Proof Framework Research Articles

PSPACE-Completeness of Reversible Deterministic Systems

We prove PSPACE-completeness of several reversible, fully deterministic systems. At the core, we develop a framework for such proofs (building on a result of Tsukiji and Hagiwara and a framework for motion planning through gadgets), showing that any system that can implement three basic gadgets is PSPACE-complete. We then apply this framework to four different systems, showing its versatility. First, we prove that Deterministic Constraint Logic is PSPACE-complete, fixing an error in a previous argument from 2008. Second, we give a new PSPACE-hardness proof for the reversible ‘billiard ball’ model of Fredkin and Toffoli from 40 years ago, newly establishing hardness when only two balls move at once. Third, we prove PSPACE-completeness of zero-player motion planning with any reversible deterministic interacting [Formula: see text]-tunnel gadget and a ‘rotate clockwise’ gadget (a zero-player analog of branching hallways). Fourth, we give simpler proofs that zero-player motion planning is PSPACE-complete with just a single gadget, the 3-spinner. These results should in turn make it even easier to prove PSPACE-hardness of other reversible deterministic systems.

SSProve: A Foundational Framework for Modular Cryptographic Proofs in Coq

State-separating proofs (SSP) is a recent methodology for structuring game-based cryptographic proofs in a modular way, by using algebraic laws to exploit the modular structure of composed protocols. While promising, this methodology was previously not fully formalized and came with little tool support. We address this by introducing SSProve, the first general verification framework for machine-checked state-separating proofs. SSProve combines high-level modular proofs about composed protocols, as proposed in SSP, with a probabilistic relational program logic for formalizing the lower-level details, which together enable constructing machine-checked cryptographic proofs in the Coq proof assistant. Moreover, SSProve is itself fully formalized in Coq, including the algebraic laws of SSP, the soundness of the program logic, and the connection between these two verification styles. To illustrate SSProve, we use it to mechanize the simple security proofs of ElGamal and pseudo-random-function–based encryption. We also validate the SSProve approach by conducting two more substantial case studies: First, we mechanize an SSP security proof of the key encapsulation mechanism–data encryption mechanism (KEM-DEM) public key encryption scheme, which led to the discovery of an error in the original paper proof that has since been fixed. Second, we use SSProve to formally prove security of the sigma-protocol zero-knowledge construction, and we moreover construct a commitment scheme from a sigma-protocol to compare with a similar development in CryptHOL. We instantiate the security proof for sigma-protocols to give concrete security bounds for Schnorr’s sigma-protocol.

Operationally-based program equivalence proofs using LCTRSs

We propose an operationally-based framework for deductive proofs of program equivalence. It is based on encoding the language semantics as logically constrained term rewriting systems (LCTRSs) and the two programs as terms. As a novelty of our method, we show that it enables relational reasoning about programs in various settings, which are encoded in the operational semantics. For example, we show how our method can be used to prove programs that are equivalent when considering an unbounded stack, but where the equivalence fails to hold if the stack is bounded. We also show how to formalize read-sets and write-sets of symbolic expressions and statements by extending the operational semantics in a conservative way. This enables the relational verification of program schemas, which we exploit to prove compiler optimizations that cannot be handled by other tools. Our method requires an extension of standard LCTRSs with axiomatized symbols, which generate new research questions. We also present a prototype implementation that proves the practical feasibility of our approach.

Assessment framework for Proof of Concept (PoC) in Industry 4.0 – an interoperability approach

ABSTRACT Large companies have been incessantly pursuing cost reduction, increased performance, and agility in decision-making to meet customers’ demands quickly. This paper presents a framework that allows efficient and agile implementation of Proofs of Concept, based on multicriteria evaluation from interoperability perspectives. The proposed model is based on a three-dimensional structure (cube) characterizing phases related to (i) the creation of a referential model, (ii) the evaluation of organizational maturity (diagnostic phase), and (iii) the proposition of a functional model. One case of an application with a high impact on the supply chain and logistics was used to evaluate the framework.

Physical Security Design Process Applicable to Chinese Border Entry Ports by IoT for 5G

Actual security ensures individuals, information, frameworks, and gear of a country. It additionally gets worldwide boundaries. Political obstruction and infringement of boundary arrangements can make line security issues. Mechanical headways in actual security diminish the weight of line security work force. On the off chance that the boundary of a nation is not all around ensured, then, at that point, it would confront a progression of illicit movement. Boundaries can be emphatically ensured by utilizing actual obstructions, observation, biomeasurements, light, security faculty, caution frameworks, sensors, radars, access control frameworks, distinguishing proof frameworks, and PC design. This paper talks about certain difficulties and their potential arrangements utilizing different actual security components at global boundaries. This paper likewise indicates the possible changes in genuine which nations’ security can consider for their lines the bosses in a common manner.

