Payment Channel Networks (PCNs) are a promising alternative to improve the scalability of a blockchain network. A PCN employs off-chain micropayment channels that do not need a global block confirmation procedure, thereby sacrificing the ability to confirm transactions instantaneously. PCN uses a routing algorithm to identify a path between two users who do not have a direct channel between them to settle a transaction. The performance of most of the existing centralized path-finding algorithms does not scale with network size. The rapid growth of Bitcoin PCN necessitates considering distributed algorithms. However, the existing decentralized algorithms suffer from resource underutilization. We present a decentralized routing algorithm, Swift, focusing on fee optimization. The concept of a secret path is used to reduce the path length between a sender and a receiver to optimize the fees. Furthermore, we reduce a network structure into combinations of cycles to theoretically study fee optimization with changes in cloud size. The secret path also helps in edge load sharing, which results in an improvement of throughput. Swift routing achieves up to 21% and 63% in fee and throughput optimization, respectively. The results from the simulations follow the trends identified in the theoretical analysis.

The use of blockchain-based cryptocurrencies has significantly increased over the last ten years; nevertheless, the broader acceptance of these currencies is hindered by scaling challenges. Payment Channel Networks (PCN), which operates as a layer two solution, presents itself as a viable option for augmenting the scalability of a blockchain network. In order to reduce the time and cost associated with the on-chain settlement, users have the option to conduct off-chain transactions through payment channels within their network. The growth of the PCN is expected to be accompanied by a corresponding increase in the number of transactions. However, the current distributed routing algorithms are unable to manage several simultaneous transactions due to deadlocks efficiently. We illustrate the possibility of deadlock in distributed routing algorithms. We prove that routing two transactions in PCN is NP-complete by reducing it from a two-commodity flow problem. In contrast to earlier work that avoided deadlock by exploiting locking or priority queues, our work emphasizes routing algorithms to avoid conditions for deadlock. We enhance the routing choices to minimize the number of saturated links that can cause deadlock. Resource allocation graphs are used to illustrate the necessary and sufficient conditions required for transactions to be in a deadlock. We also show how the dynamic behavior of resources can affect the deadlock situation in future timestamps. The deadlock trilemma and the relation between concurrency, resources, and deadlocks have also been discussed. The experimental evaluation shows that the proposed methodology yields an improvement in transaction count in the Speedy and the Webflow algorithms by 41% and 27%, respectively.

Payment Channel Networks (PCNs) are an alternative to improve the scalability of a blockchain network. The network size of Bitcoin PCN is increasing rapidly; in the past three months, the number of nodes has more than doubled. With the increase in the network size, transactions on the network will also increase. However, the existing distributed routing algorithms cannot efficiently schedule concurrent transactions due to their static nature. We propose two algorithms, maxECW and maxSCL, which can handle concurrent transactions more efficiently. Our algorithms consider channel weights and introduce the concept of rebalancing to avoid the saturation of the directional capacity of a channel. We have also developed a simulator, DRLN sim, to compare our proposed algorithms with the existing ones. The routing algorithms are evaluated on the simulator by varying relevant parameters. On average, our proposed algorithms performed 50% more efficiently than existing algorithms in handling concurrent transactions.

Fault-based testing of software checks the software implementation for a set of faults. Two previous papers on fault-based testing [Kuhn 1999; Tsuchiya and Kikuno 2002] represent the required behavior of the software as a Boolean specification represented in Disjunctive Normal Form (DNF) and then show that faults may be organized in a hierarchy. This article extends these results by identifying necessary and sufficient conditions for fault-based testing. Unlike previous solutions, the formal analysis used to derive these conditions imposes no restrictions (such as DNF) on the form of the Boolean specification.

The Modified Condition Decision Coverage (MCDC) test criterion is a mandatory requirement for the testing of avionics software as per the DO-178B standard. This paper presents a formal analysis for the three different forms of MCDC. In addition, a recently proposed test criterion, Reinforced Condition Decision Coverage (RCDC), has also been investigated in comparison with MCDC. In contrast with the earlier analysis approaches that have been based on empirical and probabilistic models, the principles of Boolean ogic are used here to study the fault detection effectiveness of the MCDC and RCDC criteria. Based on the properties of Boolean specifications, the analysis identifies the detection conditions for six kinds of faults. The results allow the measurement of the effort required in testing and the effectiveness of generated test sets satisfying the MCDC and RCDC criteria. Copyright © 2004 John Wiley & Sons, Ltd.

Abstract Fault‐detection effectiveness of coverage criteria has remained one of the controversial issues in recent years. In order to detect a fault, a test set must execute the faulty statement, cause infection of the data state and then propagate the faulty data state to bring about a failure. This paper sheds some light on the earlier contradictory results by investigating the infection aspect of coverage criteria. For a given test criterion, the number of test sets satisfying the criterion may be very large, with varying fault‐detection effectiveness. In a recent work the measure of variation in effectiveness of a test criterion was defined as ‘tolerance’. This paper presents an experimental evaluation of tolerance for control‐flow test criteria by exhaustive test set generation, wherever possible. The approach used here is complementary to earlier empirical studies that adopted analysis of some test sets using random selection techniques. Four industrially used control‐flow testing criteria, Condition Coverage (CC), Decision Condition Coverage (DCC), Full Predicate Coverage (FPC) and Modified Condition Decision Coverage (MCDC) have been analysed against four types of faults. A new test criterion, Reinforced Condition Decision Coverage (RCDC), is also analysed and compared. Copyright © 2004 John Wiley & Sons, Ltd.

Effectiveness of testing criteria is the ability to detect failure in a software program. We consider not only effectiveness of some testing criterion in itself but a variance of effectiveness of different test sets satisfied the same testing criterion. We name this property "tolerance" of a testing criterion and show that, for practical using a criterion, a high tolerance is as well important as high effectiveness. The results of empirical evaluation of tolerance for different criteria, types of faults and decisions are presented. As well as quite simple and well-known control-flow criteria, we study more complicated criteria: full predicate coverage, modified condition/decision coverage and reinforced condition/decision coverage criteria.