Proof Of Consistency Research Articles

Verification of Implementations of Cryptographic Hash Functions

Cryptographic hash functions have become the basis of modern network computing for identity authorization and secure computing; protocol consistency of cryptographic hash functions is one of the most important properties that affect the security and correctness of cryptographic implementations, and protocol consistency should be well proven before being applied in practice. Software verification has seen substantial application in safety-critical areas and has shown the ability to deliver better quality assurance for modern software; thus, applying software verification to a protocol consistency proof for cryptographic hash functions is a reasonable approach to prove their correctness. Verification of protocol consistency of cryptographic hash functions includes modeling of the cryptographic protocol and program analysis of the cryptographic implementation; these require a dedicated cryptographic implementation model that preserves the semantics of the code, efficient analysis of cryptographic operations on arrays and bits, and the ability to verify large-scale implementations. In this paper, we propose a fully automatic software verification framework, VeriHash, that brings software verification to protocol consistency proofs for cryptographic hash function implementations. It solves the above challenges by introducing a novel cryptographic model design for modeling the semantics of cryptographic hash function implementations, extended array theories for analysis of operations, and compositional verification for scalability. We evaluated our verification framework on two SHA-3 cryptographic hash function implementations: the winner of the NIST SHA-3 competition, Keccack; and an open-source hash program, RHash. We successfully verified the core parts of the two implementations and reproduced a bug in the published edition of RHash.

Risk assessment heuristics: Cues and intention to use a condom in casual sex

Objective: This study examined the relationship between three heuristic cues (consistency, liking and social proof) and condom use in casual sex relationships utilising the theory of planned behaviour. Participants: Totally, 388 US college students were surveyed. Method: Three vignettes for each cue primed students to project their willingness to use a condom during casual sex encounters. Results: Repeated-measures multivariate analysis of covariance (MANCOVA) revealed that the cues exerted significant main effects on attitude ( F(5, 1,935) = 6.16, p < .001), subjective norms ( F(5, 1,930) = 5.626, p < .001), perceived behavioural control ( F(5, 1,935) = 8.51, p < .001) and behavioural intentions ( F(5, 1,930) = 2.44, p = .033). Post hoc analysis revealed condom avoidance behavioural intentions were more likely for the vignette depicting social proof ( M = −1.26, standard deviation [ SD] = 1.08). Conclusion: Findings indicate that heuristic cues influence college students’ condom use intentions, and prevention programmes should incorporate cues to increase effectiveness.

VON NEUMANN’S CONSISTENCY PROOF

AbstractWe consider the consistency proof for a weak fragment of arithmetic published by von Neumann in 1927. This proof is rather neglected in the literature on the history of consistency proofs in the Hilbert school. We explain von Neumann’s proof and argue that it fills a gap between Hilbert’s consistency proofs for the so-called elementary calculus of free variables with a successor and a predecessor function and Ackermann’s consistency proof for second-order primitive recursive arithmetic. In particular, von Neumann’s proof is the first rigorous proof of the consistency of an axiomatization of the first-order theory of a successor function.

Realization of a timescale with an accurate optical lattice clock

Optical clocks are not only powerful tools for prime fundamental research, but are also deemed for the re-definition of the SI base unit second as they now surpass the performance of caesium atomic clocks in both accuracy and stability by more than an order of magnitude. However, an important obstacle in this transition has so far been the limited reliability of the optical clocks that made a continuous realization of a timescale impractical. In this paper, we demonstrate how this situation can be resolved and that a timescale based on an optical clock can be established that is superior to one based on even the best caesium fountain clocks. The paper also gives further proof of the international consistency of strontium lattice clocks on the $10^{-16}$ accuracy level, which is another prerequisite for a change in the definition of the second.

Partitioning estimation of local variance based on nearest neighbors under censoring

In a nonparametric and heteroscedastic setting, our primary interest is in the local variance estimation when the response variable is subject to right censoring. For the proposed partitioning local variance estimators, based on the first and second nearest neighbors, some transformations on the observed censoring times are involved, using their estimated survival functions. Proofs of consistency and rate of convergence for the presented estimators are given. Moreover, local variance estimation is demonstrated on the basis of real survival data.

