The Computational SLR: A Logic for Reasoning about Computational Indistinguishability

In this paper, we provide a simple recursive programming language with a semantics and a formal proof system, along the lines of [5], [17] and [23]. We show that the semantics used is the “best” possible if one admits the validity of Algol's copy rule, and that the proof system is complete with respect to the semantics. The definitions and methods used are meant to provide a basis for a broader theory of program schemas, which models parallel as well as sequential programs.

The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. This paper studies a deductive inference method for PC(ID), its propositional fragment.We introduce a formal proof system based on the sequent calculus (Gentzen-style deductive system) for this logic. As PC(ID) is an integration of classical propositional logic and propositional inductive definitions, our deductive system integrates inference rules for propositional calculus and definitions.We prove the soundness and completeness of this deductive system for a slightly restricted fragment of PC(ID). We also give a counter-example to show that cut-elimination does not hold in this proof system.

A non-interactive zero-knowledge proof system (NIZK) for a composite language (i.e., a language that combines distinct statements by AND or OR) is widely used in cryptographic applications. The (im)possibility of black-box constructions of such NIZKs has been studied so far. We extend it to the case of proving equality of a witness behind distinct statements that often plays a central role in cryptographic constructions as illustrated by the seminal work by Naor and Yung (STOC, 1990). In this paper, we investigate the impossibility of a black-box construction of NIZKs for equality of witnesses from those proving the validity of the witnesses. Concretely, we prove that there exists no black-box construction of NIZKs for equality of plaintexts in two distinct ciphertexts of public-key encryption schemes based on NIZKs for proving validity of ciphertexts. It implies that one has to exploit specific properties of the underlying encryption schemes or NIZKs to construct NIZKs for proving equality, and hence justifies existing constructions.

In this paper we explore a mechanized verification of the NTRUEncrypt scheme, with the formal proof system Isabelle/HOL. More precisely, the functional correctness of this algorithm, in its reduced form, is formally verified with computer support. We show that this scheme is correct what is a necessary condition for the usefulness of any cryptographic encryption scheme. Besides, we present a convenient and application specific formalization of the NTRUEncrypt scheme in the Isabelle/HOL system that can be used in further study around the functional and security analysis of NTRUEncrypt family. Index Terms—Public key encryption, Lattice, NTRUEncrypt, Formal proof system, Higher order logic, Formal verification, Isabelle/HOL, Theorem proving, Proof assistant.

This chapter deals with fuzzy logic in Zadeh’s ‘narrow sense’ [27], pointing to t-norm based truth functional logics, where the truth values model ‘degrees of truth’, identified with reals from the unit interval [0,1]. In particular, we are interested in Łukasiewicz logic Ł and some of its variants, but also in Godel logic G, and in Product logic P. The literature on formal deduction systems for these and related many-valued logics is vast and even more has been written about their algebraic background. We refer to the monographs [23], [22], and [10] for more information and references. Most authors take the usefulness of these logics in the context of approximate reasoning, i.e., reasoning with vague and imprecise notions for granted. However the corresponding proof systems are hardly ever explicitly related to models of correct reasoning with vague information. In other words: the challenge to derive particular fuzzy logics from first principles about approximate reasoning is not addressed explicitly. The reference to general models of reasoning and to theories of vagueness – a prolific discourse in contemporary analytic philosophy – is only implicit, if not simply missing, in most presentations of inference systems for fuzzy logics. Some notable exceptions, where an explicit semantic foundation for particular fuzzy logics is aimed at, are: Ruspini’s similarity semantics [35]; voting semantics [25]; ‘re-randomizing semantics’ [24]; measurement-theoretic justifications [7]; the Ulam-Renyi game based interpretation of D. Mundici [29]; and ‘acceptability semantics’ of J. Paris [31]. As we have argued elsewhere [12], these formal semantics for various t-norm based logics (in particular Łukasiewicz logic) should be placed in the wider discourse about adequate theories of vagueness, a prolific subfield of analytic philosophy.

