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Multi-weighted Automata and MSO Logic

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Abstract

Weighted automata are non-deterministic automata where the transitions are equipped with weights. They can model quantitative aspects of systems like costs or energy consumption. The value of a run can be computed, for example, as the maximum, average, or discounted sum of transition weights. In multi-weighted automata, transitions carry several weights and can model, for example, the ratio between rewards and costs, or the efficiency of use of a primary resource under some upper bound constraint on a secondary resource. Here, we introduce a general model for multi-weighted automata as well as a multi-weighted MSO logic. In our main results, we show that this multi-weighted MSO logic and multi-weighted auto-mata are expressively equivalent both for finite and infinite words. The translation process is effective, leading to decidability results for our multi-weighted MSO logic.

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Acknowledgments

The authors would like to thank the anonymous referees for helpful suggestions and comments. They would like to thank Paul Gastin for the valuable discussion and interesting ideas which helped to improve the quality of this paper.

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Authors and Affiliations

  1. Universität Leipzig, Institut für Informatik, 04109, Leipzig, Germany

    Manfred Droste & Vitaly Perevoshchikov

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  1. Manfred Droste
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  2. Vitaly Perevoshchikov
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Correspondence to Vitaly Perevoshchikov.

Additional information

A preliminary version of this paper appeared in the proceedings of the 8th International Computer Science Symposium in Russia (CSR 2013) [18]

Part of this work was done while M.D. held a “Catedra de excelencia” from Universitat Rovira i Virgili, Tarragona, Spain. He would like to thank his colleagues for their hospitality.

Supported by DFG Graduiertenkolleg 1763 (QuantLA)

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Droste, M., Perevoshchikov, V. Multi-weighted Automata and MSO Logic. Theory Comput Syst 59, 231–261 (2016). https://doi.org/10.1007/s00224-015-9658-9

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