Abstract
We study the complexity of the model-checking problem for the branching-time logic \(\text {CTL}^*\) and the alternating-time temporal logics \(\text {ATL}/\text {ATL}^*\) in one-counter processes and one-counter games respectively. The complexity is determined for all three logics when integer weights are input in unary (non-succinct) and binary (succinct) as well as when the input formula is fixed and is a parameter. Further, we show that deciding the winner in one-counter games with \(\text {LTL}\) objectives is \(\textsc {2ExpSpace}\)-complete for both succinct and non-succinct games. We show that all the problems considered stay in the same complexity classes when we add quantitative constraints that can compare the current value of the counter with a constant.
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Vester, S. (2015). On the Complexity of Model-Checking Branching and Alternating-Time Temporal Logics in One-Counter Systems. In: Finkbeiner, B., Pu, G., Zhang, L. (eds) Automated Technology for Verification and Analysis. ATVA 2015. Lecture Notes in Computer Science(), vol 9364. Springer, Cham. https://doi.org/10.1007/978-3-319-24953-7_27
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DOI: https://doi.org/10.1007/978-3-319-24953-7_27
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