Abstract

AbstractWe 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.KeywordsWinning StrategyState FormulaPath FormulaPath QuantifierCombine ComplexityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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