Related papers: Set-Theoretic Blockchains
The blockchain paradigm provides a mechanism for content dissemination and distributed consensus on Peer-to-Peer (P2P) networks. While this paradigm has been widely adopted in industry, it has not been carefully analyzed in terms of its…
This thesis concerns embeddings and self-embeddings of foundational structures in both set theory and category theory. The first part of the work on models of set theory consists in establishing a refined version of Friedman's theorem on…
We introduce order conserving embeddings as a more general form of order preserving embeddings between finite dimensional nest algebras. The structure of these embeddings is determined, in terms of order indecomposable decompositions, and…
In light of the celebrated theorem of Vop\v{e}nka (1972), proving in ZFC that every set is generic over HOD, it is natural to inquire whether the set-theoretic universe $V$ must be a class-forcing extension of HOD by some possibly…
We investigate the partial orderings of the form (P(X),\subset), where X is a countable binary relational structure and P(X) the set of the domains of its isomorphic substructures and show that if the components of X are maximally…
We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of…
It is no exaggeration to say that since the introduction of Bitcoin, blockchains have become a disruptive technology that has shaken the world. However, the rising popularity of the paradigm has led to a flurry of proposals addressing…
Blockchain technology has become a trusted method for establishing secure and transparent transactions through a distributed, encrypted network. The operation of blockchain is governed by consensus algorithms, among which Proof of Stake…
Many tasks in control, robotics, and planning can be specified using desired goal configurations for various entities in the environment. Learning goal-conditioned policies is a natural paradigm to solve such tasks. However, current…
Blockchain is one of the most discussed and highly accepted technologies, primarily due to its application in almost every field where third parties are needed for trust. Blockchain technology relies on distributed consensus for trust,…
Public blockchains should be able to scale with respect to the number of nodes and to the transactions workload. The blockchain scalability trilemma has been informally conjectured. This is related to scalability, security and…
Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of…
Blockchain is widely applied in logistics, finance, and agriculture. As single blockchain users grow, scalability becomes crucial. However, existing works lack a comprehensive summary of blockchain scalability. They focus on single chains…
Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Levy-Collapse. These show in particular that certain applications of forcing axioms require to add…
Blockchain design involves many tradeoffs, and much debate has focused on tradeoffs related to scaling parameters such as blocksize. To address some of the confusion around this subject, we present a probability proof of the DCS Triangle.…
The presented work continues the line of recent distributed computing communityefforts dedicated to the theoretical aspects of blockchains. This paper is the rst tospecify blockchains as a composition of abstract data types all together…
Bitcoin is the first successful decentralized global digital cash system. Its mining process requires intense computational resources, therefore its usefulness remains a disputable topic. We aim to solve three problems with Bitcoin and…
We analyse the Boolean-valued random forcing $B_{M,\Omega}$ in bounded arithmetics developed in Krajicek (Forcing with random variables and proof complexity, vol. 382, Cambridge University Press, 2011) from the perspective of the forcing in…
Working in the framework of Borel reducibility, we study various notions of embeddability between groups. We prove that the embeddability between countable groups, the topological embeddability between (discrete) Polish groups, and the…
In blockchain systems, especially cryptographic currencies such as Bitcoin, the double-spending and Byzantine-general-like problem are solved by reaching consensus protocols among all nodes. The state-of-the-art protocols include…