A Comprehensive Framework for Saturation Theorem Proving

A crucial operation of saturation theorem provers is deletion of subsumed formulas. Designers of proof calculi, however, usually discuss this only informally, and the rare formal expositions tend to be clumsy. This is because the equivalence of dynamic and static refutational completeness holds only for derivations where all deleted formulas are redundant, but the standard notion of redundancy is too weak: A clause C does not make an instance Csigma redundant. We present a framework for formal refutational completeness proofs of abstract provers that implement saturation calculi, such as ordered resolution and superposition. The framework modularly extends redundancy criteria derived via a familiar ground-to-nonground lifting. It allows us to extend redundancy criteria so that they cover subsumption, and also to model entire prover architectures so that the static refutational completeness of a calculus immediately implies the dynamic refutational completeness of a prover implementing the calculus within, for instance, an Otter or DISCOUNT loop. Our framework is mechanized in Isabelle/HOL.

The Hawking\u2013Penrose Singularity Theorem for C^1-Lorentzian Metrics

We extend both the Hawking–Penrose theorem and its generalisation due to Galloway and Senovilla to Lorentzian metrics of regularity C^1. For metrics of such low regularity, two main obstacles have to be addressed. On the one hand, the Ricci tensor now is distributional, and on the other hand, unique solvability of the geodesic equation is lost. To deal with the first issue in a consistent way, we develop a theory of tensor distributions of finite order, which also provides a framework for the recent proofs of the theorems of Hawking and of Penrose for C^1-metrics (Graf in Commun Math Phys 378(2):1417–1450, 2020). For the second issue, we study geodesic branching and add a further alternative to causal geodesic incompleteness to the theorem, namely a condition of maximal causal non-branching. The genericity condition is re-cast in a distributional form that applies to the current reduced regularity while still being fully compatible with the smooth and C^{1,1}-settings. In addition, we develop refinements of the comparison techniques used in the proof of the C^{1,1}-version of the theorem (Graf in Commun Math Phys 360:1009–1042, 2018). The necessary results from low regularity causality theory are collected in an appendix.

Network database security with intellectual access supervision using outlier detection techniques

With the rise of the internet, security has transformed into a critical concern. An interference distinguishing proof structure is used to redesign the security of frameworks by evaluating all inbound and outbound framework practices and by perceiving suspicious cases as possible intrusions. Masters focus on applying special case distinguishing proof frameworks for irregularity revelation in light of its promising results in perceiving bona fide ambushes and in lessening false alert rate. In this paper, characteristic acknowledgment on systems database assurance is analysed and their results are examined. In this original copy, a few noteworthy components are viewed as a framework structure and an information suspicion driven inconsistency revelation technique. We demonstrate their ampleness and results on real datasets with scholarly access administration from the regions of social, spatial, and stage walled in area frameworks. Finally, we offer an outline to widen the examined irregularity acknowledgment frameworks to the dynamic setting of graphs. In this original copy we utilised MATLAB condition for discovery of exceptions on systems database and the proposed strategy execution is likewise examined.

A Hypothesis Framework for Students’ Difficulties with Proof By Contradiction

In mathematics education, the research on proof by contradiction (PBC) often claims that this activity is more difficult for students than direct proof, or simply difficult in general. Many hypotheses have been offered to support or explain this belief, yet they span a disorientingly wide swath of journal articles, conference papers, dissertations, book chapters, etc. In addition, few attempts have been made to organize these hypotheses or carefully test them. In this paper, we conduct a thorough literature review on PBC, organize existing hypotheses about challenges with PBC into a Hypothesis Framework for (Students’ Difficulty with) Proof By Contradiction (HFPBC), discuss the state of research related to each hypothesis, and offer thoughts on the future study of these hypotheses.

Algebraic proof methods for identities of matrices and operators: Improvements of Hartwig’s triple reverse order law

When improving results about generalized inverses, the aim often is to do this in the most general setting possible by eliminating superfluous assumptions and by simplifying some of the conditions in statements. In this paper, we use Hartwig’s well-known triple reverse order law as an example for showing how this can be done using a recent framework for algebraic proofs and the software package OperatorGB. Our improvements of Hartwig’s result are proven in rings with involution and we discuss computer-assisted proofs that show these results in other settings based on the framework and a single computation with noncommutative polynomials.

