arXiv subjects

Lina Gerlach

Publications and source records attributed to Lina Gerlach.

5 recordsLinked to original sources

arXiv2026

Tractable Hyperproperties for MDPs

Probabilistic hyperproperties describe probabilistic relations between multiple sets of executions in a stochastic system. Prominent examples include information-theoretic characterizations of security and privacy policies. However, model checking for existing probabilistic hyperlogics, such as HyperPCTL and PHL, is undecidable in Markov decision processes (MDPs). In this paper, we study an underexplored problem: the verification of fragments of probabilistic hyperproperties that relate the probabilities of different events to each other, possibly across independent executions of an MDP. Representative verification questions include: Can two different target states be reached from the same initial state with the same probability? (different events), Can a given target state be reached from two different initial states with the same probability? (same event, independent executions), and natural combinations of these forms. Besides reachability, our relational probabilistic properties cover safety, B\"uchi, and coB\"uchi objectives. They can also be combined conjunctively, thereby generalizing standard multi-objective MDP properties. We provide efficient algorithms for relevant classes of relational properties, while proving computational hardness and completeness results for others. An implementation of our approach outperforms solvers for more general probabilistic hyperlogics by orders of magnitude on the subset of their benchmarks that lies within our fragment.

cs.LO↗

arXiv2025

A Hyperlogic for Strategies in Stochastic Games (Extended Version)

We propose a probabilistic hyperlogic called HyperSt$^2$ that can express hyperproperties of strategies in turn-based stochastic games. To the best of our knowledge, HyperSt$^2$ is the first hyperlogic for stochastic games. HyperSt$^2$ can relate probabilities of several independent executions of strategies in a stochastic game. For example, in HyperSt$^2$ it is natural to formalize optimality, i.e., to express that some strategy is better than all other strategies, or to express the existence of Nash equilibria. We investigate the expressivity of HyperSt$^2$ by comparing it to existing logics for stochastic games, as well as existing hyperlogics. Though the model-checking problem for HyperSt$^2$ is in general undecidable, we show that it becomes decidable for bounded memory and is in EXPTIME and PSPACE-hard over memoryless deterministic strategies, and we identify a fragment for which the model-checking problem is PSPACE-complete.

cs.LO↗

arXiv2025

Efficient Probabilistic Model Checking for Relational Reachability (Extended Version)

Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the nondeterminism such that the probability to reach an error state is above a threshold? We consider an understudied extension that relates different reachability probabilities, such as: Is there a scheduler such that two sets of states are reached with different probabilities? These questions appear naturally in the design of randomized algorithms and in various security applications. We provide a tractable algorithm for many variations of this problem, while proving computational hardness of some others. An implementation of our algorithm beats solvers for more general probabilistic hyperlogics by orders of magnitude, on the subset of their benchmarks that are within our fragment.

cs.LO↗

arXiv2025

Counterfactual Strategies for Markov Decision Processes

Counterfactuals are widely used in AI to explain how minimal changes to a model's input can lead to a different output. However, established methods for computing counterfactuals typically focus on one-step decision-making, and are not directly applicable to sequential decision-making tasks. This paper fills this gap by introducing counterfactual strategies for Markov Decision Processes (MDPs). During MDP execution, a strategy decides which of the enabled actions (with known probabilistic effects) to execute next. Given an initial strategy that reaches an undesired outcome with a probability above some limit, we identify minimal changes to the initial strategy to reduce that probability below the limit. We encode such counterfactual strategies as solutions to non-linear optimization problems, and further extend our encoding to synthesize diverse counterfactual strategies. We evaluate our approach on four real-world datasets and demonstrate its practical viability in sophisticated sequential decision-making tasks.

cs.AI↗

arXiv2023

Introducing Asynchronicity to Probabilistic Hyperproperties

Probabilistic hyperproperties express probabilistic relations between different executions of systems with uncertain behavior. HyperPCTL allows to formalize such properties, where quantification over probabilistic schedulers resolves potential non-determinism. In this paper we propose an extension named AHyperPCTL to additionally introduce asynchronicity between the observed executions by quantifying over stutter-schedulers, which may randomly decide to delay scheduler decisions by idling. To our knowledge, this is the first asynchronous extension of a probabilistic branching-time hyperlogic. We show that AHyperPCTL can express interesting information-flow security policies, and propose a model checking algorithm for a decidable fragment.

cs.LO↗