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Juarez Acosta Fernando - One of the best experts on this subject based on the ideXlab platform.
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La equivalencia de activos-derechos sobre activos en el método axiomático
'World Scientific and Engineering Academy and Society (WSEAS)', 2020Co-Authors: Juarez Acosta FernandoAbstract:"The purpose of the study is to analyze the assets-claims on assets equivalence based on the dual concept of monetary units and the Axiomatic method. The methodology is analytical, rationalistic and deductive; it uses Axiomatic Theory with set Theory and predicate logic to test set equivalence. The Axiomatic Theory involves a set of axioms, which are used in combination with accounting axioms to develop a proof of the assets-claims on the assets considered as finite sets. The analysis uses a bijective function based on the dual concept of monetary units, and proof by contraposition to test the fulfillment of the requirement of a bijective function. Results show that assets cardinality is not equal to claims on assets cardinality when taking into account the dual concept of monetary units, and as a consequence assets and claims on assets are not equivalent
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El Balance y la Relación Activos-Reclamos sobre Activos en el Método Axiomático
'World Scientific and Engineering Academy and Society (WSEAS)', 2020Co-Authors: Juarez Acosta FernandoAbstract:"The purpose of this study is to analyze the set structure of the balance sheet and assets-claims on assets relationship, considering the dual concept of monetary units, the Axiomatic Theory and accountingspecific axioms. The structure of the balance sheet and assets-claims on assets relationship are examined using a rationalistic, analytical and deductive method; this method uses the Axiomatic set Theory and predicate logic to define a set of axioms and the logical rationale to apply them to any deductive proof. The method includes accounting primitives and axioms to use in combination with those of the Axiomatic Theory. A direct proof is applied to test the balance sheet fit to a hereditary set structure according to the Axiomatic Theory, and proof by contraposition is employed to examine the assets-claims on assets equality by comparing their elements. Results show that balance sheet has a set structure that can be defined and analyzed with the Axiomatic method and fits a hereditary set structure. Also, by comparing the elements of assets and claims on assets and considering their financial classification, it is shown that these sets do not contain the same elements and, consequently, they are not equal under the postulates of the Axiomatic method.
Alexander Russell - One of the best experts on this subject based on the ideXlab platform.
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the combinatorics of the longest chain rule linear consistency for proof of stake blockchains
Symposium on Discrete Algorithms, 2020Co-Authors: Erica Blum, Aggelos Kiayias, Cristopher Moore, Saad Quader, Alexander RussellAbstract:The blockchain data structure maintained via the longest-chain rule---popularized by Bitcoin---is a powerful algorithmic tool for consensus algorithms. Such algorithms achieve consistency for blocks in the chain as a function of their depth from the end of the chain. While the analysis of Bitcoin guarantees consistency with error 2−k for blocks of depth O(k), the state-of-the-art of proof-of-stake (PoS) blockchains suffers from a quadratic dependence on k: these protocols, exemplified by Ouroboros (Crypto 2017), Ouroboros Praos (Eurocrypt 2018) and Sleepy Consensus (Asiacrypt 2017), can only establish that depth Θ(k2) is sufficient. Whether this quadratic gap is an intrinsic limitation of PoS---due to issues such as the nothing-at-stake problem---has been an urgent open question, as deployed PoS blockchains further rely on consistency for protocol correctnes. We give an Axiomatic Theory of blockchain dynamics that permits rigorous reasoning about the longest-chain rule and achieve, in broad generality, Θ(k) dependence on depth in order to achieve consistency error 2−k. In particular, for the first time we show that PoS protocols can match proof-of-work protocols for linear consistency. We analyze the associated stochastic process, give a recursive relation for the critical functionals of this process, and derive tail bounds in both i.i.d. and martingale settings via associated generating functions.
