Blackwell-Optimal Strategies in Priority Mean-Payoff Games

We examine perfect information stochastic mean-payoff games - a class of games containing as special sub-classes the usual mean-payoff games and parity games. We show that deterministic memoryless strategies that are optimal for discounted games with state-dependent discount factors close to 1 are optimal for priority mean-payoff games establishing a strong link between these two classes

Games where you can play optimally without any memory

International audienceReactive systems are often modelled as two person antagonistic games where one player represents the system while his adversary represents the environment. Undoubtedly, the most popular games in this context are parity games and their cousins (Rabin, Streett and Muller games). Recently however also games with other types of payments, like discounted or mean-payoff , previously used only in economic context, entered into the area of system modelling and verification. The most outstanding property of parity, mean-payoff and discounted games is the existence of optimal positional (memoryless) strategies for both players. This observation raises two questions: (1) can we characterise the family of payoff mappings for which there always exist optimal positional strategies for both players and (2) are there other payoff mappings with practical or theoretical interest and admitting optimal positional strategies. This paper provides a complete answer to the first question by presenting a simple necessary and sufficient condition on payoff mapping guaranteeing the existence of optimal positional strategies. As a corollary to this result we show the following remarkable property of payoff mappings: if both players have optimal positional strategies when playing solitary one-player games then also they have optimal positional strategies for two-player games

Optimal Strategies in Infinite-state Stochastic Reachability Games

We consider perfect-information reachability stochastic games for 2 players on infinite graphs. We identify a subclass of such games, and prove two interesting properties of it: first, Player Max always has optimal strategies in games from this subclass, and second, these games are strongly determined. The subclass is defined by the property that the set of all values can only have one accumulation point -- 0. Our results nicely mirror recent results for finitely-branching games, where, on the contrary, Player Min always has optimal strategies. However, our proof methods are substantially different, because the roles of the players are not symmetric. We also do not restrict the branching of the games. Finally, we apply our results in the context of recently studied One-Counter stochastic games

Perfect Information Stochastic Priority Games

International audienceWe introduce stochastic priority games - a new class of perfect information stochastic games. These games can take two different, but equivalent, forms. In stopping priority games a play can be stopped by the environment after a finite number of stages, however, infinite plays are also possible. In discounted priority games only infinite plays are possible and the payoff is a linear combination of the classical discount payoff and of a limit payoff evaluating the performance at infinity. Shapley games and parity games are special extreme cases of priority games

Deterministic Priority Mean-payoff Games as Limits of Discounted Games

International audienceInspired by the paper of de Alfaro, Henzinger and Majumdar about discounted $\mu$-calculus we show new surprising links between parity games and different classes of discounted games

Containment and equivalence of weighted automata: Probabilistic and max-plus cases

This paper surveys some results regarding decision problems for probabilistic and max-plus automata, such as containment and equivalence. Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values. Given two weighted automata, the equivalence problem asks whether their semantics are the same, and the containment problem whether one is point-wise smaller than the other one. These problems have been studied intensively and this paper will review some techniques used to show (un)decidability and state a list of open questions that still remain

Computer aided synthesis: a game theoretic approach

In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum games. The simple case of one-player games is strongly related to automata theory on infinite words. All along the article, we focus on general approaches to solve the studied problems, and we provide several illustrative examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language Theory" (DLT 2017

Distributed Synthesis in Continuous Time

We introduce a formalism modelling communication of distributed agents strictly in continuous-time. Within this framework, we study the problem of synthesising local strategies for individual agents such that a specified set of goal states is reached, or reached with at least a given probability. The flow of time is modelled explicitly based on continuous-time randomness, with two natural implications: First, the non-determinism stemming from interleaving disappears. Second, when we restrict to a subclass of non-urgent models, the quantitative value problem for two players can be solved in EXPTIME. Indeed, the explicit continuous time enables players to communicate their states by delaying synchronisation (which is unrestricted for non-urgent models). In general, the problems are undecidable already for two players in the quantitative case and three players in the qualitative case. The qualitative undecidability is shown by a reduction to decentralized POMDPs for which we provide the strongest (and rather surprising) undecidability result so far

Effect of cadmium on cytosine hydroxymethylation in gastropod hepatopancreas

5-Hydroxymethylcytosine (5hmC) is an important, yet poorly understood epigenetic DNA modification, especially in invertebrates. Aberrant genome-wide 5hmC levels have been associated with cadmium (Cd) exposure in humans, but such information is lacking for invertebrate bioindicators. Here, we aimed to determine whether this epigenetic mark is present in DNA of the hepatopancreas of the land snail Cantareus aspersus and is responsive to Cd exposure. Adult snails were reared under laboratory conditions and exposed to graded amounts of dietary cadmium for 14 days. Weight gain was used as a sublethal endpoint, whereas survival as a lethal endpoint. Our results are the first to provide evidence for the presence of 5hmC in DNA of terrestrial mollusks; 5hmC levels are generally low with the measured values falling below 0.03%. This is also the first study to investigate the interplay of Cd with DNA hydroxymethylation levels in a non-human animal study system. Cadmium retention in the hepatopancreas of C. aspersus increased from a dietary Cd dose of 1 milligram per kilogram dry weight (mg/kg d. wt). For the same treatment, we identified the only significant elevation in percentage of samples with detectable 5hmC levels despite the lack of significant mortalities and changes in weight gain among treatment groups. These findings indicate that 5hmC is an epigenetic mark that may be responsive to Cd exposure, thereby opening a new aspect to invertebrate environmental epigenetics

Field mixtures of currently used pesticides in agricultural soil pose a risk to soil invertebrates

Massive use of pesticides in conventional agriculture leads to accumulation in soil of complex mixtures, triggering questions about their potential ecotoxicological risk. This study assessed cropland soils containing pesticide mixtures sampled from conventional and organic farming systems at La Cage and Mons, France. The conventional agricultural field soils contained more pesticide residues (11 and 17 versus 3 and 11, respectively) and at higher concentrations than soils from organic fields (mean 6.6 and 10.5 versus 0.2 and 0.6 μg kg−1, respectively), including systemic insecticides belonging to neonicotinoids, carbamate herbicides and broad-spectrum fungicides mostly from the azole family. A risk quotient (RQi) approach evaluated the toxicity of the pesticide mixtures in soil, assuming concentration addition. Based on measured concentrations, both conventional agricultural soils posed high risks to soil invertebrates, especially due to the presence of epoxiconazole and imidacloprid, whereas soils under organic farming showed negligible to medium risk. To confirm the outcome of the risk assessment, toxicity of the soils was determined in bioassays following standardized test guidelines with seven representative non-target invertebrates: earthworms (Eisenia andrei, Lumbricus rubellus, Aporrectodea caliginosa), enchytraeids (Enchytraeus crypticus), Collembola (Folsomia candida), oribatid mites (Oppia nitens), and snails (Cantareus aspersus). Collembola and enchytraeid survival and reproduction and land snail growth were significantly lower in soils from conventional compared to organic agriculture. The earthworms displayed different responses: L. rubellus showed higher mortality on soils from conventional agriculture and large body mass loss in all field soils, E. andrei showed considerable mass loss and strongly reduced reproduction, and A. caliginosa showed significantly reduced acetylcholinesterase activity in soils from conventional agriculture. The oribatid mites did not show consistent differences between organic and conventional farming soils. These results highlight that conventional agricultural practices pose a high risk for soil invertebrates and may threaten soil functionality, likely due to additive or synergistic “cocktail effects”