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Complexity of propositional projection temporal logic with star

  • CONG TIAN (a1) and ZHENHUA DUAN (a1)
  • DOI:
  • Published online: 01 February 2009

This paper investigates the complexity of Propositional Projection Temporal Logic with Star (PPTL*). To this end, Propositional Projection Temporal Logic (PPTL) is first extended to include projection star. Then, by reducing the emptiness problem of star-free expressions to the problem of the satisfiability of PPTL* formulas, the lower bound of the complexity for the satisfiability of PPTL* formulas is proved to be non-elementary. Then, to prove the decidability of PPTL*, the normal form, normal form graph (NFG) and labelled normal form graph (LNFG) for PPTL* are defined. Also, algorithms for transforming a formula to its normal form and LNFG are presented. Finally, a decision algorithm for checking the satisfiability of PPTL* formulas is formalised using LNFGs.

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This research is supported by the NSFC Grant No. 60433010, and Defence Pre-Research Project of China, No. 51315050105, and NSFC Grant No. 60873018 jointly sponsored by Microsoft Asia Research Academy.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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