How to Win First-Order Safety Games

First-order (FO) transition systems have recently attracted attention for the verification of parametric systems such as network protocols, software-defined networks or multi-agent workflows like conference management systems. Functional correctness or noninterference of these systems have conveniently been formulated as safety or hypersafety properties, respectively. In this article, we take the step from verification to synthesis---tackling the question whether it is possible to automatically synthesize predicates to enforce safety or hypersafety properties like noninterference. For that, we generalize FO transition systems to FO safety games. For FO games with monadic predicates only, we provide a complete classification into decidable and undecidable cases. For games with non-monadic predicates, we concentrate on universal first-order invariants, since these are sufficient to express a large class of properties---for example noninterference. We identify a non-trivial sub-class where invariants can be proven inductive and FO winning strategies be effectively constructed. We also show how the extraction of weakest FO winning strategies can be reduced to SO quantifier elimination itself. We demonstrate the usefulness of our approach by automatically synthesizing nontrivial FO specifications of messages in a leader election protocol as well as for paper assignment in a conference management system to exclude unappreciated disclosure of reports

How Much Lookahead is Needed to Win Infinite Games?

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. For $\omega$-regular winning conditions it is known that such games can be solved in doubly-exponential time and that doubly-exponential lookahead is sufficient. We improve upon both results by giving an exponential time algorithm and an exponential upper bound on the necessary lookahead. This is complemented by showing EXPTIME-hardness of the solution problem and tight exponential lower bounds on the lookahead. Both lower bounds already hold for safety conditions. Furthermore, solving delay games with reachability conditions is shown to be PSPACE-complete. This is a corrected version of the paper https://arxiv.org/abs/1412.3701v4 published originally on August 26, 2016

Quantitative Games under Failures

We study a generalisation of sabotage games, a model of dynamic network games introduced by van Benthem. The original definition of the game is inherently finite and therefore does not allow one to model infinite processes. We propose an extension of the sabotage games in which the first player (Runner) traverses an arena with dynamic weights determined by the second player (Saboteur). In our model of quantitative sabotage games, Saboteur is now given a budget that he can distribute amongst the edges of the graph, whilst Runner attempts to minimise the quantity of budget witnessed while completing his task. We show that, on the one hand, for most of the classical cost functions considered in the literature, the problem of determining if Runner has a strategy to ensure a cost below some threshold is EXPTIME-complete. On the other hand, if the budget of Saboteur is fixed a priori, then the problem is in PTIME for most cost functions. Finally, we show that restricting the dynamics of the game also leads to better complexity

The Complexity of Admissibility in Omega-Regular Games

Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games played on graphs with omega-regular objectives. In this paper, we study the algorithmic properties of this concept for such games. We settle the exact complexity of natural decision problems on the set of strategies that survive iterated elimination of dominated strategies. As a byproduct of our construction, we obtain automata which recognize all the possible outcomes of such strategies

Are NFL Athletes Receiving Over-Valued Contracts?

Many sport research studies have been conducted that examine the performance of professional athletes and their corresponding effect on franchise winning percentages, team revenues, economic repercussions, performance-based compensation, and much more. Research in the National Football League, however, has been found to be somewhat limited due to the numerous possible positions and resulting vastness of position-specific variables. The NFL lockout in 2011 caused many to question the specific relationship between professional athlete performance and salary distribution. This study’s purpose was to find a collection of variables with which all NFL athletes could be compared, and to identify relationships existing between a player’s performance and his value/salary. Data was collected from USAToday.com, Pro-football-reference.com, and AdvancedNFLStats.com. This data was then organized and manipulated into a format that allowed all players in the league during the 2009 season to be compared. Of the nine variables considered for this study, four were found to have a significant relationship with a player’s value/salary. These results were utilized to create a Player Valuation model and then analyze the overall salary distribution throughout the NFL. From this, it was observed while there are many athletes in the NFL that receive extravagant salaries well over their projected value, there is a much larger portion of the league that is undervalued and receive less than their projected value. It was then concluded that a super-star variable would be necessary to create a more accurate Player Valuation model, and the reason there is a larger proportion of NFL players receiving a lower salary than they deserve is due to franchise cap limits. These cap limits place pressure on franchises to push down the salaries of non-superstar athletes in order to compensate for the salaries required for the super-star athletes on their rosters

Finite-state Strategies in Delay Games (full version)

What is a finite-state strategy in a delay game? We answer this surprisingly non-trivial question by presenting a very general framework that allows to remove delay: finite-state strategies exist for all winning conditions where the resulting delay-free game admits a finite-state strategy. The framework is applicable to games whose winning condition is recognized by an automaton with an acceptance condition that satisfies a certain aggregation property. Our framework also yields upper bounds on the complexity of determining the winner of such delay games and upper bounds on the necessary lookahead to win the game. In particular, we cover all previous results of that kind as special cases of our uniform approach