Decentralized public platforms are becoming increasingly popular due to a growing number of applications for various areas ofbusiness, finance, and social life. Authorless nodes can easily join such networks without any confirmation, making a transparent system of rewards and punishments crucial for the self-sustainability of public platforms. To achieve this, a system for incentivizing and punishing Workers’ behavior should be tightly harmonized with the corresponding consensus protocol, taking into account all of its features, and facilitating a favorable and supportive environment with equal rights for all participants. The main purpose of re-wards is to incentivize Workers to follow the protocol properly, and to penalize them for any type of misbehavior. The issues of block rewarding and punishing in decentralized networks have been well studied, but the DAG referential structure of the distributed ledger forces us to design methods that are more relevant. Since referential structures cannot be reliably validated due to the fact that they are built on the basis of the instantaneous visibility of blocks by a certain node, we propose to set rewards for blocksin the DAG network based on the degree of confidence of topological structures. In doing so, all honest nodes make common decisions based only on information recorded into the ledger, without overloading the network with additional interactions, since such data are al-ways identical and available.The main goal of this work is to design a fair distribution of rewards among honest Workers and estab-lish values for penalties for faulty ones, to ensure the general economic equilibrium of the Waterfall platform. The proposedap-proach has a flexible and transparent architecture that allows for its use for a wide range of PoS-based consensus protocols. The core principles are that Workers' rewards depend on the importance of the conducted work for block producing and achieving consensusand their penalties must not be less than the potential profit from possible attacks. The incentivizing system can facilitate protection from various kinds of attacks, namely, so-called Nothing-at-stake, Rich-get-richer, Sybil, and Splitting attacks, and from some specif-ic threats related to a DAG structure.Keywords: Tokenomics;incentivizing; blockchain; directed acyclic graph; consensus protocolCopyright©Odessa Polytechnic National University, 2022. All rights reservedFor citation:Mazurok I., Leonchyk Y., Grybniak S., Nashyvan O., Masalskyi R.An incentive system for decentralized DAG-based platforms. Applied Aspects of Information Technology.2022; Vol.5No.3: 196–207. DOI:https://doi.org/10.15276/aait.05.2022.13INTRODUCTIONThis work deals with the incentivizationof nodes of the Waterfall platform to honestly perform their duties for achieving a sustainable, secure, and high-performing network, by driving behaviors of all participants with economic leverages. However, it can be considered as a standalone work thatpresents an incentive system that can be implemented, in part or in whole, to other Proof-of-Stake (PoS) [1] consensus protocols of decentralized networks. ©Mazurok I., Leonchyk Y., Grybniak S.,Nashyvan O., Masalskyi R., 2022The issues of creating a fair distribution of rewards among platform Workers and setting values of penalties are addressed in detail.The incentive mechanism is the backbone of any tokenomics system(tokenomics is a term that captures a token’s economics). Itshould facilitate nodes’ positive actions such as processing transactions,validating blocks,and finalizing the ledger.We should note that users can join or leave public networks at their own discretion. Obviously, ifrewards do not cover Workers’ expenditures or are distributed unfairly, honest participants have no incentive to participate in such a network. A good tokenomics practice includes buildingacommunityThis is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0)

Decentralized platforms like blockchain have been attracting significant attention in recent years, especially in the context of financial and payment systems. They are designed to provide a transparent, secure, and reliable environment for digital transactions without the need for a central authority. The core of a decentralized platform like blockchain is a consensus layer that allows all participants (called Workers), who properly operate and follow all network protocols and have access to the same state of the distributed ledger, to coordinate their actions and arrive at the same decisions. However, some Workers may be temporarily offline at their own discretion, without any confirmation, or their work may be faulty due to technical circumstances, resulting in unpredictable behavior. The goal of this article is to present an approach for multi-objective optimizing of Byzantine fault tolerance (BFT)-based consensus protocols, to reduce the impact on the network of faulty participants. Two criteria were considered – minimization of the number of sent service messages, and maximization of the mathematical expectation of the number of produced blocks. The result is a method to determine the optimal committee size and distribution of Workers, depending on their total number in the network and the expected proportion of Byzantine faulty nodes. All protocol amendments presented in this work are tested with corresponding simulation models and have demonstrated notable enhancements in the performance of the system and decreased the load on network nodes. These improvements will be implemented to the consensus protocol Gozalandia on the Waterfall platform, enhancing its overall reliability, performance, and security. In addition, the presented optimizing algorithm can be applied to a wide range of consensus protocols in blockchains, where blocks must be signed by randomly selected committees to confirm their validity

Nowadays,Decentralized Networks based on Blockchain technology are actively researched. A special place in these researches is occupied by Smart Contracts that are widely used in many areas, such as Decentralized Finance (DeFi), real estate, gambling, electoral process, etc. Nevertheless, the possibility of their widespread adoption is still not a solved problem. This is caused by the fact of their limited flexibility and scalability. In other words, Smart Contracts cannot process a large number of contract calls per second, lack of direct Internet access, inability to operate with a large amount of data, etc. This article is devoted to the development of the Sharding Concept for Decentralized Applications (DApps) that are expressed in form of Smart Contracts written in WebAssembly. The aim of the research is to offer a new Concept of Smart Contract that will increase the scaling due to applying the idea of Sharding that allows avoiding doing the same work by all nodes on the Network and flexibility due to thepossibility of interaction with the Internet without special Oracles.During the research, decentralized 0ata storages with the possibility of collective decision-making were developed. The scheme of forming Drives that assumes that each Contract is executed by a set of randomly selected nodes that allows avoiding cahoots and prevents Sybil Attack is offered. Such an approach allowed using Drives as a base layer for Smart Contracts. Moreover, Drives can be used as a standalone solution for decentralized data storing.The features of coordination of results of Contracts execution that greatly expands the possibilities of the Contracts compared to Ethereum Smart Contracts, and, in particular, allow the Contracts to interact with the Internet are described. The Rewards Concept that incentivizes all nodes that honestly execute the Contracts, unlike other systems where only the block producer is rewarded, is developed. It is based on the specially developed Proof of Execution –a special algorithm that allows detecting all the nodes that honestly execute the Contracts. In order to make the Proof of Execution more compact, an extension for the existing discrete logarithm zero-knowledge proofs that makes it possible to consistentlyprove knowledge of dynamically expanding set of values with minimal computational and memory complexity so-called Cumulative Discrete Logarithm Zero-Knowledge Proof is developed.Thus, in this article, the new concept of Smart Contracts Sharding empowered by economic leverages is researched. The main advantages of the proposed approach are the possibility of interaction with the Internet and big data processing. Moreover, the mechanism of incentivizing nodes to honestly execute the Smart Contracts is developed. In addition, the Cumulative Proof that is necessary for the cryptographic strength of the specified mechanism is offered and its correctness is proven. The obtained results can be used to implement Smart Contracts in decentralized systems, in particular, working on the basis of Blockchain technology, especially in the case of demanding high bandwidth and performance