Editors: Serge Haddad and Daniele Varacca

We study stochastic zero-sum games on graphs, which are prevalent tools to model decision-making in presence of an antagonistic opponent in a random environment. In this setting, an important question is the one of strategy complexity: what kinds of strategies are sufficient or required to play optimally (e.g., randomization or memory requirements)? Our contributions further the understanding of arena-independent finite-memory (AIFM) determinacy, i.e., the study of objectives for which memory is needed, but in a way that only depends on limited parameters of the game graphs. First, we show that objectives for which pure AIFM strategies suffice to play optimally also admit pure AIFM subgame perfect strategies. Second, we show that we can reduce the study of objectives for which pure AIFM strategies suffice in two-player stochastic games to the easier study of one-player stochastic games (i.e., Markov decision processes). Third, we characterize the sufficiency of AIFM strategies through two intuitive properties of objectives. This work extends a line of research started on deterministic games to stochastic ones.

We provide a generic algorithm for constructing formulae that distinguish behaviourally inequivalent states in systems of various transition types such as nondeterministic, probabilistic or weighted; genericity over the transition type is achieved by working with coalgebras for a set functor in the paradigm of universal coalgebra. For every behavioural equivalence class in a given system, we construct a formula which holds precisely at the states in that class. The algorithm instantiates to deterministic finite automata, transition systems, labelled Markov chains, and systems of many other types. The ambient logic is a modal logic featuring modalities that are generically extracted from the functor; these modalities can be systematically translated into custom sets of modalities in a postprocessing step. The new algorithm builds on an existing coalgebraic partition refinement algorithm. It runs in time O((m+n) log n) on systems with n states and m transitions, and the same asymptotic bound applies to the dag size of the formulae it constructs. This improves the bounds on run time and formula size compared to previous algorithms even for previously known specific instances, viz. transition systems and Markov chains; in particular, the best previous bound for transition systems was O(mn).

We study countably infinite Markov decision processes (MDPs) with real-valued transition rewards. Every infinite run induces the following sequences of payoffs: 1. Point payoff (the sequence of directly seen transition rewards), 2. Mean payoff (the sequence of the sums of all rewards so far, divided by the number of steps), and 3. Total payoff (the sequence of the sums of all rewards so far). For each payoff type, the objective is to maximize the probability that the $\liminf$ is non-negative. We establish the complete picture of the strategy complexity of these objectives, i.e., how much memory is necessary and sufficient for $\varepsilon$-optimal (resp. optimal) strategies. Some cases can be won with memoryless deterministic strategies, while others require a step counter, a reward counter, or both.

We provide time lower bounds for sequential and parallel algorithms deciding bisimulation on labeled transition systems that use partition refinement. For sequential algorithms this is $\Omega((m \mkern1mu {+} \mkern1mu n ) \mkern-1mu \log \mkern-1mu n)$ and for parallel algorithms this is $\Omega(n)$, where $n$ is the number of states and $m$ is the number of transitions. The lowerbounds are obtained by analysing families of deterministic transition systems, ultimately with two actions in the sequential case, and one action for parallel algorithms. For deterministic transition systems with one action, bisimilarity can be decided sequentially with fundamentally different techniques than partition refinement. In particular, Paige, Tarjan, and Bonic give a linear algorithm for this specific situation. We show, exploiting the concept of an oracle, that this approach is not of help to develop a faster generic algorithm for deciding bisimilarity. For parallel algorithms there is a similar situation where these techniques may be applied, too.

Hyperproperties are system properties that relate multiple computation paths in a system and are commonly used to, e.g., define information-flow policies. In this paper, we study a novel class of hyperproperties that allow reasoning about strategic abilities in multi-agent systems. We introduce HyperATL*, an extension of computation tree logic with path variables and strategy quantifiers. Our logic supports quantification over paths in a system - as is possible in hyperlogics such as HyperCTL* - but resolves the paths based on the strategic choices of a coalition of agents. This allows us to capture many previously studied (strategic) security notions in a unifying hyperlogic. Moreover, we show that HyperATL* is particularly useful for specifying asynchronous hyperproperties, i.e., hyperproperties where the execution speed on the different computation paths depends on the choices of a scheduler. We show that finite-state model checking of HyperATL* is decidable and present a model checking algorithm based on alternating automata. We establish that our algorithm is asymptotically optimal by proving matching lower bounds. We have implemented a prototype model checker for a fragment of HyperATL* that can check various security properties in small finite-state systems.

This paper introduces Hypersequent GV (HGV), a modular and extensible core calculus for functional programming with session types that enjoys deadlock freedom, confluence, and strong normalisation. HGV exploits hyper-environments, which are collections of type environments, to ensure that structural congruence is type preserving. As a consequence we obtain an operational correspondence between HGV and HCP -- a process calculus based on hypersequents and in a propositions-as-types correspondence with classical linear logic (CLL). Our translations from HGV to HCP and vice-versa both preserve and reflect reduction. HGV scales smoothly to support Girard's Mix rule, a crucial ingredient for channel forwarding and exceptions.

What payoffs are positionally determined for deterministic two-player antagonistic games on finite directed graphs? In this paper we study this question for payoffs that are continuous. The main reason why continuous positionally determined payoffs are interesting is that they include the multi-discounted payoffs. We show that for continuous payoffs, positional determinacy is equivalent to a simple property called prefix-monotonicity. We provide three proofs of it, using three major techniques of establishing positional determinacy -- inductive technique, fixed point technique and strategy improvement technique. A combination of these approaches provides us with better understanding of the structure of continuous positionally determined payoffs as well as with some algorithmic results.

In this paper, we provide an effective characterization of all the subgame-perfect equilibria in infinite duration games played on finite graphs with mean-payoff objectives. To this end, we introduce the notion of requirement, and the notion of negotiation function. We establish that the plays that are supported by SPEs are exactly those that are consistent with a fixed point of the negotiation function. Finally, we use that characterization to prove that the SPE threshold problem, who status was left open in the literature, is decidable.