---
res:
bibo_abstract:
- 'We consider Markov decision processes (MDPs) with Büchi (liveness) objectives.
We consider the problem of computing the set of almost-sure winning states from
where the objective can be ensured with probability 1. Our contributions are as
follows: First, we present the first subquadratic symbolic algorithm to compute
the almost-sure winning set for MDPs with Büchi objectives; our algorithm takes
O(n · √ m) symbolic steps as compared to the previous known algorithm that takes
O(n 2) symbolic steps, where n is the number of states and m is the number of
edges of the MDP. In practice MDPs have constant out-degree, and then our symbolic
algorithm takes O(n · √ n) symbolic steps, as compared to the previous known O(n
2) symbolic steps algorithm. Second, we present a new algorithm, namely win-lose
algorithm, with the following two properties: (a) the algorithm iteratively computes
subsets of the almost-sure winning set and its complement, as compared to all
previous algorithms that discover the almost-sure winning set upon termination;
and (b) requires O(n · √ K) symbolic steps, where K is the maximal number of edges
of strongly connected components (scc''s) of the MDP. The win-lose algorithm requires
symbolic computation of scc''s. Third, we improve the algorithm for symbolic scc
computation; the previous known algorithm takes linear symbolic steps, and our
new algorithm improves the constants associated with the linear number of steps.
In the worst case the previous known algorithm takes 5×n symbolic steps, whereas
our new algorithm takes 4×n symbolic steps.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Krishnendu
foaf_name: Chatterjee, Krishnendu
foaf_surname: Chatterjee
foaf_workInfoHomepage: http://www.librecat.org/personId=2E5DCA20-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-4561-241X
- foaf_Person:
foaf_givenName: Monika
foaf_name: Henzinger, Monika
foaf_surname: Henzinger
- foaf_Person:
foaf_givenName: Manas
foaf_name: Joglekar, Manas
foaf_surname: Joglekar
- foaf_Person:
foaf_givenName: Nisarg
foaf_name: Shah, Nisarg
foaf_surname: Shah
bibo_doi: 10.1007/s10703-012-0180-2
bibo_issue: '3'
bibo_volume: 42
dct_date: 2013^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: Symbolic algorithms for qualitative analysis of Markov decision processes
with Büchi objectives@
...