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Efficient approach of translating LTL formulae into Büchi automata

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Abstract

In explicit-state model checking, system properties are typically expressed in linear temporal logic (LTL), and translated into a Büchi automaton (BA) to be checked. In order to improve performance of the conversion algorithm, some model checkers involve the intermediate automata, such as a generalized Büchi automaton (GBA). The de-generalization is a translation from a GBA to a BA. In this paper, we present a conversion algorithm to translate an LTL formula to a BA directly. A labeling, acceptance degree, is presented to record acceptance conditions satisfied in each state and transition. Acceptance degree is a set of U-subformulae or F-subformulae of the given LTL formula. According to the acceptance degree, on-the-fly degeneralization algorithm, which is different from the standard de-generalization algorithm, is conceived and implemented. On-the-fly de-generalization algorithm is carried out during the expansion of the given LTL formula. It is performed in the case of the given LTL formula contains U-subformulae and F-subformulae, that is, the on-the-fly de-generalization algorithm is performed as required. In order to get a more deterministic BA, the shannon expansion is used recursively during expanding LTL formulae. Ordered binary decision diagrams are used to represent the BA and simplify LTL formulae.We compare the conversion algorithm presented in this paper to previousworks, and show that it is more efficient for five families LTL formulae in common use and four sets of random formulae generated by LBTT (an LTL-to-Büchi translator testbench).

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Authors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China

    Laixiang Shan

  2. School of Education Science, East China Normal University, Shanghai, 200241, China

    Xiaomin Du

  3. School of Software, Tsinghua University, Beijing, 100084, China

    Zheng Qin

Authors
  1. Laixiang Shan
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  2. Xiaomin Du
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  3. Zheng Qin
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Correspondence to Laixiang Shan.

Additional information

Laixiang Shan received his MS from School of Computer Science and Technology of University of Science and Technology of China, China. He is now a doctoral student in the Department of Computer Science and Technology of Tsinghua University, China. His research interest includes software formal, model checking, and modeling theory.

Xiaomin Du received her MS in the School of Chemistry and Chemical Engineering of Qufu Normal University, China. She is now a doctoral student in School of Education Science of East China Normal University, China. Her research interest now focuses on teacher education, professional training for potential teacher, curriculum and teaching, and educational management.

Zheng Qin is a professor in the School of Software, Tsinghua University, China. His major research interest includes software architecture, data fusion, and artificial intelligence.

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Shan, L., Du, X. & Qin, Z. Efficient approach of translating LTL formulae into Büchi automata. Front. Comput. Sci. 9, 511–523 (2015). https://doi.org/10.1007/s11704-015-4302-2

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