Formal Specification and Verification of Few Combined Fragments of UML Sequence Diagram

UML has become a de-facto standard for design and development of object-oriented systems. On the other hand, UML includes various diagrams and notations which are missing of formal semantics. There does not exist much work to transform completely UML models to executable codes by any of the computer-aided software engineering tools because of the hidden semantics under the UML diagrams. Moreover, UML models cannot be used for automated analysis for validation and verification of the systems. Therefore, an integration of UML and semantics-based techniques such as formal methods is required to overcome such type of issues. Further, proof of correctness of software models plays a key role to ensure the quality of the final system to be developed. This paper presents a systematic method for transformation and verification of UML sequence diagrams into Z specification. The method works by translating and analysing few important combined fragments of sequence diagrams using Z notation. At first, formal specification of primary constructs is provided by capturing the hidden semantics under the diagram. Formal analysis of interaction operators namely options, alternatives, loops and break of the fragments is provided. The combined fragments are important because it allows multiple scenarios to increase an expressive power of sequence diagram by various control flows. Finally, formal analysis is provided by Z/Eves tool to check the syntax, type and proof for consistency and correctness of the specification.

A Common Rationale for Global Sensitivity Measures and Their Estimation.

Measures of sensitivity and uncertainty have become an integral part of risk analysis. Many such measures have a conditional probabilistic structure, for which a straightforward Monte Carlo estimation procedure has a double-loop form. Recently, a more efficient single-loop procedure has been introduced, and consistency of this procedure has been demonstrated separately for particular measures, such as those based on variance, density, and information value. In this work, we give a unified proof of single-loop consistency that applies to any measure satisfying a common rationale. This proof is not only more general but invokes less restrictive assumptions than heretofore in the literature, allowing for the presence of correlations among model inputs and of categorical variables. We examine numerical convergence of such an estimator under a variety of sensitivity measures. We also examine its application to a published medical case study.

Penalized maximum likelihood estimation for Gaussian hidden Markov models

ABSTRACTThe likelihood function of a Gaussian hidden Markov model is unbounded, which is why the maximum likelihood estimator (MLE) is not consistent. A penalized MLE is introduced along with a rigorous consistency proof.

1階算術に対するゲンツェンの1935年版無矛盾性証明がもつ哲学的意義

Gentzen remarked that one of the aims of his 1935/36 consistency proofs for first-order arithmetic was to give a “finitist” interpretation for the implication-formulas in first-order arithmetic. He imposed the following requirement on such an interpretation: a “finitist” interpretation for the implication-formulas must be able to avoid the circularity of implication that was urged by himself. However, Gentzen did not present his “finitist” interpretation explicitly. Moreover, he gave no argument for its non-circularity. In this paper, first we formulate an interpretation for the implication-formulas in first-order arithmetic by using Gentzen’s 1935 consistency proof. Next, we argue that this interpretation avoids the circularity urged by Gentzen.

FROM STENIUS’ CONSISTENCY PROOF TO SCHÜTTE’S CUT ELIMINATION FOR ω-ARITHMETIC

AbstractThe book Das Interpretationsproblem der Formalisierten Zahlentheorie und ihre Formale Widerspruchsfreiheit by Erik Stenius published in 1952 contains a consistency proof for infinite ω-arithmetic based on a semantical interpretation. Despite the proof’s reference to semantics the truth definition is in fact equivalent to a syntactical derivability or reduction condition. Based on this reduction condition Stenius proves that the complexity of formulas in a derivation can be limited by the complexity of the conclusion. This independent result can also be proved by cut elimination for ω-arithmetic which was done by Schütte in 1951.In this paper we interpret the syntactic reduction in Stenius’ work as a method for cut elimination based on invertibility of the logical rules. Through this interpretation the constructivity of Stenius’ proof becomes apparent. This improvement was explicitly requested from Stenius by Paul Bernays in private correspondence (In a letter from Bernays begun on the 19th of September 1952 (Stenius & Bernays, 1951–75)). Bernays, who took a deep interest in Stenius’ manuscript, applied the described method in a proof Herbrand’s theorem. In this paper we prove Herbrand’s theorem, as an application of Stenius’ work, based on lecture notes of Bernays (Bernays, 1961). The main result completely resolves Bernays’ suggestions for improvement by eliminating references to Stenius’ semantics and by showing the constructive nature of the proof. A comparison with Schütte’s cut elimination proof shows how Stenius’ simplification of the reduction of universal cut formulas, which in Schütte’s proof requires duplication and repositioning of the cuts, shifts the problematic case of reduction to implications.

