Quantitative Robustness Analysis of Quantum Programs (Extended Version)

Quantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum resources (e.g., qubits) are scarce, classical error correction techniques applied at the level of the architecture are currently cost-prohibitive. But while this reality means that quantum programs are almost certain to have errors, there as yet exists no principled means to reason about erroneous behavior. This paper attempts to fill this gap by developing a semantics for erroneous quantum while-programs, as well as a logic for reasoning about them. This logic permits proving a property we have identified, called $\epsilon$-robustness, which characterizes possible "distance" between an ideal program and an erroneous one. We have proved the logic sound, and showed its utility on several case studies, notably: (1) analyzing the robustness of noisy versions of the quantum Bernoulli factory (QBF) and quantum walk (QW); (2) demonstrating the (in)effectiveness of different error correction schemes on single-qubit errors; and (3) analyzing the robustness of a fault-tolerant version of QBF.Comment: 34 pages, LaTeX; v2: fixed typo

Computer-aided proofs for multiparty computation with active security

Secure multi-party computation (MPC) is a general cryptographic technique that allows distrusting parties to compute a function of their individual inputs, while only revealing the output of the function. It has found applications in areas such as auctioning, email filtering, and secure teleconference. Given its importance, it is crucial that the protocols are specified and implemented correctly. In the programming language community it has become good practice to use computer proof assistants to verify correctness proofs. In the field of cryptography, EasyCrypt is the state of the art proof assistant. It provides an embedded language for probabilistic programming, together with a specialized logic, embedded into an ambient general purpose higher-order logic. It allows us to conveniently express cryptographic properties. EasyCrypt has been used successfully on many applications, including public-key encryption, signatures, garbled circuits and differential privacy. Here we show for the first time that it can also be used to prove security of MPC against a malicious adversary. We formalize additive and replicated secret sharing schemes and apply them to Maurer's MPC protocol for secure addition and multiplication. Our method extends to general polynomial functions. We follow the insights from EasyCrypt that security proofs can be often be reduced to proofs about program equivalence, a topic that is well understood in the verification of programming languages. In particular, we show that in the passive case the non-interference-based definition is equivalent to a standard game-based security definition. For the active case we provide a new NI definition, which we call input independence

Preface Volume 30, Issue 3

AbstractOne of the main areas of research in logic programming is the design and implementation of sequential and parallel (constraint) logic programming systems. This research goes broadly from the design and specification of novel implementation technology to its actual evaluation in real life situations. A series of workshops on Implementations of Logic Programming Systems, previously held in Budapest (1993), Ithaca (1994), Portland (1995), Bonn (1996), Port Jefferson (1997), Manchester (1998) and Las Cruces (1999) provided a forum for ongoing research on the design and implementation of sequential and parallel (constraint) logic programming systems.This volume contains a collection of papers presented at the Workshop on Parallelism and Implementation Technology for (Constraint) Logic Programming, held in Las Cruces on December 1st, 1999, in conjunction with ICLP'99. The workshop was sponsored and organised by COMPULOG AMERICAS. The workshop also received support from the Association for Logic Programming and from the Department of Computer Science, New Mexico State University.Papers from both academia and industry were invited. Preference was given to the analysis and description of implemented systems (or currently under implementation) and their associated techniques, problems found in their development or design, and steps taken towards the solution of these problems.Topics included, but were not limited to: •standard and non—standard sequential implementation schemes (e.g., generalization/modification of WAM, translation to C, etc.);implementation of parallel logic programming systems;balance between compile-time effort and run-time machinery;techniques for the implementation of different declarative programming paradigms based on, or extending, logic programming (e.g., constraint logic programming, concurrent constraint languages, equational-logic languages);performance evaluation of sequential and parallel logic programming systems, both through benchmarking and using real world applications;other implementation-related issues, such as memory management, register allocation, use of global optimisations, etc.We were very fortunate to have so many interesting research papers, ranging over widely different subjects and giving a broad coverage of current research in sequential and parallel implementation of logic programming systems. Papers on sequential logic programming systems, focus on varied topics: constraint evaluation, support for extensions to logic programming, and abstract machines for performance evaluation. Papers on parallel logic programming systems also focus on diverse topics ranging from distributed implementations, garbage collection, to optimisations for exploiting and-or parallelism.The editors would like to thank all authors that chose to submit their work to this book, and also for their cooperation in making this document possible. We would also like to thank all referees involved in assessing the papers in this special volume.This volume will be published as volume 30, Issue 3 in the series Electronic Notes in Theoretical Computer Science (ENTCS). This series is published electronically through the facilities of Elsevier Science B.V. and its auspices. The volumes in the ENTCS series can be accessed at the URL http://www.elsevier.nl/locate/entcs March 14, 2000Horst Reiche