When the beginner approaches the study of politics, one of the most natural questions for him to ask is: what is it that political science studies? This is a way of asking what is the political scientist's conception of reality. More often than not, the teacher finds the student looking for an objective physical structure, simplified yet concrete, like the astronomer's reduced-scale construction of the solar system, the biologist's photographic reproduction of microscopic cellular organisms, or the physicist's diagram of atomic structure. It is important for the student of human affairs to realize that while individuals, small groups, mass meetings, and even whole cities can be photographed or diagrammed, social scientists have never succeeded in reproducing satisfactory physical models of such concepts as personality, social structure, bureaucratic organization, the price system, or government. Nor do the ends and criteria of government, like order, justice, freedom, welfare or security, lend themselves to analysis in terms of physical or chemical elements like oxygen, carbon, iron, or uranium. Perhaps the closest physical analogy to politics and government is an automobile engine or an electric power plant; but no one would claim that the driver of a car has learned the principles of the engine if all he knows is how to operate it, any more than the power plant engineer understands generation if all he learns is how to read dials and pull switches. Theory is required, and its function is to identify and abstract from total reality the essential minimal concepts and to formulate statements describing the relationships between those concepts whereby the world of experience becomes comprehensible. Theory is never identical with the totality of phenomenal experience; the propositions and principles of theory provide a means by which aspects of reality can be explicitly analyzed and verified, in the hope that some synthesizing minds will make the efforts toward a synthetic reconstruction of reality on the basis of understood principles.

Purpose This paper aims to survey the need for full capacity utilisation of transmission lines in power systems network operations. It proposes a review of the N-1 security criterion that does not ensure reliable dispatch of optimum power flow during outage contingency. The survey aims to enlarge the network capacity utilisation to rely on the entire transmission lines network operation. Design/methodology/approach The paper suggests transmission line switching (TLS) approach as a viable corrective mechanism for power dispatch. The TLS process is incorporated into a constraint programming language extension optimisation solver that selects the switchable line candidates as integer variables in the mixed integer programming problem. Findings The paper provides a practical awareness of reserve capacity in the lines that provide network security in outage contingency. At optimum power flow dispatch, the TLS is extended to optimal transmission line switching (OTLS) that indicates optimal capacity utilisation (OCU) of the available reserve capacity (ARC) in the network lines. Practical implications Computational efficiency influenced the extension of the OTLS to optimal transmission switching of power flow (OTSPF). The application of OTSPF helps reduce the use of flexible AC transmission systems (FACTS) and construction of new transmission lines.. Originality/value The paper surveys TLS efforts in network capacity utilisation. The suggested ARC fulfils the need for an index with which the dispatchable lines may be identified for the optimal capacity utilisation of transmission lines network.

The aim of AEMINIUM is to study the implications of having a concurrent-by-default programming language. This includes language design, runtime system, performance and software engineering considerations. We conduct our study through the design of the concurrent-by-default AEMINIUM programming language. AEMINIUM leverages the permission flow of object and group permissions through the program to validate the program's correctness and to automatically infer a possible parallelization strategy via a dataflow graph. AEMINIUM supports not only fork-join parallelism but more general dataflow patterns of parallelism. In this paper we present a formal system, called μAEMINIUM, modeling the core concepts of AEMINIUM. μAEMINIUM's static type system is based on Featherweight Java with AEMINIUM-specific extensions. Besides checking for correctness AEMINIUM's type system it also uses the permission flow to compute a potential parallel execution strategy for the program. μAEMINIUM's dynamic semantics use a concurrent-by-default evaluation approach. Along with the formal system we present its soundness proof. We provide a full description of the implementation along with the description of various optimization techniques we used. We implemented AEMINIUM as an extension of the Plaid programming language, which has first-class support for permissions built-in. The AEMINIUM implementation and all case studies are publicly available under the General Public License. We use various case studies to evaluate AEMINIUM's applicability and to demonstrate that AEMINIUM parallelized code has performance improvements compared to its sequential counterpart. We chose to use case studies from common domains or problems that are known to benefit from parallelization, to show that AEMINIUM is powerful enough to encode them. We demonstrate through a webserver application, which evaluates AEMINIUM's impact on latency-bound applications, that AEMINIUM can achieve a 70% performance improvement over the sequential counterpart. In another case study we chose to implement a dictionary function to evaluate AEMINIUM's capabilities to express essential data structures. Our evaluation demonstrates that AEMINIUM can be used to express parallelism in such data-structures and that the performance benefits scale with the amount of annotation effort which is put into the implementation. We chose an integral computationally example to evaluate pure functional programming and computational intensive use cases. Our experiments show that AEMINIUM is capable of extracting parallelism from functional code and achieving performance improvements up to the limits of Plaid's inherent performance bounds. Overall, we hope that the work helps to advance concurrent programming in modern programming environments.

We provide a treatment of encryption and zero-knowledge in terms of uniform complexity measures. This treatment is appropriate for cryptographic settings modeled by probabilistic polynomial-time machines. Our uniform treatment allows the construction of secure encryption schemes and zero-knowledge proof systems (for allNP) using only uniform complexity assumptions.We show that uniform variants of the two definitions of security, presented in the pioneering work of Goldwasser and Micali, are in fact equivalent. Such a result was known before only for nonuniform formalization.Nonuniformity is implicit in all previous treatments of zero-knowledge in the sense that a zero-knowledge proof is required to “leak no knowledge” onall instances. For practical purposes, it suffices to require that it isinfeasible to find instances on which a zero-knowledge proof “leaks knowledge.” We show how to construct such zero-knowledge proof systems for every language inNP, using only a uniform complexity assumption. Properties of uniformly zero-knowledge proofs are investigated and their utility is demonstrated.