Maximum Likelihood Phylogenetic Inference is Consistent on Multiple Sequence Alignments, with or without Gaps.

We prove that maximum likelihood phylogenetic inference is consistent on gapped multiple sequence alignments (MSAs) as long as substitution rates across each edge are greater than zero, under mild assumptions on the structure of the alignment. Under these assumptions, maximum likelihood will asymptotically recover the tree with edge lengths corresponding to the mean number of substitutions per site on each edge. This refutes Warnow's recent suggestion (Warnow 2012) that maximum likelihood phylogenetic inference might be statistically inconsistent when gaps are treated as missing data, even if the MSA is correct. We also derive a simple new proof of maximum likelihood consistency of ungapped alignments.

The parallel replica method for computing equilibrium averages of Markov chains

Abstract An algorithm is proposed for computing equilibrium averages of Markov chains which suffer from metastability – the tendency to remain in one or more subsets of state space for long time intervals. The algorithm, called the parallel replica method (or ParRep), uses many parallel processors to explore these subsets more efficiently. Numerical simulations on a simple model demonstrate consistency of the method. A proof of consistency is given in an idealized setting. The parallel replica method can be considered a generalization of A. F. Voter's parallel replica dynamics, originally developed to efficiently simulate metastable Langevin stochastic dynamics.

Consistency of Probability Measure Quantization by Means of Power Repulsion–Attraction Potentials

This paper is concerned with the study of the consistency of a variational method for probability measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The proof of consistency is based on the construction of a target energy functional whose unique minimizer is actually the given probability measure $$\omega $$ to be quantized. Then we show that the discrete functionals, defining the discrete quantizers as their minimizers, actually $$\Gamma $$ -converge to the target energy with respect to the narrow topology on the space of probability measures. A key ingredient is the reformulation of the target functional by means of a Fourier representation, which extends the characterization of conditionally positive semi-definite functions from points in generic position to probability measures. As a byproduct of the Fourier representation, we also obtain compactness of sublevels of the target energy in terms of uniform moment bounds, which already found applications in the asymptotic analysis of corresponding gradient flows. To model situations where the given probability is affected by noise, we further consider a modified energy, with the addition of a regularizing total variation term and we investigate again its point mass approximations in terms of $$\Gamma $$ -convergence. We show that such a discrete measure representation of the total variation can be interpreted as an additional nonlinear potential, repulsive at a short range, attractive at a medium range, and at a long range not having effect, promoting a uniform distribution of the point masses.

On asymptotics related to classical inference in stochastic differential equations with random effects

Delattre et al. (2013) considered n independent stochastic differential equations (SDE’s), where in each case the drift term is associated with a random effect, the distribution of which depends upon unknown parameters. Assuming the independent and identical (iid) situation the authors provide independent proofs of weak consistency and asymptotic normality of the maximum likelihood estimators (MLE’s) of the hyper-parameters of their random effects parameters.In this article, as an alternative route to proving consistency and asymptotic normality in the SDE set-up involving random effects, we verify the regularity conditions required by existing relevant theorems. In particular, this approach allowed us to prove strong consistency under weaker assumption. But much more importantly, we further consider the independent, but non-identical set-up associated with the random effects based SDE framework, and prove asymptotic results associated with the MLE’s.

The structure of steady, relativistic, magnetized jets with rotation

We present equilibrium models of relativistic magnetized, infinite, axisymmetric jets with rotation propagating through an homogeneous, unmagnetized ambient medium at rest. The jet models are characterized by six functions defining the radial profiles of density, pressure, and the toroidal and axial components of velocity and magnetic field. Fixing the ambient pressure and the jet rest-mass density and axial components of the flow velocity and magnetic field, we analyse the influence of the toroidal magnetic field and several rotation laws on the structure of the equilibrium models. Our approach excludes by construction the analysis of the self-consistently magnetically launched jet models or the force-free equilibrium solutions. Several forbidden regions in the magnetic pitch angle/magnetization plane are found where models of the class considered in our study could not be settled. These forbidden regions are associated with the existence of maximum axial and toroidal magnetic field components compatible with the prescribed equilibrium condition at the jet surface, and/or an excess of centrifugal force producing gaps with negative pressures in the jet. The present study can be easily extended to jet models with different transversal profiles and magnetic field configurations. In the last part of the paper, we test the ability of our relativistic magnetohydrodynamics (RMHD) code to maintain steady equilibrium models of axisymmetric RMHD jets in one and two spatial dimensions. The one-dimensional numerical simulations serve also as a consistency proof of the fidelity of the analytical steady solutions discussed in the first part of the paper. The present study allows us to build initial equilibrium jet models with selected properties for dynamical (and emission) simulations of magnetized relativistic jets with rotation.

