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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 B\"uchi objectives and mean-payoff coB\"uchi objectives whicharXiv:2202.02660v1 fatcat:pjrm5gx5mbgsxefhowxgryccmy