Related papers: Set-Theoretic Blockchains
A detailed exploration of blockchain technology and its applications across various fields is provided, beginning with an introduction to cryptography fundamentals, including symmetric and asymmetric encryption, and their roles in ensuring…
In the rapidly evolving domain of distributed ledger technology, scalability and interoperability have become paramount challenges for both academic and industry sectors. In this paper, we introduce a comprehensive formal model to address…
In this survey we describe a recently-developed technique for bounding the number (and controlling the typical structure) of finite objects with forbidden substructures. This technique exploits a subtle clustering phenomenon exhibited by…
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
The first generation of blockchain focused on digital currencies and secure storage, management and transfer of tokenized values. Thereafter, the focus has been shifting from currencies to a broader application space. In this paper, we…
Computability on uncountable sets has no standard formalization, unlike that on countable sets, which is given by Turing machines. Some of the approaches to define computability in these sets rely on order-theoretic structures to translate…
We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains.
The cross-blockchain transaction remains one of the most challenging problems in blockchains. The root cause of the challenge lies in the nondeterministic nature of blockchains: A $n$-party transaction across multiple blockchains might be…
We study a composition operation on monads, equivalently presented as large equational theories. Specifically, we discuss the existence of tensors, which are combinations of theories that impose mutual commutation of the operations from the…
Blockchain technology constitutes a paradigm shift in the way we conceive distributed architectures. A Blockchain system lets us build platforms where data are immutable and tamper-proof, with some constraints on the throughput and the…
We introduce and study Polish topologies on various spaces of countable enumerated groups, where an enumerated group is simply a group whose underlying set is the set of natural numbers. Using elementary tools and well known examples from…
We propose a blockchain architecture in which mining requires a quantum computer. The consensus mechanism is based on proof of quantum work, a quantum-enhanced alternative to traditional proof of work that leverages quantum supremacy to…
Decentralized Ledger Technology, popularized by the Bitcoin network, aims to keep track of a ledger of valid transactions between agents of a virtual economy without a central institution for coordination. In order to keep track of a…
The modal logic of forcing arises when one considers a model of set theory in the context of all its forcing extensions, interpreting necessity as "in all forcing extensions" and possibility as "in some forcing extension". In this modal…
We study the problem of checking whether an existential sentence (that is, a first-order sentence in prefix form built using existential quantifiers and all Boolean connectives) is true in a finite partially ordered set (in short, a poset).…
Emerging applications of blockchains, such as grocery supply chains, require frequent updates to the data structure. This is in contrast with typical analyses of the Bitcoin blockchain, in which updates occur infrequently. With more…
In this paper we describe an approach to construct large extendable collections of vectors in predefined spaces of given dimensions. These collections are useful for neural network latent space configuration and training. For classification…
Let M be the generic poset, defined as the Fra\"iss\'e limit of the class of finite posets. We show that every countably infinite poset A can be embedded with coinfinite image into M so that each automorphism of the image of A extends…
Blockchain systems run consensus rules as code to agree on the state of the distributed ledger and secure the network. Changing these rules can be risky and challenging. In addition, it can often be controversial and take much effort to…
We study the existence of uncountable first-order structures that are homogeneous with respect to their finitely generated substructures. In many classical cases this is either well-known or follows from general facts, for example, if the…