Oracle-guided inductive synthesis (OGIS) is a widely-used framework to apply program synthesis techniques in practice. The question selection problem aims at reducing the number of iterations in OGIS by selecting a proper input for each OGIS iteration. Theoretically, a question selector can generally improve the performance of OGIS solvers on both interactive and non-interactive tasks if it is not only effective for reducing iterations but also efficient. However, all existing effective question selectors fail in satisfying the requirement of efficiency. To ensure effectiveness, they convert the question selection problem into an optimization one, which is difficult to solve within a short time. In this paper, we propose a novel question selector, named LearnSy . LearnSy is both efficient and effective and thus achieves general improvement for OGIS solvers for the first time. Since we notice that the optimization tasks in previous studies are difficult because of the complex behavior of operators, we estimate these behaviors in LearnSy as simple random events. Subsequently, we provide theoretical results for the precision of this estimation and design an efficient algorithm for its calculation. According to our evaluation, when dealing with interactive tasks, LearnSy can offer competitive performance compared to existing selectors while being more efficient and more general. Moreover, when working on non-interactive tasks, LearnSy can generally reduce the time cost of existing CEGIS solvers by up to 43.0%.

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The selfish mining attack, arguably the most famous game-theoretic attack in blockchain, indicates that the Bitcoin protocol is not incentive-compatible. Most subsequent works mainly focus on strengthening the selfish mining strategy, thus enabling a single strategic agent more likely to deviate. In sharp contrast, little attention has been paid to the resistant behavior against the selfish mining attack, let alone further equilibrium analysis for miners and mining pools in the blockchain as a multi-agent system.In this paper, first, we propose a strategy called insightful mining to counteract selfish mining. By infiltrating an undercover miner into the selfish pool, the insightful pool could acquire the number of its hidden blocks. We prove that, with this extra insight, the utility of the insightful pool could be strictly greater than the selfish pool's when they have the same mining power. Then we investigate the mining game where all pools can either choose to be honest or take the insightful mining strategy. We characterize the Nash equilibrium of this mining game, and derive three corollaries: (a) each mining game has a pure Nash equilibrium; (b) honest mining is a Nash equilibrium if the largest mining pool has a fraction of mining power no more than 1/3; (c) there are at most two insightful pools under equilibrium no matter how the mining power is distributed.