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linear consistency for proof of stake blockchains
arXiv: Cryptography and Security, 2019Co-Authors: Erica Blum, Aggelos Kiayias, Cristopher Moore, Saad Quader, Alexander RussellAbstract:The blockchain data structure maintained via the longest-chain rule---popularized by Bitcoin---is a powerful algorithmic tool for consensus algorithms. Such algorithms achieve consistency for blocks in the chain as a function of their depth from the end of the chain. While the analysis of Bitcoin guarantees consistency with error $2^{-k}$ for blocks of depth $O(k)$, the state-of-the-art of proof-of-stake (PoS) blockchains suffers from a quadratic dependence on $k$: these protocols, exemplified by Ouroboros (Crypto 2017), Ouroboros Praos (Eurocrypt 2018) and Sleepy Consensus (Asiacrypt 2017), can only establish that depth $\Theta(k^2)$ is sufficient. Whether this quadratic gap is an intrinsic limitation of PoS---due to issues such as the nothing-at-stake problem---has been an urgent open question, as deployed PoS blockchains further rely on consistency for protocol correctness. We give an Axiomatic Theory of blockchain dynamics that permits rigorous reasoning about the longest-chain rule and achieve, in broad generality, $\Theta(k)$ dependence on depth in order to achieve consistency error $2^{-k}$. In particular, for the first time, we show that PoS protocols can match proof-of-work protocols for linear consistency. We analyze the associated stochastic process, give a recursive relation for the critical functionals of this process, and derive tail bounds in both i.i.d. and martingale settings via associated generating functions.
Walter Trockel - One of the best experts on this subject based on the ideXlab platform.
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on non cooperative foundation and implementation of the nash solution in subgame perfect equilibrium via rubinstein s game
Social Science Research Network, 2016Co-Authors: Papatya Duman, Walter TrockelAbstract:In their seminal article in the Rand Journal of Economics Binmore, Rubinstein and Wolinsky (1986) analyze “the relation between the static Axiomatic Theory of bargaining and the sequential strategic approach to bargaining”. They consider two related but different strategic models of alternating offers based on Rubinstein´s famous article in Econometrica (1982) that differ in the employed utility functions representing time preferences in one model and risk of breakdown of bargaining in the other one. In each model “when the motivation to reach agreement is made [almost] negligible, the unique [subgame] perfect equilibrium outcome approaches the Nash bargaining solution with utilities that reflect the incentive to settle and with the proper disagreement point chosen”. Their results are intended to “provide a guide for the application of the Nash bargaining solution in economic modelling”.While these models provide approximate non-cooperative supports for the Nash solution there does not exist a limit model with an exact non-cooperative support.In our paper we first provide a modification of the Rubinstein game that allows such an exact non-cooperative support in weak sub- game perfect equilibrium. That concept as well as the method underlying our modification had been introduced by Trockel (2011) in JME for a direct non-cooperative foundation of the Discrete Raiffa solution.After establishing in our Proposition 1 the direct non-cooperative support of the Nash solution in weak sub-game perfect equilibrium we state in our Proposition 2 and prove a direct non-cooperative support in sub-game perfect equilibrium. In both games there is an infinite number of (weak) sub-game perfect equilibria. But all have the same payoffs namely those of the Nash bargaining solution in the utility space generated from the respective underlying utility functions of the two models. And these payoffs are reaches after the first stage where the proposer suggests the Nash bargaining payoffs while the follower accepts exactly those payoffs granting himself at least his coordinate of the Nash solution.Finally we discuss the relation of our non-cooperative support results (in the sense of the Nash Program) to mechanism theoretic implementation in (weak) sub-game perfect equilibria. It turns out that a sensible implementation can be provided only in that model where players do not discount time but rather where expected utilities of payoffs more remote in time decrease due to probabilities of breakdown of negotiation that are not part of players´ characteristics but rather instruments of design in the hands of the planner.
Erica Blum - One of the best experts on this subject based on the ideXlab platform.
