@inproceedings{2237,
abstract = {We describe new extensions of the Vampire theorem prover for computing tree interpolants. These extensions generalize Craig interpolation in Vampire, and can also be used to derive sequence interpolants. We evaluated our implementation on a large number of examples over the theory of linear integer arithmetic and integer-indexed arrays, with and without quantifiers. When compared to other methods, our experiments show that some examples could only be solved by our implementation.},
author = {Blanc, Régis and Gupta, Ashutosh and Kovács, Laura and Kragl, Bernhard},
location = {Stellenbosch, South Africa},
pages = {173 -- 181},
publisher = {Springer},
title = {{Tree interpolation in Vampire}},
doi = {10.1007/978-3-642-45221-5_13},
volume = {8312},
year = {2013},
}
@inproceedings{2238,
abstract = {We study the problem of achieving a given value in Markov decision processes (MDPs) with several independent discounted reward objectives. We consider a generalised version of discounted reward objectives, in which the amount of discounting depends on the states visited and on the objective. This definition extends the usual definition of discounted reward, and allows to capture the systems in which the value of different commodities diminish at different and variable rates.
We establish results for two prominent subclasses of the problem, namely state-discount models where the discount factors are only dependent on the state of the MDP (and independent of the objective), and reward-discount models where they are only dependent on the objective (but not on the state of the MDP). For the state-discount models we use a straightforward reduction to expected total reward and show that the problem whether a value is achievable can be solved in polynomial time. For the reward-discount model we show that memory and randomisation of the strategies are required, but nevertheless that the problem is decidable and it is sufficient to consider strategies which after a certain number of steps behave in a memoryless way.
For the general case, we show that when restricted to graphs (i.e. MDPs with no randomisation), pure strategies and discount factors of the form 1/n where n is an integer, the problem is in PSPACE and finite memory suffices for achieving a given value. We also show that when the discount factors are not of the form 1/n, the memory required by a strategy can be infinite.
},
author = {Chatterjee, Krishnendu and Forejt, Vojtěch and Wojtczak, Dominik},
location = {Stellenbosch, South Africa},
pages = {228 -- 242},
publisher = {Springer},
title = {{Multi-objective discounted reward verification in graphs and MDPs}},
doi = {10.1007/978-3-642-45221-5_17},
volume = {8312},
year = {2013},
}
@inproceedings{2243,
abstract = {We show that modal logic over universally first-order definable classes of transitive frames is decidable. More precisely, let K be an arbitrary class of transitive Kripke frames definable by a universal first-order sentence. We show that the global and finite global satisfiability problems of modal logic over K are decidable in NP, regardless of choice of K. We also show that the local satisfiability and the finite local satisfiability problems of modal logic over K are decidable in NEXPTIME.},
author = {Michaliszyn, Jakub and Otop, Jan},
location = {Torino, Italy},
pages = {563 -- 577},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Elementary modal logics over transitive structures}},
doi = {10.4230/LIPIcs.CSL.2013.563},
volume = {23},
year = {2013},
}
@inproceedings{2244,
abstract = {We consider two systems (α1,...,αm) and (β1,...,βn) of curves drawn on a compact two-dimensional surface ℳ with boundary. Each αi and each βj is either an arc meeting the boundary of ℳ at its two endpoints, or a closed curve. The αi are pairwise disjoint except for possibly sharing endpoints, and similarly for the βj. We want to "untangle" the βj from the αi by a self-homeomorphism of ℳ; more precisely, we seek an homeomorphism φ: ℳ → ℳ fixing the boundary of ℳ pointwise such that the total number of crossings of the αi with the φ(βj) is as small as possible. This problem is motivated by an application in the algorithmic theory of embeddings and 3-manifolds. We prove that if ℳ is planar, i.e., a sphere with h ≥ 0 boundary components ("holes"), then O(mn) crossings can be achieved (independently of h), which is asymptotically tight, as an easy lower bound shows. In general, for an arbitrary (orientable or nonorientable) surface ℳ with h holes and of (orientable or nonorientable) genus g ≥ 0, we obtain an O((m + n)4) upper bound, again independent of h and g. },
author = {Matoušek, Jiří and Sedgwick, Eric and Tancer, Martin and Wagner, Uli},
location = {Bordeaux, France},
pages = {472 -- 483},
publisher = {Springer},
title = {{Untangling two systems of noncrossing curves}},
doi = {10.1007/978-3-319-03841-4_41},
volume = {8242},
year = {2013},
}
@article{2247,
abstract = {Cooperative behavior, where one individual incurs a cost to help another, is a wide spread phenomenon. Here we study direct reciprocity in the context of the alternating Prisoner's Dilemma. We consider all strategies that can be implemented by one and two-state automata. We calculate the payoff matrix of all pairwise encounters in the presence of noise. We explore deterministic selection dynamics with and without mutation. Using different error rates and payoff values, we observe convergence to a small number of distinct equilibria. Two of them are uncooperative strict Nash equilibria representing always-defect (ALLD) and Grim. The third equilibrium is mixed and represents a cooperative alliance of several strategies, dominated by a strategy which we call Forgiver. Forgiver cooperates whenever the opponent has cooperated; it defects once when the opponent has defected, but subsequently Forgiver attempts to re-establish cooperation even if the opponent has defected again. Forgiver is not an evolutionarily stable strategy, but the alliance, which it rules, is asymptotically stable. For a wide range of parameter values the most commonly observed outcome is convergence to the mixed equilibrium, dominated by Forgiver. Our results show that although forgiving might incur a short-term loss it can lead to a long-term gain. Forgiveness facilitates stable cooperation in the presence of exploitation and noise.},
author = {Zagorsky, Benjamin and Reiter, Johannes and Chatterjee, Krishnendu and Nowak, Martin},
journal = {PLoS One},
number = {12},
publisher = {Public Library of Science},
title = {{Forgiver triumphs in alternating prisoner's dilemma }},
doi = {10.1371/journal.pone.0080814},
volume = {8},
year = {2013},
}