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Present-Future Form of Linear Time \(\mu \)-Calculus

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Structured Object-Oriented Formal Language and Method (SOFL+MSVL 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8332))

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Abstract

This paper presents the notion of Present-Future form (PF form) for linear time \(\mu \)-calculus (\(\nu \)TL) formulas consisting of the present and future parts: the present part is the conjunction of atomic propositions or their negations while the future part is a closed \(\nu \)TL formula under the next operator. We show every closed \(\nu \)TL formula can be rewritten into its corresponding PF form. Finally, based on PF form, the idea of constructing a graph that describing models of a \(\nu \)TL formula is discussed.

This research is supported by the NSFC Grant Nos. 61133001, 61272118, 61272117, 61202038, 91218301, 61322202, 61373043, and National Program on Key Basic Research Project (973 Program) Grant No. 2010CB328102.

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Authors and Affiliations

  1. ICTT and ISN Lab, Xidian University, Xi’an, 710071, China

    Yao Liu, Zhenhua Duan & Cong Tian

  2. Beijing Institute of Control Engineering, Beijing, 100000, China

    Bo Liu

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  1. Yao Liu
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  2. Zhenhua Duan
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  3. Cong Tian
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Correspondence to Zhenhua Duan .

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Editors and Affiliations

  1. Hosei University, Koganei-shi, Tokyo, Japan

    Shaoying Liu

  2. Technology, Xidian University, Xi’an, China

    Zhenhua Duan

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Liu, Y., Duan, Z., Tian, C., Liu, B. (2014). Present-Future Form of Linear Time \(\mu \)-Calculus. In: Liu, S., Duan, Z. (eds) Structured Object-Oriented Formal Language and Method. SOFL+MSVL 2013. Lecture Notes in Computer Science(), vol 8332. Springer, Cham. https://doi.org/10.1007/978-3-319-04915-1_6

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  • DOI: https://doi.org/10.1007/978-3-319-04915-1_6

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