Abstract
We study qualitative multi-objective reachability problems for Ordered Branching Markov Decision Processes (OBMDPs), or equivalently context-free MDPs, building on prior results for single-target reachability on Branching Markov Decision Processes (BMDPs). We provide two separate algorithms for “almost-sure” and “limit-sure” multi-target reachability for OBMDPs. Specifically, given an OBMDP, A, given a starting non-terminal, and given a set of target non-terminals K of size k = |K|, our first algorithm decides whether the supremum probability, of generating a tree that contains every target non-terminal inset K, is 1. Our second algorithm decides whether there is a strategy for the player to almost-surely (with probability 1) generate a tree that contains every target non-terminal in set K. The two separate algorithms are needed: we give examples showing that indeed “almost-sure” ≠ “limit-sure” for multi-target reachability in OBMDPs. Both algorithms run intime 2O(k)·|A|O(1), where |A| is the bit encoding length of A. Hence they run in P-time when k is fixed, and are fixed-parameter tractable with respect to k. Moreover, we show that the qualitative almost-sure (and limit-sure) multi-target reachability decision problem is in general NP-hard, when k is not fixed.
Original language | English |
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Title of host publication | Reachability Problems (RP 2020) |
Editors | Sylvain Schmitz, Igor Potapov |
Publisher | Springer |
Pages | 67-82 |
Number of pages | 16 |
ISBN (Electronic) | 978-3-030-61739-4 |
ISBN (Print) | 978-3-030-61738-7 |
DOIs | |
Publication status | Published - 15 Oct 2020 |
Event | 14th International Conference on Reachability Problems - Paris, France Duration: 19 Oct 2020 → 21 Oct 2020 https://www.irif.fr/~rp2020/ |
Publication series
Name | Lecture Notes in Computer Science |
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Publisher | Springer |
Volume | 12448 |
ISSN (Print) | 1611-3349 |
ISSN (Electronic) | 1611-3349 |
Conference
Conference | 14th International Conference on Reachability Problems |
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Abbreviated title | IRIF 2020 |
Country/Territory | France |
City | Paris |
Period | 19/10/20 → 21/10/20 |
Internet address |
Keywords / Materials (for Non-textual outputs)
- markov decision processes
- branching processes
- stochastic context-free grammars
- multi-objective
- reachability
- almost-sure
- limit-sure