Additional Winning Strategies in Two-Player Games

Abstract. We study the problem of checking whether a two-player reachability game admits more than a winning strategy. We investigate this in case of perfect and imperfect information, and, by means of an automata approach we provide a linear-time procedure and an exponential-time procedure, respectively. In both cases, the results are tight

On CTL* With graded path modalities

Graded path modalities count the number of paths satisfying a property, and generalize the existential (E) and universal (A) path modalities of CTL. The resulting logic is denoted GCTL, and is a very powerful logic since (as we show) it is equivalent, over trees, to monadic path logic. We settle the complexity of the satisfiability problem of GCTL, i.e., 2ExpTime-Complete, and the complexity of the model checking problem of GCTL, i.e., PSpace-Complete. The lower bounds already hold for CTL, and so we supply the upper bounds. The significance of this work is two-fold: GCTL is much more expressive than CTL as it adds to it a form of quantitative reasoning, and this is done at no extra cost in computational complexity.The final publication is available via https://doi.org/10.1007/978-3-662-48899-7_20.(VLID)2806554Accepted versio