Examining the Principles of Influence on Safer Sex Communication During Casual and Committed Sexual Encounters

Teens and young people are at risk for contracting sexually transmitted infections. Understanding how relationship context may moderate the effectiveness of safer sex communication strategies among this demographic is important information for practitioners striving to promote safer sex behaviors. In this study, focus groups (N = 9) with college students were conducted and analyzed to examine the relation between 6 principles of influence (authority, consistency, liking, reciprocity, scarcity, and social proof) and safer sex communication during committed and casual sexual encounters. Results revealed that with the exceptions of social proof and consistency, the principles of influence were endorsed more frequently for casual than committed sexual encounters. For casual sexual encounters, the principles of authority, reciprocity, and scarcity arose as influential principles. For committed sexual encounters, the principles of consistency, liking, and reciprocity arose as influential principles. These results are discussed with an emphasis on the theoretical and practical implications.

Predicativity, the Russell-Myhill Paradox, and Church’s Intensional Logic

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other axioms of Church’s intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin’s intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions.

The middle ground-ancestral logic

Many efforts have been made in recent years to construct formal systems for mechanizing general mathematical reasoning. Most of these systems are based on logics which are stronger than first-order logic (FOL). However, there are good reasons to avoid using full second-order logic (SOL) for this task. In this work we investigate a logic which is intermediate between FOL and SOL, and seems to be a particularly attractive alternative to both: ancestral logic. This is the logic which is obtained from FOL by augmenting it with the transitive closure operator. While the study of this logic has so far been mostly model-theoretical, this work is devoted to its proof theory (which is much more relevant for the task of mechanizing mathematics). Two natural Gentzen-style proof systems for ancestral logic are presented: one for the reflexive transitive closure, and one for the non-reflexive one. We show that these systems are sound for ancestral logic and provide evidence that they indeed encompass all forms of reasoning for this logic that are used in practice. The two systems are shown to be equivalent by providing translation algorithms between them. We end with an investigation of two main proof-theoretical properties: cut elimination and constructive consistency proof.

More on explicit estimators for a banded covariance matrix

The problem of estimating mean and covariances of a multivariate normally distributed random vector has been studied in many forms. This paper focuses on the estimators proposed by Ohlson et al. (2011) for a banded covariance structure with m-dependence. We rewrite the estimator when m = 1, which makes it easier to analyze. This leads to an adjustment, and an unbiased estimator can be proposed. A new and easier proof of consistency is then presented.This theory is also generalized to a general linear model where the corresponding theorems and propositions are stated to establish unbiasedness and consistency.

A general proof of consistency of heuristic classification for cognitive diagnosis models

The Asymptotic Classification Theory of Cognitive Diagnosis (Chiu et al., 2009, Psychometrika, 74, 633-665) determined the conditions that cognitive diagnosis models must satisfy so that the correct assignment of examinees to proficiency classes is guaranteed when non-parametric classification methods are used. These conditions have only been proven for the Deterministic Input Noisy Output AND gate model. For other cognitive diagnosis models, no theoretical legitimization exists for using non-parametric classification techniques for assigning examinees to proficiency classes. The specific statistical properties of different cognitive diagnosis models require tailored proofs of the conditions of the Asymptotic Classification Theory of Cognitive Diagnosis for each individual model – a tedious undertaking in light of the numerous models presented in the literature. In this paper a different way is presented to address this task. The unified mathematical framework of general cognitive diagnosis models is used as a theoretical basis for a general proof that under mild regularity conditions any cognitive diagnosis model is covered by the Asymptotic Classification Theory of Cognitive Diagnosis.