Almost-Minimal-Round BBB-Secure Tweakable Key-Alternating Feistel Block Cipher

This paper focuses on designing a tweakable block cipher via by tweaking the Key-Alternating Feistel (KAF for short) construction. Very recently Yan et al. published a tweakable KAF construction. It provides a birthday-bound security with 4 rounds and Beyond-Birthday-Bound (BBB for short) security with 10 rounds. Following their work, we further reduce the number of rounds in order to improve the efficiency while preserving the same level of security bound. More specifically, we rigorously prove that 6-round tweakable KAF cipher is BBB- secure. The main technical contribution is presenting a more refined security proof framework, which makes significant efforts to deal with several subtle and complicated sub-events. Note that Yan et al. showed that 4-round KAF provides exactly Birthday-Bound security by a concrete attack. Thus, 6 rounds are (almost) minimal rounds to achieve BBB security for tweakable KAF construction.

Proof of Concept Research

Researchers often pursue proof of concept research, but criteria for evaluating such research remain poorly specified. This article proposes a general framework for proof of concept research that knits together and augments earlier discussions. The framework includes prototypes, proof of concept demonstrations, and post facto demonstrations. With a case from theoretical evolutionary genetics, the article illustrates the general framework and articulates some of the reasoning strategies used within that field. This article provides both specific tools with which to understand how researchers evaluate models in theoretical evolutionary genetics and general tools that apply to proof of concept research more generally.

Extensional Higher-Order Paramodulation in Leo-III

Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice. Reasoning with primitive equality is enabled by adapting paramodulation-based proof search to higher-order logic. The prover may cooperate with multiple external specialist reasoning systems such as first-order provers and SMT solvers. Leo-III is compatible with the TPTP/TSTP framework for input formats, reporting results and proofs, and standardized communication between reasoning systems, enabling e.g. proof reconstruction from within proof assistants such as Isabelle/HOL. Leo-III supports reasoning in polymorphic first-order and higher-order logic, in all normal quantified modal logics, as well as in different deontic logics. Its development had initiated the ongoing extension of the TPTP infrastructure to reasoning within non-classical logics.

Sequence Convergence of Inexact Nonconvex and Nonsmooth Algorithms with More Realistic Assumptions

The sequence convergence of inexact nonconvex and nonsmooth algorithms is proved with an unrealistic assumption on the noise. In this paper, we focus on removing the assumption. Without the assumption, the algorithm consequently cannot be proved with previous framework and tricks. Thus, we build a new proof framework which employs a pseudo sufficient descent condition and a pseudo relative error condition both related to an auxiliary sequence; and a continuity condition is assumed to hold. In fact, a lot of classical inexact nonconvex and nonsmooth algorithms allow these three conditions. Under an assumption on the auxiliary sequence, we prove the sequence generated by the general algorithm converges to a critical point of the objective function if being assumed semi-algebraic property. The core of the proofs lies in building a new Lyapunov function, whose successive difference provides a bound for the successive difference of the points generated by the algorithm. And then, we apply our findings to the inexact nonconvex proximal inertial gradient algorithm and derive the corresponding convergence results.

Semantic Correctness of Dependence-based Slicing for Interprocedural, Possibly Nonterminating Programs

Existing proofs of correctness for dependence-based slicing methods are limited either to the slicing of intraprocedural programs [2, 39], or the proof is only applicable to a specific slicing method [4, 41]. We contribute a general proof of correctness for dependence-based slicing methods such as Weiser [50, 51], or Binkley et al. [7, 8], for interprocedural, possibly nonterminating programs. The proof uses well-formed weak and strong control closure relations, which are the interprocedural extensions of the generalised weak/strong control closure provided by Danicic et al. [13], capturing various nonterminating-insensitive and nontermination-sensitive control-dependence relations that have been proposed in the literature. Thus, our proof framework is valid for a whole range of existing control-dependence relations. We have provided a definition of semantically correct (SC) slice. We prove that SC slices agree with Weiser slicing, that deterministic SC slices preserve termination, and that nondeterministic SC slices preserve the nondeterministic behavior of the original programs.

