There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Journal of the ACM

In recent years, the rapid development of blockchain technology and cryptocurrencies has influenced the financial industry by creating a new crypto-economy. Then, next-generation decentralized applications without involving a trusted third-party have emerged thanks to the appearance of smart contracts, which are computer protocols designed to facilitate, verify, and enforce automatically the negotiation and agreement among multiple untrustworthy parties. Despite the bright side of smart contracts, several concerns continue to undermine their adoption, such as security threats, vulnerabilities, and legal issues. In this paper, we present a comprehensive survey of blockchain-enabled smart contracts from both technical and usage points of view. To do so, we present a taxonomy of existing blockchain-enabled smart contract solutions, categorize the included research papers, and discuss the existing smart contract-based studies. Based on the findings from the survey, we identify a set of challenges and open issues that need to be addressed in future studies. Finally, we identify future trends.

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Blockchain smart contracts: Applications, challenges, and future trends

A fundamental fact for the algebraic theory of constraint satisfaction problems (CSPs) over a fixed template is that pp-interpretations between at most countable ω-categorical relational structures have two algebraic counterparts for their polymorphism clones: a semantic one via the standard algebraic operators H, S, P, and a syntactic one via clone homomorphisms (capturing identities). We provide a similar characterization which incorporates all relational constructions relevant for CSPs, that is, homomorphic equivalence and adding singletons to cores in addition to ppinterpretations. For the semantic part we introduce a new construction, called reflection, and for the syntactic part we find an appropriate weakening of clone homomorphisms, called h1 clone homomorphisms (capturing identities of height 1). As a consequence, the complexity of the CSP of an at most countable ω-categorical structure depends only on the identities of height 1 satisfied in its polymorphism clone as well as the natural uniformity thereon. This allows us in turn to formulate a new elegant dichotomy conjecture for the CSPs of reducts of finitely bounded homogeneous structures. Finally, we reveal a close connection between h1 clone homomorphisms and the notion of compatibility with projections used in the study of the lattice of interpretability types of varieties.

/pdf/the-wonderland-of-reflections-3w3l5o1kw5.pdf

The wonderland of reflections

The group testing problem concerns discovering a small number of defective items within a large population by performing tests on pools of items. A test is positive if the pool contains at least one defective, and negative if it contains no defectives. This is a sparse inference problem with a combinatorial flavour, with applications in medical testing, biology, telecommunications, information technology, data science, and more. In this monograph, we survey recent developments in the group testing problem from an information-theoretic perspective. We cover several related developments: efficient algorithms with practical storage and computation requirements, achievability bounds for optimal decoding methods, and algorithm-independent converse bounds. We assess the theoretical guarantees not only in terms of scaling laws, but also in terms of the constant factors, leading to the notion of the {\em rate} of group testing, indicating the amount of information learned per test. Considering both noiseless and noisy settings, we identify several regimes where existing algorithms are provably optimal or near-optimal, as well as regimes where there remains greater potential for improvement. In addition, we survey results concerning a number of variations on the standard group testing problem, including partial recovery criteria, adaptive algorithms with a limited number of stages, constrained test designs, and sublinear-time algorithms.

/pdf/group-testing-an-information-theory-perspective-21ckdmzbna.pdf

Group Testing: An Information Theory Perspective

Motivated by recent emerging systems that can leverage partially correct packets in wireless networks, this paper investigates the novel concept of error estimating codes (EEC). Without correcting the errors in the packet, EEC enables the receiver of the packet to estimate the packet's bit error rate, which is perhaps the most important meta-information of a partially correct packet. Our EEC algorithm provides provable estimation quality, with rather low redundancy and computational overhead. To demonstrate the utility of EEC, we exploit and implement EEC in two wireless network applications, Wi-Fi rate adaptation and real-time video streaming. Our real-world experiments show that these applications can significantly benefit from EEC.

