Abstract
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.
This research was partially supported by NSF awards CCF 1137084, CCF 1138996, and CCF 0915777.
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Alur, R., Kannan, S., Tian, K., Yuan, Y. (2013). On the Complexity of Shortest Path Problems on Discounted Cost Graphs. In: Dediu, AH., MartÃn-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2013. Lecture Notes in Computer Science, vol 7810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37064-9_6
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DOI: https://doi.org/10.1007/978-3-642-37064-9_6
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