scholarly journals Higher-order probabilistic adversarial computations: categorical semantics and program logics

2021 ◽  
Vol 5 (ICFP) ◽  
pp. 1-30
Author(s):  
Alejandro Aguirre ◽  
Gilles Barthe ◽  
Marco Gaboardi ◽  
Deepak Garg ◽  
Shin-ya Katsumata ◽  
...  
Keyword(s):  
Higher Order ◽  
General Notion ◽  
Memory Footprint ◽  
Resource Policy ◽  
Expected Values ◽  
Error Probabilities ◽  
The Cost ◽  
Relational Logic ◽  
Categorical Semantics ◽  
Develop Program

Adversarial computations are a widely studied class of computations where resource-bounded probabilistic adversaries have access to oracles, i.e., probabilistic procedures with private state. These computations arise routinely in several domains, including security, privacy and machine learning. In this paper, we develop program logics for reasoning about adversarial computations in a higher-order setting. Our logics are built on top of a simply typed λ-calculus extended with a graded monad for probabilities and state. The grading is used to model and restrict the memory footprint and the cost (in terms of oracle calls) of computations. Under this view, an adversary is a higher-order expression that expects as arguments the code of its oracles. We develop unary program logics for reasoning about error probabilities and expected values, and a relational logic for reasoning about coupling-based properties. All logics feature rules for adversarial computations, and yield guarantees that are valid for all adversaries that satisfy a fixed resource policy. We prove the soundness of the logics in the category of quasi-Borel spaces, using a general notion of graded predicate liftings, and we use logical relations over graded predicate liftings to establish the soundness of proof rules for adversaries. We illustrate the working of our logics with simple but illustrative examples.

scholarly journals Analysis of the Fee-to-Tax Reform on Water Resources in China

2021 ◽  
Author(s):  
Zi-rui Chen ◽  
Pu-yan Nie
Keyword(s):  
Water Resources ◽  
Water Resource ◽  
Tax Reform ◽  
Low Cost ◽  
Production Capacity ◽  
Cost Difference ◽  
Tax Rate ◽  
Leading Position ◽  
Resource Policy ◽  
The Cost

Abstract Background: The Resource Tax Law has been officially implemented on September 1, 2020 in China. This law presents the “Fee-to-Tax” reform of water resources. Methods: This article compares the effects of the “Fee-to-Tax” reform under an asymmetric duopoly with perfect information. Results: First, an analysis when all firms simultaneously respond to the water resource policy is conducted. The mechanisms of the two policies are different: the water resource fee affects output by reducing market size, while the water resource tax reduces output by amplifying the weighted cost difference effects between companies. It is shown that the tax works better than the fee for eliminating backward production capacity. Then, a comparison of the situation when companies respond sequentially is carried out. When a low-cost firm is in the leading position, the collection of fees actually reduces the output difference, whereas the tax improves it. When a high-cost firm acts as a leader, the effects depend on the cost difference. When the cost difference between firms is small, the first-move advantage of high-cost firms dominates the cost advantages of low-cost firms. Therefore, a higher tax rate yields a smaller output difference. Conclusions: When cost differences are relatively larger, the cost advantage of low-cost firms dominates the first-move advantage of high-cost firms. Therefore, the “Fee-to-Tax” reform provides some benefits to maintain the environmental development of some water-mining or related industries.

Modeling of Long-Range Reverberation Signal for Rough Bottom Consisting of Polygon Facets

2018 ◽  
Vol 26 (04) ◽  
pp. 1850041
Author(s):  
Youngmin Choo ◽  
Woojae Seong
Keyword(s):  
Long Range ◽  
Order Approximation ◽  
Higher Order ◽  
Ocean Bottom ◽  
Analytic Surface ◽  
Surface Integral ◽  
Computational Burden ◽  
Analytic Integration ◽  
The Cost ◽  
Delay Difference

To acquire a stable reverberation signal from an irregular ocean bottom, we derive the analytic surface integral of a scattered signal using Stokes’ theorem while approximating the bottom using a combination of polygon facets. In this approach, the delay difference in the elemental scattering area is considered, while the representative delay is used for the elemental scattering area in the standard reverberation model. Two different reverberation models are applied to a randomly generated rough bottom, which is composed of triangular facets. Their results are compared, and the scheme using analytic integration shows a converged reverberation signal, even with a large elemental scattering area, at the cost of an additional computational burden caused by a higher order approximation in the surface integral of the scattered signals.

scholarly journals Continuous Distribution Approximation and Thresholds Optimization in Serial Multi-Modal Biometric Systems

2016 ◽  
Vol 11 (5) ◽  
pp. 720
Author(s):  
Milan Stanojević, ◽  
Ivan Milenković ◽  
Dušan Starčević ◽  
Bogdana Stanojević
Keyword(s):  
Continuous Distribution ◽  
Rejection Rate ◽  
Biometric Verification ◽  
Biometric Systems ◽  
Expected Values ◽  
Thresholds Optimization ◽  
Error Probabilities ◽  
Verification Systems ◽  
And Control ◽  
Score Distributions

