**Conclusions and Discussions, Acknowledgment and References**

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by Aiding in the focused exploration of potential solutions.April 27th, 2024

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**Authors:**

(1) Falke B. Ø. Carlsen, Department of Computer Science, Aalborg University, Denmark & [email protected];

(2) Lars Bo P. Frydenskov, Department of Computer Science, Aalborg University, Denmark & [email protected];

(3) Nicolaj Ø. Jensen, Department of Computer Science, Aalborg University, Denmark & [email protected];

(4) Jener Rasmussen, [email protected];

(5) Mathias M. Sørensen, [email protected];

(6) Asger G. Weirsøe, [email protected];

(7) Mathias C. Jensen, Department of Computer Science, Aalborg University, Denmark & [email protected];

(8) Kim G. Larsen, Department of Computer Science, Aalborg University, Denmark & [email protected].

In this paper, we present CGAAL, our model checker of alternating-time temporal logic properties in concurrent games. CGAAL checks such properties by encoding the problem as an extended dependency graph and then computes the satisfaction relation using the distributed local on-the-fly CERTAINZERO algorithm by Dalsgaard et al. [4]. We provide multiple novel search strategies for the algorithm and allow concurrent games to be expressed in our language LCGS. Our experiments show that the local on the-fly algorithm outperforms the global algorithm in the majority of cases.

We also find that CGAAL outperforms the state-of-the-art tool PRISM-games by being up to two orders of magnitude faster, especially in models where synchronisations affect the internal state of modules and whenever we are not required to compute the entire fixed point. However, this comparison is unfair, since our test only uses a fraction of PRISM-games feature set.

CGAAL is still in early development and much work is needed before it competes with PRISM in terms of capabilities. However, dependency graphs have been used for encoding various model checking problems, and we intend to incorporate these techniques into CGAAL.

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