Abstract
Cost-parity games are a fundamental tool in system design for the analysis of reactive and distributed systems that recently have received a lot of attention from the formal methods research community. They allow to reason about the time delay on the requests granted by systems, with a bounded consumption of resources, in their executions.In this paper, we contribute to research on cost-parity games by combining them with hierarchical systems, a successful method for the succinct representation of models. We show that determining the winner of a Hierarchical Cost-parity Game is Pspace-complete, thus matching the complexity of the proper special case of Hierarchical Parity Games. This shows that reasoning about temporal delay can be addressed at a free cost in terms of complexity.
Highlights
In formal system design and verification [11, 12, 20, 26], Parity Games represent a fundamental machinery for the automatic synthesis and verification of concurrent and reactive systems [5, 6, 7, 21, 22]
We further investigate the power of hierarchical representation by introducing and studying Cost-parity Games over Hierarchical Systems (HCPG)
Cost-parity games represent a powerful machinery for the verification of temporal requirements that are bounded in time
Summary
In formal system design and verification [11, 12, 20, 26], Parity Games represent a fundamental machinery for the automatic synthesis and verification of concurrent and reactive systems [5, 6, 7, 21, 22]. The impact of the concurrent setting on analysis problems is well-known: it costs an exponential, leading to the so called state-explosion problem Another source of the blow-up in the translation of systems into FSMs is that in high-level sequential programming, one can specify components only once and can reuse them in different contexts, leading to modularity and succinct system representation. The proposed approach for solving the considered problem generalizes in a non-trivial and sophisticated manner the one exploited in [5] for solving HPG, and is based on the notion of summary function for a memoryless strategy σ of Player 0 in a given sub-arena Such a function records in a finite and efficient way the overall behavior of all the finite plays of σ leading to exit states of the sub-arena with respect to requests and responses, by finitely abstracting the set of associated costs and delays.
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