We initiate a study of super-perfect zero-knowledge proof systems. Loosely speaking, these are proof systems for which the interaction can be perfectly simulated in strict probabilistic polynomial-time. In contrast, the standard definition of perfect zero-knowledge only requires that the interaction can be perfectly simulated by a strict probabilistic polynomial-time that is allowed to fail with probability at most one half.

Mathematics, at the beginning, is sometimes described as the science of Number and Space—better, of Number, Time, Space, and Motion. The need for such a science arises with the most primitive human activities. These activities presently involve counting, timing, measuring, and moving, using numbers, intervals, distances, and shapes. Facts about these operations and ideas are gradually assembled, calculations are made, until finally there develops an extensive body of knowledge, based on a few central ideas and providing formal rules for calculation. Eventually this body of knowledge is organized by a formal system of concepts, axioms, definitions, and proofs. Thus Euclid provided an axiomatization of geometry, with careful demonstrations of the theorems from the axioms; this axiomatization was perfected by Hilbert about 1900, as we will indicate in Chapter III. Similarly the natural numbers arise from counting, with notation which provides to every number the next one—its successor, and with formal rules for calculating sums and products of numbers. It then turns out that all these formal rules can be deduced from a short list of axioms (Peano-Dedekind) on the successor function (Chapter II). Finally, the measurements of time and space eventually are codified in the axioms (Chapter IV) for the real numbers.

Formal generative design systems may describe large and complex spaces, making good designs hard to find. The problem of directing generation towards good solutions is addressed by considering the shape annealing algorithm. The algorithm is modified in an attempt to make optimization over the final generation sequence more uniform. Seven variations of the algorithm are investigated, and their performance compared. The results suggest that an enhanced backtracking ability may significantly improve the performance of the algorithm.

The B Method is a means for specifying, designing and coding software systems. The long-awaited B-Book is the standard reference for everything concerning this method. It contains the mathematical basis on which it is founded, the precise definitions of the notations used, and a large number of examples illustrating its use in practice. J.-R. Abrial, the inventor of B, has written the book in such a way that it can be used for self-study or for reference. It is in four parts, the first dealing with the mathematical foundations and the definition of the various mathematical structures that are needed to formalise software systems; special emphasis is placed on the notion of proof. The second part contains a presentation of the Generalised Substitution Language and of the Abstract Machine Notation; examples are given to show how large specifications can be constructed systematically. The next part introduces the two basic programming features of sequencing and loop. The last part covers the very important notion of refinement. It shows how to construct large software systems by means of layered architectures of modules. With the appearance of The B-Book, formal methods practitioners, computer scientists, and systems developers at last will have access to the definitive account of what will become one of the standard approaches to the construction of software systems.

This paper presents a communication model and nominal definition of advertising images on the Internet, here called the netvertising image (Stern 2001). The model and attribute-based definition facilitate the construction of a formal language system for theory development and hypothesis testing specific to images in the multimedia context. The necessity for so doing is that netvertising has inherited a legacy of fuzzy meanings from marketing, advertising, and consumer behavior research, in which “image” is used variously across the domains of media, message, mental responses, and marketplace behavior. Transformation from this ordinary but ambiguous language system to a formal scientific one proceeds through building a model, sourcing the roots of ordinary meanings, recasting them as attributes, and setting forth a nominal definition. The paper ends with suggestions for future research.

Automation of fixpoint reasoning has been extensively studied for various mathematical structures, logical formalisms, and computational domains, resulting in specialized fixpoint provers for heaps, for streams, for term algebras, for temporal properties, for program correctness, and for many other formal systems and inductive and coinductive properties. However, in spite of great theoretical and practical interest, there is no unified framework for automated fixpoint reasoning. Although several attempts have been made, there is no evidence that such a unified framework is possible, or practical. In this paper, we propose a candidate based on matching logic, a formalism recently shown to theoretically unify the above mentioned formal systems. Unfortunately, the (Knaster-Tarski) proof rule of matching logic, which enables inductive reasoning, is not syntax-driven. Worse, it can be applied at any step during a proof, making automation seem hopeless. Inspired by recent advances in automation of inductive proofs in separation logic, we propose an alternative proof system for matching logic, which is amenable for automation. We then discuss our implementation of it, which although not superior to specialized state-of-the-art automated provers for specific domains, we believe brings some evidence and hope that a unified framework for automated reasoning is not out of reach.