István Majzik | Searcharxiv

arXiv2024

A Lazy Abstraction Algorithm for Markov Decision Processes: Theory and Initial Evaluation

Analysis of Markov Decision Processes (MDP) is often hindered by state space explosion. Abstraction is a well-established technique in model checking to mitigate this issue. This paper presents a novel lazy abstraction method for MDP analysis based on adaptive simulation graphs. Refinement is performed only when new parts of the state space are explored, which makes partial exploration techniques like Bounded Real-Time Dynamic Programming (BRTDP) retain more merged states. Therefore, we propose a combination of lazy abstraction and BRTDP. To evaluate the performance of our algorithm, we conduct initial experiments using the Quantitative Verification Benchmark Set.

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arXiv2017

Exploiting Hierarchy in the Abstraction-Based Verification of Statecharts Using SMT Solvers

Statecharts are frequently used as a modeling formalism in the design of state-based systems. Formal verification techniques are also often applied to prove certain properties about the behavior of the system. One of the most efficient techniques for formal verification is Counterexample-Guided Abstraction Refinement (CEGAR), which reduces the complexity of systems by automatically building and refining abstractions. In our paper we present a novel adaptation of the CEGAR approach to hierarchical statechart models. First we introduce an encoding of the statechart to logical formulas that preserves information about the state hierarchy. Based on this encoding we propose abstraction and refinement techniques that utilize the hierarchical structure of statecharts and also handle variables in the model. The encoding allows us to use SMT solvers for the systematic exploration and verification of the abstract model, including also bounded model checking. We demonstrate the applicability and efficiency of our abstraction techniques with measurements on an industry-motivated example.

cs.LO↗