data are examined in light of the recent work by W.-C. Lee and P. Phillips (arXiv:1110.5917v2). We also study how joule heating in the PCS junctions impacts the spectra. Spectroscopic information is only obtained from those PCS junctions that are free of heating effects while those PCS junctions that are in the thermal regime display bulk resistivity phenomenon.Comment: Accepted for publication in Physical Review

Quantum critical point for stripe order: An organizing principle of cuprate superconductivity

A spin density-wave quantum critical point (QCP) is the central organizing principle of organic, iron-pnictide, heavy-fermion and electron-doped cuprate superconductors. It accounts for the superconducting Tc dome, the non-Fermi-liquid resistivity, and the Fermi-surface reconstruction. Outside the magnetically ordered phase above the QCP, scattering and pairing decrease in parallel as the system moves away from the QCP. Here we argue that a similar scenario, based on a stripe-order QCP, is a central organizing principle of hole-doped cuprate superconductors. Key properties of Eu-LSCO, Nd-LSCO and YBCO are naturally unified, including stripe order itself, its QCP, Fermi-surface reconstruction, the linear-T resistivity, and the nematic character of the pseudogap phase.Comment: Written for a special issue of Physica C on "Stripes and electronic liquid crystal

A Comprehensive Evaluation of Nasal and Bronchial Cytokines and Chemokines Following Experimental Rhinovirus Infection in Allergic Asthma: Increased Interferons (IFN-γ and IFN-λ) and Type 2 Inflammation (IL-5 and IL-13).

BACKGROUND: Rhinovirus infection is a major cause of asthma exacerbations. OBJECTIVES: We studied nasal and bronchial mucosal inflammatory responses during experimental rhinovirus-induced asthma exacerbations. METHODS: We used nasosorption on days 0, 2-5 and 7 and bronchosorption at baseline and day 4 to sample mucosal lining fluid to investigate airway mucosal responses to rhinovirus infection in patients with allergic asthma (n=28) and healthy non-atopic controls (n=11), by using a synthetic absorptive matrix and measuring levels of 34 cytokines and chemokines using a sensitive multiplex assay. RESULTS: Following rhinovirus infection asthmatics developed more upper and lower respiratory symptoms and lower peak expiratory flows compared to controls (all P<0.05). Asthmatics also developed higher nasal lining fluid levels of an anti-viral pathway (including IFN-γ, IFN-λ/IL-29, CXCL11/ITAC, CXCL10/IP10 and IL-15) and a type 2 inflammatory pathway (IL-4, IL-5, IL-13, CCL17/TARC, CCL11/eotaxin, CCL26/eotaxin-3) (area under curve day 0-7, all P<0.05). Nasal IL-5 and IL-13 were higher in asthmatics at day 0 (P<0.01) and levels increased by days 3 and 4 (P<0.01). A hierarchical correlation matrix of 24 nasal lining fluid cytokine and chemokine levels over 7days demonstrated expression of distinct interferon-related and type 2 pathways in asthmatics. In asthmatics IFN-γ, CXCL10/IP10, CXCL11/ITAC, IL-15 and IL-5 increased in bronchial lining fluid following viral infection (all P<0.05). CONCLUSIONS: Precision sampling of mucosal lining fluid identifies robust interferon and type 2 responses in the upper and lower airways of asthmatics during an asthma exacerbation. Nasosorption and bronchosorption have potential to define asthma endotypes in stable disease and at exacerbation