On the Complexity of Shortest Path Problems on Discounted Cost Graphs
نویسندگان
چکیده
Discounted Cost Register Automata (DCRA) associate costs with strings in a regular manner using the operation of discounted sum. The min-cost optimization problem for DCRAs corresponds to computing shortest paths in graphs with more general forms of discounting than the well-studied notion of future discounting. We present solutions to two classes of such shortest path problems: in presence of both past and future discounting, we show the decision problem is NP-complete, but has a polynomial-time approximation scheme; in presence of two future discounting criteria that are composed in a prioritized manner, we show that the problem is solvable in Nexptime.
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