/pdf/efficient-error-estimating-coding-feasibility-and-13m1vv6nt1.pdf

Efficient error estimating coding: feasibility and applications

The group testing problem consists of determining a small set of defective items from a larger set of items based on tests on groups of items, and is relevant in applications such as medical testing, communication protocols, pattern matching, and many more. While rigorous group testing algorithms have long been known with runtime at least linear in the number of items, a recent line of works has sought to reduce the runtime to ${\mathrm{ poly}}({k} \log {n})$ , where n is the number of items and k is the number of defectives. In this paper, we present such an algorithm for non-adaptive group testing termed bit mixing coding (BMC), which builds on techniques that encode item indices in the test matrix, while incorporating novel ideas based on erasure-correction coding. We show that BMC achieves asymptotically vanishing error probability with ${O}({k} \log {n})$ tests and ${O}({k}^{2} \cdot \log {k} \cdot \log {n})$ runtime, in the limit as ${n} \to \infty $ (with k having an arbitrary dependence on n). This closes an open problem of simultaneously achieving ${\mathrm{ poly}}({k} \log {n})$ decoding time using ${O}({k} \log {n})$ tests without any assumptions on k. In addition, we show that the same scaling laws can be attained in a commonly-considered noisy setting, in which each test outcome is flipped with constant probability.

Sublinear-Time Non-Adaptive Group Testing With O ( k log n ) Tests via Bit-Mixing Coding

Motivated by recent emerging systems that can leverage partially correct packets in wireless networks, this paper proposes the novel concept of error estimating coding (EEC). Without correcting the errors in the packet, EEC enables the receiver of the packet to estimate the packet's bit error rate, which is perhaps the most important meta-information of a partially correct packet. Our EEC design provides provable estimation quality with rather low redundancy and computational overhead. To demonstrate the utility of EEC, we exploit and implement EEC in two wireless network applications, Wi-Fi rate adaptation and real-time video streaming. Our real-world experiments show that these applications can significantly benefit from EEC.

/pdf/efficient-error-estimating-coding-feasibility-and-4xv7oocfjn.pdf

Multi-party communication complexity involves distributed computation of a function over inputs held by multiple distributed players. A key focus of distributed computing research, since the very beginning, has been to tolerate failures. It is thus natural to ask “If we want to compute a certain function in a fault-tolerant way, what will the communication complexity beq” For this question, this article will focus specifically on (i) tolerating node crash failures, and (ii) computing the function over general topologies (instead of, e.g., just cliques).One way to approach this question is to first develop results in a simpler failure-free setting, and then “amend” the results to take into account failures' impact. Whether this approach is effective largely depends on how big a difference failures can make. This article proves that the impact of failures is significant, at least for the Sum aggregate function in general topologies: As our central contribution, we prove that there exists (at least) an exponential gap between the non-fault-tolerant and fault-tolerant communication complexity of Sum. This gap attests that fault-tolerant communication complexity needs to be studied separately from non-fault-tolerant communication complexity, instead of being considered as an “amended” version of the latter. Such exponential gap is not obvious: For some other functions such as the Max aggregate function, the gap is only logarithmic.Part of our results are obtained via a novel reduction from a new two-party problem UnionSizeCP that we introduce. UnionSizeCP comes with a novel cycle promise, which is the key enabler of our reduction. We further prove that this cycle promise and UnionSizeCP likely play a fundamental role in reasoning about fault-tolerant communication complexity.

/pdf/the-cost-of-fault-tolerance-in-multi-party-communication-3bvitmdmcm.pdf

The Cost of Fault Tolerance in Multi-Party Communication Complexity

Scheduling to avoid packet collisions is a long-standing challenge in networking, and has become even trickier in wireless networks with multiple senders and multiple receivers. In fact, researchers have proved that even perfect scheduling can only achieve $\mathbf{R}=O(\frac{1}{\ln N})$ . Here N is the number of nodes in the network, and R is the medium utilization rate. Ideally, one would hope to achieve $\mathbf{R}=\Theta(1)$ , while avoiding all the complexities in scheduling. To this end, this paper proposes cross-sender bit-mixing coding (BMC), which does not rely on scheduling. Instead, users transmit simultaneously on suitably-chosen slots, and the amount of overlap in different user's slots is controlled via coding. We prove that in all possible network topologies, using BMC enables us to achieve $\mathbf{R}=\Theta(1)$ . We also prove that the space and time complexities of BMC encoding/decoding are all low-order polynomials.

/pdf/cross-sender-bit-mixing-coding-vhq2c0ykrh.pdf

Yuda Zhao

Papers

Efficient error estimating coding: feasibility and applications

Sublinear-Time Non-Adaptive Group Testing With O ( k log n ) Tests via Bit-Mixing Coding

Efficient error estimating coding: feasibility and applications

The Cost of Fault Tolerance in Multi-Party Communication Complexity

Cross-sender bit-mixing coding