Abstract
In this paper, we study linear time \(\mu \)-calculus interpreted over finite traces, namely \(\nu \)TL\(_f\). We define Present Future form (PF form) for \(\nu \)TL\(_f\) formulas and prove that every closed \(\nu \)TL\(_f\) formula can be converted into this form. PF form decomposes a formula into two parts: what to be satisfied at the current state and what to be satisfied at the next one. Based on PF form, we provide an algorithm for constructing Present Future form Graph (PFG) that can be employed to depict models of a formula. In addition, a decision procedure for checking satisfiability of \(\nu \)TL\(_f\) formulas based on PFG is proposed.
This research is supported by the NSFC Grant Nos. 61133001, 61322202, 91418201, and 61420106004.
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Liu, Y., Duan, Z., Tian, C., Cui, B. (2016). Satisfiability of Linear Time Mu-Calculus on Finite Traces. In: Dinh, T., Thai, M. (eds) Computing and Combinatorics . COCOON 2016. Lecture Notes in Computer Science(), vol 9797. Springer, Cham. https://doi.org/10.1007/978-3-319-42634-1_49
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