Energy Mean-Payoff Games

In this paper, we study one-player and two-player energy mean-payoff games. Energy mean-payoff games are games of infinite duration played on a finite graph with edges labeled by 2-dimensional weight vectors. The objective of the first player (the protagonist) is to satisfy an energy objective on the first dimension and a mean-payoff objective on the second dimension. We show that optimal strategies for the first player may require infinite memory while optimal strategies for the second player (the antagonist) do not require memory. In the one-player case (where only the first player has choices), the problem of deciding who is the winner can be solved in polynomial time while for the two-player case we show co-NP membership and we give effective constructions for the infinite-memory optimal strategies of the protagonist

On the Complexity of Heterogeneous Multidimensional Games

We study two-player zero-sum turn-based games played on multidimensional weighted graphs with heterogeneous quantitative objectives. Our objectives are defined starting from the measures Inf, Sup, LimInf, and LimSup of the weights seen along the play, as well as on the window mean-payoff (WMP) measure recently introduced in [Krishnendu,Doyen,Randour,Raskin, Inf. Comput., 2015]. Whereas multidimensional games with Boolean combinations of classical mean-payoff objectives are undecidable [Velner, FOSSACS, 2015], we show that CNF/DNF Boolean combinations for heterogeneous measures taken among {WMP, Inf, Sup, LimInf, LimSup} lead to EXPTIME-completeness with exponential memory strategies for both players. We also identify several interesting fragments with better complexities and memory requirements, and show that some of them are solvable in PTIME

Parameterized complexity of games with monotonically ordered ω-regular objectives

In recent years, two-player zero-sum games with multiple objectives have received a lot of interest as a model for the synthesis of complex reactive systems. In this framework, Player 1 wins if he can ensure that all objectives are satisfied against any behavior of Player 2. When this is not possible to satisfy all the objectives at once, an alternative is to use some preorder on the objectives according to which subset of objectives Player 1 wants to satisfy. For example, it is often natural to provide more significance to one objective over another, a situation that can be modelled with lexicographically ordered objectives for instance. Inspired by recent work on concurrent games with multiple ω-regular objectives by Bouyer et al. we investigate in detail turned-based games with monotonically ordered and ω-regular objectives. We study the threshold problem which asks whether player 1 can ensure a payo greater than or equal to a given threshold w.r.t. a given monotonic preorder. As the number of objectives is usually much smaller than the size of the game graph, we provide a parametric complexity analysis and we show that our threshold problem is in FPT for all monotonic preorders and all classical types of ω-regular objectives. We also provide polynomial time algorithms for Büchi, coBüchi and explicit Muller objectives for a large subclass of monotonic preorders that includes among others the lexicographic preorder. In the particular case of lexicographic preorder, we also study the complexity of computing the values and the memory requirements of optimal strategies.SCOPUS: cp.pinfo:eu-repo/semantics/publishe

Window parity games: An alternative approach toward parity games with time bounds

Classical objectives in two-player zero-sum games played on graphs often deal with limit behaviors of infinite plays: e.g. mean-payoff and total-payoff in the quantitative setting, or parity in the qualitative one (a canonical way to encode ω-regular properties). Those objectives offer powerful abstraction mechanisms and often yield nice properties such as memoryless determinacy. However, their very nature provides no guarantee on time bounds within which something good can be witnessed. In this work, we consider two approaches toward inclusion of time bounds in parity games. The first one, parity-response games, is based on the notion of finitary parity games [8] and parity games with costs [16, 29]. The second one, window parity games, is inspired by window mean-payoff games [5]. We compare the two approaches and show that while they prove to be equivalent in some contexts, window parity games offer a more tractable alternative when the time bound is given as a parameter (P-c. vs. PSPACE-c.). In particular, it provides a conservative approximation of parity games computable in polynomial time. Furthermore, we extend both approaches to the multi-dimension setting. We give the full picture for both types of games with regard to complexity and memory bounds.SCOPUS: cp.pinfo:eu-repo/semantics/publishe

Rare predicted loss-of-function variants of type I IFN immunity genes are associated with life-threatening COVID-19

BackgroundWe previously reported that impaired type I IFN activity, due to inborn errors of TLR3- and TLR7-dependent type I interferon (IFN) immunity or to autoantibodies against type I IFN, account for 15-20% of cases of life-threatening COVID-19 in unvaccinated patients. Therefore, the determinants of life-threatening COVID-19 remain to be identified in similar to 80% of cases.MethodsWe report here a genome-wide rare variant burden association analysis in 3269 unvaccinated patients with life-threatening COVID-19, and 1373 unvaccinated SARS-CoV-2-infected individuals without pneumonia. Among the 928 patients tested for autoantibodies against type I IFN, a quarter (234) were positive and were excluded.ResultsNo gene reached genome-wide significance. Under a recessive model, the most significant gene with at-risk variants was TLR7, with an OR of 27.68 (95%CI 1.5-528.7, P=1.1x10(-4)) for biochemically loss-of-function (bLOF) variants. We replicated the enrichment in rare predicted LOF (pLOF) variants at 13 influenza susceptibility loci involved in TLR3-dependent type I IFN immunity (OR=3.70[95%CI 1.3-8.2], P=2.1x10(-4)). This enrichment was further strengthened by (1) adding the recently reported TYK2 and TLR7 COVID-19 loci, particularly under a recessive model (OR=19.65[95%CI 2.1-2635.4], P=3.4x10(-3)), and (2) considering as pLOF branchpoint variants with potentially strong impacts on splicing among the 15 loci (OR=4.40[9%CI 2.3-8.4], P=7.7x10(-8)). Finally, the patients with pLOF/bLOF variants at these 15 loci were significantly younger (mean age [SD]=43.3 [20.3] years) than the other patients (56.0 [17.3] years; P=1.68x10(-5)).ConclusionsRare variants of TLR3- and TLR7-dependent type I IFN immunity genes can underlie life-threatening COVID-19, particularly with recessive inheritance, in patients under 60 years old