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Journal of Applied Mathematics
Volume 2015, Article ID 516104, 10 pages
Research Article

Degeneralization Algorithm for Generation of Büchi Automata Based on Contented Situation

1School of Software, Tsinghua University, Beijing 100084, China
2Credit Reference Center, People’s Bank of China, Beijing 100800, China
3Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received 7 September 2014; Revised 15 December 2014; Accepted 16 December 2014

Academic Editor: Carlos Conca

Copyright © 2015 Laixiang Shan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present on-the-fly degeneralization algorithm used to transform generalized Büchi automata (GBA) into Büchi Automata (BA) different from the standard degeneralization algorithm. Contented situation, which is used to record what acceptance conditions are satisfiable during expanding LTL formulae, is attached to the states and transitions in the BA. In order to get the deterministic BA, the Shannon expansion is used recursively when we expand LTL formulae by applying the tableau rules. On-the-fly degeneralization algorithm is carried out in each step of the expansion of LTL formulae. Ordered binary decision diagrams are used to represent the BA and simplify LTL formulae. The temporary automata are stored as syntax directed acyclic graph in order to save storage space. These ideas are implemented in a conversion algorithm used to build a property automaton corresponding to the given LTL formulae. We compare our method to previous work and show that it is more efficient for four sets of random formulae generated by LBTT.