IST Austria Technical Report
Simulation is an attractive alternative for language inclusion for automata as it is an under-approximation of language inclusion, but usually has much lower complexity. For non-deterministic automata, while language inclusion is PSPACE-complete, simulation can be computed in polynomial time. Simulation has also been extended in two orthogonal directions, namely, (1) fair simulation, for simulation over specified set of infinite runs; and (2) quantitative simulation, for simulation between weighted automata. Again, while fair trace inclusion is PSPACE-complete, fair simulation can be computed in polynomial time. For weighted automata, the (quantitative) language inclusion problem is undecidable for mean-payoff automata and the decidability is open for discounted-sum automata, whereas the (quantitative) simulation reduce to mean-payoff games and discounted-sum games, which admit pseudo-polynomial time algorithms. In this work, we study (quantitative) simulation for weighted automata with Büchi acceptance conditions, i.e., we generalize fair simulation from non-weighted automata to weighted automata. We show that imposing Büchi acceptance conditions on weighted automata changes many fundamental properties of the simulation games. For example, whereas for mean-payoff and discounted-sum games, the players do not need memory to play optimally; we show in contrast that for simulation games with Büchi acceptance conditions, (i) for mean-payoff objectives, optimal strategies for both players require infinite memory in general, and (ii) for discounted-sum objectives, optimal strategies need not exist for both players. While the simulation games with Büchi acceptance conditions are more complicated (e.g., due to infinite-memory requirements for mean-payoff objectives) as compared to their counterpart without Büchi acceptance conditions, we still present pseudo-polynomial time algorithms to solve simulation games with Büchi acceptance conditions for both weighted mean-payoff and weighted discounted-sum automata.
Chatterjee K, Henzinger TA, Otop J, Velner Y. Quantitative Fair Simulation Games. IST Austria; 2014. doi:10.15479/AT:IST-2014-315-v1-1
Chatterjee, K., Henzinger, T. A., Otop, J., & Velner, Y. (2014). Quantitative fair simulation games. IST Austria. https://doi.org/10.15479/AT:IST-2014-315-v1-1
Chatterjee, Krishnendu, Thomas A Henzinger, Jan Otop, and Yaron Velner. Quantitative Fair Simulation Games. IST Austria, 2014. https://doi.org/10.15479/AT:IST-2014-315-v1-1.
K. Chatterjee, T. A. Henzinger, J. Otop, and Y. Velner, Quantitative fair simulation games. IST Austria, 2014.
Chatterjee K, Henzinger TA, Otop J, Velner Y. 2014. Quantitative fair simulation games, IST Austria, 26p.
Chatterjee, Krishnendu, et al. Quantitative Fair Simulation Games. IST Austria, 2014, doi:10.15479/AT:IST-2014-315-v1-1.
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