¹The Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
²School of Software, Tsinghua University, Beijing 100084, China
³Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China

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Abstract—The size of B¨uchi Automata(BA) is a key factor during converting Linear-Time Temporal Logic(LTL) formulae to BA in model checking. Most algorithms for generating BA from LTL formulas involved intermediate automata, degeneralization algorithm and simplification of the formulas, but size of BA and time of converting can be reduced further. In this paper, we present an improved Tableau-based algorithm, which converts LTL formulae to Transition-based B¨uchi Automata(TBA) more efficiently. The algorithm is geared towards being used in model checking in on-the-fly fashion. By attaching the satisfy information of [-formula on states and transitions, we can decide whether the sequences of the BA are acceptable by using only one acceptance condition set, not multiple ones. Binary Decision Diagrams(BDD) is used to describe BA and simplify formulae. A better data structure, syntax Directed Acyclic Graph(DAG), is adopted in the algorithm. The size of product BA and computational complexity can be reduced significantly by using on-the-fly degeneralization. The algorithm can expand the state nodes while detecting the validity of nodes, removing the invalid nodes and combining equivalent states and transitions. Compared with other recent conversion tools, the algorithm proposed in this paper runs faster, with the smaller size of BA.

Index Terms—B¨uchi Automata, Linear-Time Temporal Logic, Binary Decision Diagrams, Transition-based B¨uchi Automata

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Cite: Laixiang Shan, Zheng Qin, Shengnan Li, Renwei Zhang, Xiao Yang, "Conversion Algorithm of Linear-Time Temporal Logic to B¨uchi Automata," Journal of Software vol. 9, no. 4, pp. 970-976, 2014.