Related papers: Set-Theoretic Blockchains
Hamkins and Kikuchi (2016 and 2017) show that in both set theory and class theory the definable subset ordering of the universe interprets a complete and decidable theory. If $\mathcal{M}$ is a model of set theory, then $\langle M,…
Fix a set-theoretic universe $V$. We look at small extensions of $V$ as generalised degrees of computability over $V$. We also formalise and investigate the complexity of certain methods one can use to define, in $V$, subclasses of degrees…
We explore a wider theoretical framework that has quantum field theory built-in, taking the fact that quantum mechanics is reconstructed from quantum field theory as a hint. We formulate a quantum theory with an embedded structure by…
The applications of the blockchain technology are still being discov-ered. When a new potential disruptive technology emerges, there is a tendency to try to solve every problem with that technology. However, it is still necessary to…
The purpose of this paper is to investigate forcing as a tool to construct universal models. In particular, we look at theories of initial segments of the universe and show that any model of a sufficiently rich fragment of those theories…
The full implementation of the metaverse requires the integration of the physical and digital worlds. Applications built on Distributed Ledger Technology (DLT) hold the power to move society closer towards the ideal metaverse through…
Blockchain technology is a breakthrough in changing the ways of business and organization operations, in which the consensus problem is challenging with practical constraints, such as computational power and consensus standard. In this…
Algorithmic meta-theorems state that problems definable in a fixed logic can be solved efficiently on structures with certain properties. An example is Courcelle's Theorem, which states that all problems expressible in monadic second-order…
We study sheaves in the context of a duality theory for lattice structure endowed with extra operations, and in the context of forcing in a topos. Using Sheaf duality theory of Comer for cylindric algebras, we give a representation theorem…
We continue the study of the theories of Baldwin-Shi hypergraphs from $[5]$. Restricting our attention to when the rank $\delta$ is rational valued, we show that each countable model of the theory of a given Baldwin-Shi hypergraph is…
We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of simpler components. The crucial results required by the…
Decentralized payment systems such as Bitcoin have become massively popular in the last few years, yet there is still much to be done in understanding their formal properties. The vast majority of decentralized payment systems work by…
For any finite totally ordered set, the multisets of intervals form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some…
A decentralized blockchain is a distributed ledger that is often used as a platform for exchanging goods and services. This ledger is maintained by a network of nodes that obeys a set of rules, called a consensus protocol, which helps to…
The index of a subgroup of a group counts the number of cosets of that subgroup. A subgroup of finite index often shares structural properties with the group, and the existence of a subgroup of finite index with some particular property can…
Existing blockchain systems scale poorly because of their distributed consensus protocols. Current attempts at improving blockchain scalability are limited to cryptocurrency. Scaling blockchain systems under general workloads (i.e.,…
This master thesis deals with Blockchain Technology in mobile turn based peer to peer games. First, it investigates the capabilities of Blockchain Technology to be used for gaming applications. In this regard, among others,…
We present a matrix-theoretic approach for studying and enumerating finite posets through their incidence representations, referred to as poset matrices. Naturally labelled posets are encoded as Boolean lower triangular matrices, allowing a…
As an emerging service framework built by combining cryptography, P2P network, consensus mechanism and innovative contract technology, blockchain has been widely used in digital finance, data sharing, message traceability and electronic…
The cross-blockchain transaction (CBT) serves as a cornerstone for the next-generation, blockchain-based data management systems. However, state-of-the-art CBT models do not address the effect of the possible local fork suspension that…