@inproceedings{4542,
abstract = {Weighted automata are finite automata with numerical weights on transitions. Nondeterministic weighted automata define quantitative languages L that assign to each word w a real number L(w) computed as the maximal value of all runs over w, and the value of a run r is a function of the sequence of weights that appear along r. There are several natural functions to consider such as Sup, LimSup, LimInf, limit average, and discounted sum of transition weights.
We introduce alternating weighted automata in which the transitions of the runs are chosen by two players in a turn-based fashion. Each word is assigned the maximal value of a run that the first player can enforce regardless of the choices made by the second player. We survey the results about closure properties, expressiveness, and decision problems for nondeterministic weighted automata, and we extend these results to alternating weighted automata.
For quantitative languages L 1 and L 2, we consider the pointwise operations max(L 1,L 2), min(L 1,L 2), 1 − L 1, and the sum L 1 + L 2. We establish the closure properties of all classes of alternating weighted automata with respect to these four operations.
We next compare the expressive power of the various classes of alternating and nondeterministic weighted automata over infinite words. In particular, for limit average and discounted sum, we show that alternation brings more expressive power than nondeterminism.
Finally, we present decidability results and open questions for the quantitative extension of the classical decision problems in automata theory: emptiness, universality, language inclusion, and language equivalence.},
author = {Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A},
location = {Wroclaw, Poland},
pages = {3 -- 13},
publisher = {Springer},
title = {{Alternating weighted automata}},
doi = {10.1007/978-3-642-03409-1_2},
volume = {5699},
year = {2009},
}
@misc{5393,
abstract = {Gist is a tool that (a) solves the qualitative analysis problem of turn-based probabilistic games with ω-regular objectives; and (b) synthesizes reasonable environment assumptions for synthesis of unrealizable specifications. Our tool provides efficient implementations of several reduction based techniques to solve turn-based probabilistic games, and uses the analysis of turn-based probabilistic games for synthesizing environment assumptions for unrealizable specifications.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Jobstmann, Barbara and Radhakrishna, Arjun},
issn = {2664-1690},
pages = {12},
publisher = {IST Austria},
title = {{Gist: A solver for probabilistic games}},
doi = {10.15479/AT:IST-2009-0003},
year = {2009},
}
@inproceedings{4543,
abstract = {The synthesis of a reactive system with respect to all omega-regular specification requires the solution of a graph game. Such games have been extended in two natural ways. First, a game graph can be equipped with probabilistic choices between alternative transitions, thus allowing the, modeling of uncertain behaviour. These are called stochastic games. Second, a liveness specification can he strengthened to require satisfaction within all unknown but bounded amount of time. These are called finitary objectives. We study. for the first time, the, combination of Stochastic games and finitary objectives. We characterize the requirements on optimal strategies and provide algorithms for Computing the maximal achievable probability of winning stochastic games with finitary parity or Street, objectives. Most notably the set of state's from which a player can win with probability . for a finitary parity objective can he computed in polynomial time even though no polynomial-time algorithm is known in the nonfinitary case.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Horn, Florian},
location = {High Tatras, Slovakia},
pages = {34 -- 54},
publisher = {Springer},
title = {{Stochastic games with finitary objectives}},
doi = {10.1007/978-3-642-03816-7_4},
volume = {5734},
year = {2009},
}
@misc{5394,
abstract = {We consider two-player games played on graphs with request-response and finitary Streett objectives. We show these games are PSPACE-hard, improving the previous known NP-hardness. We also improve the lower bounds on memory required by the winning strategies for the players.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Horn, Florian},
issn = {2664-1690},
pages = {11},
publisher = {IST Austria},
title = {{Improved lower bounds for request-response and finitary Streett games}},
doi = {10.15479/AT:IST-2009-0002},
year = {2009},
}
@article{3870,
abstract = {Games on graphs with omega-regular objectives provide a model for the control and synthesis of reactive systems. Every omega-regular objective can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens “eventually.” Two main strengths of the classical, infinite-limit formulation of liveness are robustness (independence from the granularity of transitions) and simplicity (abstraction of complicated time bounds). However, the classical liveness formulation suffers from the drawback that the time until something good happens may be unbounded. A stronger formulation of liveness, so-called finitary liveness, overcomes this drawback, while still retaining robustness and simplicity. Finitary liveness requires that there exists an unknown, fixed bound b such that something good happens within b transitions. While for one-shot liveness (reachability) objectives, classical and finitary liveness coincide, for repeated liveness (Buchi) objectives, the finitary formulation is strictly stronger. In this work we study games with finitary parity and Streett objectives. We prove the determinacy of these games, present algorithms for solving these games, and characterize the memory requirements of winning strategies. We show that finitary parity games can be solved in polynomial time, which is not known for infinitary parity games. For finitary Streett games, we give an EXPTIME algorithm and show that the problem is NP-hard. Our algorithms can be used, for example, for synthesizing controllers that do not let the response time of a system increase without bound.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Horn, Florian},
journal = {ACM Transactions on Computational Logic (TOCL)},
number = {1},
publisher = {ACM},
title = {{Finitary winning in omega-regular games}},
doi = {10.1145/1614431.1614432},
volume = {11},
year = {2009},
}
@misc{5395,
abstract = {We study observation-based strategies for partially-observable Markov decision processes (POMDPs) with omega-regular objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past sequence of observa- tions. We consider the qualitative analysis problem: given a POMDP with an omega-regular objective, whether there is an observation-based strategy to achieve the objective with probability 1 (almost-sure winning), or with positive probability (positive winning). Our main results are twofold. First, we present a complete picture of the computational complexity of the qualitative analysis of POMDPs with parity objectives (a canonical form to express omega-regular objectives) and its subclasses. Our contribution consists in establishing several upper and lower bounds that were not known in literature. Second, we present optimal bounds (matching upper and lower bounds) on the memory required by pure and randomized observation-based strategies for the qualitative analysis of POMDPs with parity objectives and its subclasses.},
author = {Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A},
issn = {2664-1690},
pages = {20},
publisher = {IST Austria},
title = {{Qualitative analysis of partially-observable Markov decision processes}},
doi = {10.15479/AT:IST-2009-0001},
year = {2009},
}