Multi-modal biometric verification systems use information from several biometric modalities to verify an identity of a person. The false acceptance rate (FAR)and false rejection rate (FRR) are metrics generally used to measure the performance of such systems.In this paper, we first approximate the score distributions of both genuine users and impostors by continuous distributions. Then we incorporate the exact expressions of the distributions in the formulas for the expected values of both FAR and FRR for each matcher. In order to determine the upper and lower acceptance thresholds in the sequential multi-modal biometric matching, we further minimize the expected values of FAR and FRR for the entire processing chain. We propose a non-linear bi-objective programming problem whose objective functions are the two error probabilities. We analyze the efficient set of the bi-objective problem, and derive an efficient solution as a best compromise between the error probabilities. Replacing the least squares approximation of the score distributions by a continuous distributionapproximation, this approach modifies the method presented in Stanojević et al. [15] (doi: 10.1109/ICCCC.2016.7496752) (a).The results of our experiments showed a good performance of the sequential multiple biometric matching system based on continuous distribution approximation and optimized thresholds.(a)Reprinted (partial) and extended, with permission based on License Number3938230385072 © [2016] IEEE, from "Computers Communications and Control (ICCCC), 2016 6th International Conference on".

A General Notion of Realizability

2002 ◽  
Vol 8 (2) ◽  
pp. 266-282
Author(s):  
Lars Birkedal
Keyword(s):  
Predicate Logic ◽  
Higher Order ◽  
Order Logic ◽  
General Notion ◽  
Higher Order Logic ◽  
Cartesian Closed Categories ◽  
Cartesian Closed

AbstractWe present a general notion of realizability encompassing both standard Kleene style realizability over partial combinatory algebras and Kleene style realizability over more general structures, including all partial cartesian closed categories. We show how the general notion of realizability can be used to get models of dependent predicate logic, thus obtaining as a corollary (the known result) that the category Equ of equilogical spaces models dependent predicate logic. Moreover, we characterize when the general notion of realizability gives rise to a topos, i.e., a model of impredicative intuitionistic higher-order logic.

scholarly journals A relational logic for higher-order programs

2017 ◽  
Vol 1 (ICFP) ◽  
pp. 1-29 ◽  
Author(s):  
Alejandro Aguirre ◽  
Gilles Barthe ◽  
Marco Gaboardi ◽  
Deepak Garg ◽  
Pierre-Yves Strub
Keyword(s):  
Higher Order ◽  
Relational Logic

Categorical semantics for higher order polymorphic lambda calculus

1987 ◽  
Vol 52 (4) ◽  
pp. 969-989 ◽  
Author(s):  
R. A. G. Seely
Keyword(s):  
Lambda Calculus ◽  
Higher Order ◽  
Algebraic Semantics ◽  
Categorical Structure ◽  
Categorical Semantics ◽  
Definitional Extension

AbstractA categorical structure suitable for interpreting polymorphic lambda calculus (PLC) is defined, providing an algebraic semantics for PLC which is sound and complete. In fact, there is an equivalence between the theories and the categories. Also presented is a definitional extension of PLC including “subtypes”, for example, equality subtypes, together with a construction providing models of the extended language, and a context for Girard's extension of the Dialectica interpretation.

scholarly journals New high order FDTD method to solve EMC problems

2015 ◽  
Vol 4 (2) ◽  
pp. 17 ◽  
Author(s):  
N. Deymier ◽  
T. Volpert ◽  
X. Ferrieres ◽  
V. Mouysset ◽  
B. Pecqueux
Keyword(s):  
Electromagnetic Compatibility ◽  
Numerical Approximation ◽  
Fdtd Method ◽  
Higher Order ◽  
Small Cell ◽  
Small Cell Size ◽  
Dg Method ◽  
The Time Domain ◽  
Spatial Approximation ◽  
The Cost

In electromagnetic compatibility (EMC) context, we are interested in developing new ac- curate methods to solve efficiently and accurately Maxwell’s equations in the time domain. Indeed, usual methods such as FDTD or FVTD present im- portant dissipative and/or dispersive errors which prevent to obtain a good numerical approximation of the physical solution for a given industrial scene unless we use a mesh with a very small cell size. To avoid this problem, schemes like the Discontinuous Galerkin (DG) method, based on higher order spa- tial approximations, have been introduced and stud- ied on unstructured meshes. However the cost of this kind of method can become prohibitive accord- ing to the mesh used. In this paper, we first present a higher order spatial approximation method on carte- sian meshes. It is based on a finite element ap- proach and recovers at the order 1 the well-known Yee’s schema. Next, to deal with EMC problem, a non-oriented thin wire formalism is proposed for this method. Finally, several examples are given to present the benefits of this new method by compar- ison with both Yee’s schema and DG approaches.

Reducing the Cost of Higher-Order Mutation Testing

2018 ◽  
Vol 43 (12) ◽  
pp. 7473-7486
Author(s):  
Ahmed S. Ghiduk ◽  
Moheb R. Girgis ◽  
Marwa H. Shehata
Keyword(s):  
Mutation Testing ◽  
Higher Order ◽  
The Cost
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