Related papers: Set-Theoretic Blockchains
Blockchain technology has gained tremendous popularity both in practice and academia. The goal of this article is to develop a coherent overview of the state of the art in blockchain technology, using a systematic(i.e.,protocol-based,…
We obtain several results concerning the concept of isotypic structures. Namely we prove that any field of finite transcendence degree over a prime subfield is defined by types; then we construct isotypic but not isomorphic structures with…
Blockchain technologies are facing a scalability challenge, which must be overcome to guarantee a wider adoption of the technology. This scalability issue is mostly caused by the use of consensus algorithms to guarantee the total order of…
This thesis introduces a formal general framework for scaling blockchain protocols by sharding. The framework is modular and it can be adjusted for different needs or sets of assumptions. We prove that sharded protocols obtained by…
Modern blockchain systems are a fresh look at the paradigm of distributed computing, applied under assumptions of large-scale public networks. They can be used to store and share information without a trusted central party. There has been…
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…
Recently, the blockchain technique was put in the spotlight as it introduced a systematic approach for multiple parties to reach consensus without needing trust. However, the application of this technique in practice is severely restricted…
Proof of Stake (PoS) protocols rely on voting mechanisms to reach consensus on the current state. If an enhanced majority of staking nodes, also called validators, agree on a proposed block, then this block is appended to the blockchain.…
A brief introduction to the theory of ordered sets and lattice theory is given. To illustrate proof techniques in the theory of ordered sets, a generalization of a conjecture of Daykin and Daykin, concerning the structure of posets that can…
We initiate the study of model structures on (categories induced by) lattice posets, a subject we dub homotopical combinatorics. In the case of a finite total order $[n]$, we enumerate all model structures, exhibiting a rich combinatorial…
A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper…
Decentralization has been touted as the principal security advantage which propelled blockchain systems at the forefront of developments in the financial technology space. Its exact semantics nevertheless remain highly contested and…
Bitcoin's global success has led to the rise of blockchain, but many systems labeled as "blockchain" deviate from its core principles, adding complexity to the ecosystem. This survey addresses the need for a comprehensive review and…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…
Blockchain has attracted significant attention in recent years due to its potential to revolutionize various industries by providing trustlessness. To comprehensively examine blockchain systems, this article presents both a macro-level…
Blockchain is a type of decentralized distributed database. Unlike traditional relational database management systems, it does not require management or maintenance by a third party. All data management and update processes are open and…
Modern blockchain applications benefit from the ability to specify sequencing constraints on the transactions that interact with them. This paper proposes a principled and axiomatically justified way of adding sequencing constraints on…
Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…
Higher order set theory has been a topic of interest for some time, with recent efforts focused on the strength of second order set theories [KW16]. In this paper we strive to present one 'theory of collections' that allows for a formal…