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Optimal Run Problem for Weighted Register Automata

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Theoretical Aspects of Computing – ICTAC 2019 (ICTAC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11884))

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Abstract

Register automata (RA) are a computational model that can handle data values by adding registers to finite automata. Recently, weighted register automata (WRA) were proposed by extending RA so that weights can be specified for transitions. In this paper, we first investigate decidability and complexity of decision problems on the weights of runs in WRA. We then propose an algorithm for the optimum run problem related to the above decision problems. For this purpose, we use a register type as an abstraction of the contents of registers, which is determined by binary relations (such as \(=\), <, etc.) handled by WRA. Also, we introduce a subclass where both the applicability of transition rules and the weights of transitions are determined only by a register type. We present a method of transforming a given WRA satisfying the assumption to a weighted directed graph such that the optimal run of WRA and the minimum weight path of the graph correspond to each other. Lastly, we discuss the optimal run problem for weighted timed automata as an example.

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Notes

  1. 1.

    We do not include the size of the weight part because of the assumption that the computation of the weights of a single transition and a single register can be done in constant time.

  2. 2.

    If there is no such a switch \((p,\theta ) \vdash _{t^\prime ,d} (q,\theta [\varLambda \leftarrow d])\) for any \(d\in D\), we define the infimum as \(\infty \).

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Acknowledgements

The authors thank the reviewers for providing valuable comments to the paper. This work was supported by JSPS KAKENHI Grant Number JP19H04083.

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Authors and Affiliations

  1. Nagoya University, Nagoya, Japan

    Hiroyuki Seki & Reo Yoshimura

  2. Kochi University of Technology, Kami, Japan

    Yoshiaki Takata

Authors
  1. Hiroyuki Seki
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  2. Reo Yoshimura
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  3. Yoshiaki Takata
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Corresponding author

Correspondence to Hiroyuki Seki .

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Editors and Affiliations

  1. University of Sheffield, Sheffield, UK

    Robert Mark Hierons

  2. University of Bordeaux, Talence, France

    Mohamed Mosbah

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Seki, H., Yoshimura, R., Takata, Y. (2019). Optimal Run Problem for Weighted Register Automata. In: Hierons, R., Mosbah, M. (eds) Theoretical Aspects of Computing – ICTAC 2019. ICTAC 2019. Lecture Notes in Computer Science(), vol 11884. Springer, Cham. https://doi.org/10.1007/978-3-030-32505-3_6

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  • DOI: https://doi.org/10.1007/978-3-030-32505-3_6

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  • Online ISBN: 978-3-030-32505-3

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