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the combinatorics of the longest chain rule linear consistency for proof of stake blockchains
Symposium on Discrete Algorithms, 2020Co-Authors: Erica Blum, Aggelos Kiayias, Cristopher Moore, Saad Quader, Alexander RussellAbstract:The blockchain data structure maintained via the longest-chain rule---popularized by Bitcoin---is a powerful algorithmic tool for consensus algorithms. Such algorithms achieve consistency for blocks in the chain as a function of their depth from the end of the chain. While the analysis of Bitcoin guarantees consistency with error 2−k for blocks of depth O(k), the state-of-the-art of proof-of-stake (PoS) blockchains suffers from a quadratic dependence on k: these protocols, exemplified by Ouroboros (Crypto 2017), Ouroboros Praos (Eurocrypt 2018) and Sleepy Consensus (Asiacrypt 2017), can only establish that depth Θ(k2) is sufficient. Whether this quadratic gap is an intrinsic limitation of PoS---due to issues such as the nothing-at-stake problem---has been an urgent open question, as deployed PoS blockchains further rely on consistency for protocol correctnes. We give an Axiomatic Theory of blockchain dynamics that permits rigorous reasoning about the longest-chain rule and achieve, in broad generality, Θ(k) dependence on depth in order to achieve consistency error 2−k. In particular, for the first time we show that PoS protocols can match proof-of-work protocols for linear consistency. We analyze the associated stochastic process, give a recursive relation for the critical functionals of this process, and derive tail bounds in both i.i.d. and martingale settings via associated generating functions.
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linear consistency for proof of stake blockchains
arXiv: Cryptography and Security, 2019Co-Authors: Erica Blum, Aggelos Kiayias, Cristopher Moore, Saad Quader, Alexander RussellAbstract:The blockchain data structure maintained via the longest-chain rule---popularized by Bitcoin---is a powerful algorithmic tool for consensus algorithms. Such algorithms achieve consistency for blocks in the chain as a function of their depth from the end of the chain. While the analysis of Bitcoin guarantees consistency with error $2^{-k}$ for blocks of depth $O(k)$, the state-of-the-art of proof-of-stake (PoS) blockchains suffers from a quadratic dependence on $k$: these protocols, exemplified by Ouroboros (Crypto 2017), Ouroboros Praos (Eurocrypt 2018) and Sleepy Consensus (Asiacrypt 2017), can only establish that depth $\Theta(k^2)$ is sufficient. Whether this quadratic gap is an intrinsic limitation of PoS---due to issues such as the nothing-at-stake problem---has been an urgent open question, as deployed PoS blockchains further rely on consistency for protocol correctness. We give an Axiomatic Theory of blockchain dynamics that permits rigorous reasoning about the longest-chain rule and achieve, in broad generality, $\Theta(k)$ dependence on depth in order to achieve consistency error $2^{-k}$. In particular, for the first time, we show that PoS protocols can match proof-of-work protocols for linear consistency. We analyze the associated stochastic process, give a recursive relation for the critical functionals of this process, and derive tail bounds in both i.i.d. and martingale settings via associated generating functions.
Andrei Rodin - One of the best experts on this subject based on the ideXlab platform.
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on constructive Axiomatic method
Logique Et Analyse, 2014Co-Authors: Andrei RodinAbstract:The formal Axiomatic method popularized by Hilbert and recently defended by Hintikka is not fully adequate to the recent practice of axiomatizing mathematical theories. The Axiomatic architecture of Topos Theory and Homotopy type Theory do not fit the pattern of the formal Axiomatic Theory in the standard sense of the word. However these theories fall under a more general and in some respects more traditional notion of Axiomatic Theory, which I call after Hilbert constructive. I show that the formal Axiomatic method always requires a support of some more basic constructive method.
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Axiomatic method and category Theory
2013Co-Authors: Andrei RodinAbstract:Lawvere’s axiomatization of topos Theory and Voevodsky’s axiomatization of heigher homotopy Theory exemplify a new way of Axiomatic Theory-building, which goes beyond the classical Hibert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in Categorical logic opens new possibilities for using this method in physics and other natural sciences.