A syntactic analysis of the Portela Urbanization using prolog

Portela is a paradigmatic modern housing complex located at the vicinity of Lisbon. Developed since the late 1960s, it combines several syntactic schemes, namely, concentric towers, asymmetric blocks and primary open-closed cells typically distributed along a ring-shaped road. It is also structured by a central space with a mall and other facilities. In this paper we introduce Prolog, a Logic Programming language used in Artificial Intelligence, to describe the internal logic of Portela Urbanization. Firstly, we explain how the syntactic schemes present in Portela can be generated in a recursive way using Prolog and following an approach like the ideographic language introduced by Bill Hillier and Julienne Hanson in their seminal book The Social Logic of Space (1984). Secondly, we performed a settlement (alpha) analysis of Portela by computing connectivity, control, depth, integration and other syntactic measures using Prolog predicates. These two complementary approaches proved to be useful to understand the ideal of the Modern city as far as the Portela complex is concerned. And show how Logic Programming is a useful tool to describe the patterns of discrete systems as social knowables due to its declarative nature. In fact, a Prolog program represents a certain amount of knowledge, namely, of an urban settlement (or building), which is used to answer queries about the social and economic consequences of some spatial design.info:eu-repo/semantics/publishedVersio

Modular Constraint Solver Cooperation via Abstract Interpretation

Cooperation among constraint solvers is difficult because different solving paradigms have different theoretical foundations. Recent works have shown that abstract interpretation can provide a unifying theory for various constraint solvers. In particular, it relies on abstract domains which capture constraint languages as ordered structures. The key insight of this paper is viewing cooperation schemes as abstract domains combinations. We propose a modular framework in which solvers and cooperation schemes can be seamlessly added and combined. This differs from existing approaches such as SMT where the cooperation scheme is usually fixed (e.g., Nelson-Oppen). We contribute to two new cooperation schemes: (i) interval propagators completion that allows abstract domains to exchange bound constraints, and (ii) delayed product which exchanges over-approximations of constraints between two abstract domains. Moreover, the delayed product is based on delayed goal of logic programming, and it shows that abstract domains can also capture control aspects of constraint solving. Finally, to achieve modularity, we propose the shared product to combine abstract domains and cooperation schemes. Our approach has been fully implemented, and we provide various examples on the flexible job shop scheduling problem. Under consideration for acceptance in TPLP.Comment: Paper presented at the 36th International Conference on Logic Programming (ICLP 2020), University Of Calabria, Rende (CS), Italy, September 2020, 17 pages. v2: Fix an example in Section 3.2 (improved closure

Quantum Picturalism

The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the arrays of 0s and 1s of the early days of computer programming practice. In this review we present steps towards a diagrammatic `high-level' alternative for the Hilbert space formalism, one which appeals to our intuition. It allows for intuitive reasoning about interacting quantum systems, and trivialises many otherwise involved and tedious computations. It clearly exposes limitations such as the no-cloning theorem, and phenomena such as quantum teleportation. As a logic, it supports `automation'. It allows for a wider variety of underlying theories, and can be easily modified, having the potential to provide the required step-stone towards a deeper conceptual understanding of quantum theory, as well as its unification with other physical theories. Specific applications discussed here are purely diagrammatic proofs of several quantum computational schemes, as well as an analysis of the structural origin of quantum non-locality. The underlying mathematical foundation of this high-level diagrammatic formalism relies on so-called monoidal categories, a product of a fairly recent development in mathematics. These monoidal categories do not only provide a natural foundation for physical theories, but also for proof theory, logic, programming languages, biology, cooking, ... The challenge is to discover the necessary additional pieces of structure that allow us to predict genuine quantum phenomena.Comment: Commissioned paper for Contemporary Physics, 31 pages, 84 pictures, some colo

Математические модели схем компромисса в многокритериальных задачах математического программирования с размытыми ограничениями

Сформульовано однокритеріальні та багатокритеріальні задачі математичного програмування з розмитими обмеженнями як задачі векторної оптимізації. Розглядаються постановки, математичні моделі, схеми компромісу, критерії ефективності та методи розв’язання сформульованих задач. Функції обліку втрат у випадку порушення окремих обмежень задачі запропоновано у формі функцій приналежності Fuzzy-Logic. Розглянуто методи нормалізації локальних критеріїв. Наведено алгоритми і обчислювальні схеми розв’язання цих задач при виборі розв’язків із кінцевої множини альтернатив, які ілюструються числовим прикладом.Single- and multicriteria problems of mathematical programming with fuzzy constraints are formulated as vector optimization problems. Formulations of such problems, their mathematical models, compromise schemes, efficiency criteria, and solution methods are considered. Fuzzy-Logic functions are offered to represent losses from violations of some boundary conditions; methods of normalization of local criteria are given. Algorithms and computational schemes for choosing a solution from a finite set of alternatives are illustrated by an example