Abstract-Automatic synthesis of a reactive system from its formal specification is appealing but often difficult due to the tedium of writing auxiliary specifications, especially on the environment. In several instances, specifications are found unrealizable as a result of insufficient environmental assumptions. We present an approach to this problem for synthesis from LTL based on specification mining. For a satisfiable but unrealizable specification, a counter-strategy can be computed from the synthesis game as a witness to unrealizability. Our algorithm mines environment assumptions from this counter-strategy as well as user scenarios if they are provided. We argue that our approach is a natural way to discover the designer's intent. We demonstrate the effectiveness of our approach on examples from the domains of digital circuits and robotic controllers.

Learning in finitely repeated games of cooperation remains poorly understood in part because their dynamics play out over a timescale exceeding that of traditional lab experiments. Here, we report results of a virtual lab experiment in which 94 subjects play up to 400 ten-round games of Prisoner's Dilemma over the course of twenty consecutive weekdays. Consistent with previous work, the typical round of first defection moves earlier for several days; however, this unravelling process stabilizes after roughly one week. Analysing individual strategies, we find that approximately 40% of players behave as resilient cooperators who avoid unravelling even at significant cost to themselves. Finally, using a standard learning model we predict that a sufficiently large minority of resilient cooperators can permanently stabilize unravelling among a majority of rational players. These results shed hopeful light on the long-term dynamics of cooperation, and demonstrate the importance of long-run experiments.

We consider the problem of learning from revealed preferences in an online setting. In our framework, each period a consumer buys an optimal bundle of goods from a merchant according to her (linear) utility function and current prices, subject to a budget constraint. The merchant observes only the purchased goods, and seeks to adapt prices to optimize his profits. We give an efficient algorithm for the merchant's problem that consists of a learning phase in which the consumer's utility function is (perhaps partially) inferred, followed by a price optimization step. We also give an alternative online learning algorithm for the setting where prices are set exogenously, but the merchant would still like to predict the bundle that will be bought by the consumer, for purposes of inventory or supply chain management. In contrast with most prior work on the revealed preferences problem, we demonstrate that by making stronger assumptions on the form of utility functions, efficient algorithms for both learning and profit maximization are possible, even in adaptive, online settings.

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We report the results of a computational study of repacking in the FCC Incentive Auctions. Our interest lies in the structure and constraints of the solution space of feasible repackings. Our analyses are "mechanism-free", in the sense that they identify constraints that must hold regardless of the reverse auction mechanism chosen or the prices offered for broadcaster clearing. We examine topics such as the amount of spectrum that can be cleared nationwide, the geographic distribution of broadcaster clearings required to reach a clearing target, and the likelihood of reaching clearing targets under various models for broadcaster participation. Our study uses FCC interference data and a satisfiability-checking approach, and elucidates both the unavoidable mathematical constraints on solutions imposed by interference, as well as additional constraints imposed by assumptions on the participation decisions of broadcasters. * Research conducted on behalf of AT&T. All experiments, analyses, exposition, and opinions are exclusively the work of the authors. Contact author M. Kearns may be reached at mkearns@cis.upenn.edu 1 Throughout the paper, we shall assume the reader is familiar with the Incentive Auctions, and in particular the nature of the repacking problem in the reverse auction and the formulation of its feasibility as an instance of Boolean formula satisfiability.2 Our focus on nationwide clearing targets is done for simplicity of exposition; we offer no opinion on whether a nationwide or more variable approach is appropriate for any resulting wireless band plan.