Highly Secure Nonce-based MACs from the Sum of Tweakable Block Ciphers

Tweakable block ciphers (TBCs) have proven highly useful to boost the security guarantees of authentication schemes. In 2017, Cogliati et al. proposed two MACs combining TBC and universal hash functions: a nonce-based MAC called NaT and a deterministic MAC called HaT. While both constructions provide high security, their properties are complementary: NaT is almost fully secure when nonces are respected (i.e., n-bit security, where n is the block size of the TBC, and no security degradation in terms of the number of MAC queries when nonces are unique), while its security degrades gracefully to the birthday bound (n/2 bits) when nonces are misused. HaT has n-bit security and can be used naturally as a nonce-based MAC when a message contains a nonce. However, it does not have full security even if nonces are unique.This work proposes two highly secure and efficient MACs to fill the gap: NaT2 and eHaT. Both provide (almost) full security if nonces are unique and more than n/2-bit security when nonces can repeat. Based on NaT and HaT, we aim at achieving these properties in a modular approach. Our first proposal, Nonce-as-Tweak2 (NaT2), is the sum of two NaT instances. Our second proposal, enhanced Hash-as-Tweak (eHaT), extends HaT by adding the output of an additional nonce-depending call to the TBC and prepending nonce to the message. Despite the conceptual simplicity, the security proofs are involved. For NaT2 in particular, we rely on the recent proof framework for Double-block Hash-then-Sum by Kim et al. from Eurocrypt 2020.

Анализ подтверждения соответствия, обеспечение качества и безопасности микропроцессорных систем железнодорожной автоматики

The article analyzes the current regulatory framework for proof of safety, quality assurance, and confi rmation of the conformity of microprocessor-based railway automation and remote control systems in the EAEU. CENELEC standards are briefl y discussed. A brief overview is provided as regards measures to ensure the required level of safety of microprocessor-based railway automation and remote control systems from the point of view of quality management of development, safety management, and confi rmation of the proper functioning of microprocessor systems. The practice of confi rming the railway transport automated process control systems comply with standards in the form of a declaration of conformity per TR CU 003/2011 has been analyzed. It is concluded that there is a need to develop a regulatory framework to ensure regulated analysis and assessment of railway automation and remote control systems following the requirements of functional safety, as well as further development of standardization documents to regulate methods for assessing functional safety.

Towards a unified proof framework for automated fixpoint reasoning using matching logic

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.

Single-forward-step projective splitting: exploiting cocoercivity

This work describes a new variant of projective splitting for solving maximal monotone inclusions and complicated convex optimization problems. In the new version, cocoercive operators can be processed with a single forward step per iteration. In the convex optimization context, cocoercivity is equivalent to Lipschitz differentiability. Prior forward-step versions of projective splitting did not fully exploit cocoercivity and required two forward steps per iteration for such operators. Our new single-forward-step method establishes a symmetry between projective splitting algorithms, the classical forward–backward splitting method (FB), and Tseng’s forward-backward-forward method. The new procedure allows for larger stepsizes for cocoercive operators: the stepsize bound is $$2\beta$$ for a $$\beta$$ -cocoercive operator, the same bound as has been established for FB. We show that FB corresponds to an unattainable boundary case of the parameters in the new procedure. Unlike FB, the new method allows for a backtracking procedure when the cocoercivity constant is unknown. Proving convergence of the algorithm requires some departures from the prior proof framework for projective splitting. We close with some computational tests establishing competitive performance for the method.

Design Pattern Elicitation Framework for Proof of Integrity in Blockchain Applications

An emerging technology with a secure and a decentralized nature, blockchain has the potential to transform conventional practices in an efficient and dynamic manner. However, migrating to blockchain can be challenging due to the complexity of its infrastructure and processes. The complexity of building applications on blockchain has been highlighted by many studies, thus stressing the need to investigate practical solutions further. A commonly known software engineering concept, software design pattern contributes to the acceleration of software development. It offers a holistic reusable solution for commonly occurring problems in a given context. It helps to identify problems that occur repetitively and describes best practices to address them. The present study is one of the first investigations to inquire into design patterns for blockchain application. Seeking to reduce the complexity in understanding and building applications on blockchain, this paper identifies a design pattern elicitation framework from similar blockchain applications. Next, it provides a demonstration of the Proof of Integrity (PoI) pattern elicited from two different applications on the blockchain. The applicability of the pattern is evaluated by building a blockchain application to verify the integrity of the academic certificates and by explaining how this integrity has been achieved empirically.