利用图算法的力量：计算机辅助验证的有效算法
Leveraging the Power of Graph Algorithms: Efficient Algorithms for Computer-Aided Verification
摘要：
本论文的目标是利用快速图算法和现代算法技术解决图、MDP和博弈图上的模型检验和综合问题。结果包括符号算法，一个众所周知的算法在模型检验，贸易有限的访问输入模型的有效表示。特别是，我们提出了以下结果：算法的游戏图的平均回报Büchi目标和平均回报coBüchi目标相匹配的最佳运行时间的平均回报目标的界限之一。图和MDP中Streett目标的近线性时间随机算法。图中有界Büchi目标的次三次时间算法和对策图的三次时间算法。博弈图和MDP中可达性目标查询的条件下界。图和MDP中顺序可达性目标的线性和近线性时间算法。博弈图中奇偶目标的第一个拟多项式时间符号算法。我们打破了一个长期的运行时间界MEC分解从90年代提供了一个次二次时间符号算法。
英文摘要：
The goal of the thesis is to leverage fast graph algorithms and modern algorithmic techniques for problems in model checking and synthesis on graphs, MDPs, and game graphs. The results include symbolic algorithms, a well-known class of algorithms in model checking that trades limited access to the input model for an efficient representation. In particular, we present the following results: Algorithms for game graphs with mean-payoff Büchi objectives and mean-payoff coBüchi objectives which match one of the best running time bounds for mean-payoff objectives. A near-linear time randomized algorithm for Streett objectives in graphs and MDPs. A sub-cubic time algorithm for bounded Büchi objectives in graphs and a cubic time algorithm for game graphs. Conditional lower bounds for queries of reachability objectives in game graphs and MDPs. Linear and near-linear time algorithms for sequential reachability objectives in graphs and MDPs respectively. The first quasi-polynomial time symbolic algorithm for parity objectives in game graphs. We break a long-standing running time bound for MEC decomposition from the '90s by providing a sub-quadratic time symbolic algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
