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Complexity of propositional projection temporal logic with star†

Published online by Cambridge University Press:  01 February 2009

CONG TIAN  and
ZHENHUA DUAN
CONG TIAN
Affiliation:
Institute of Computing Theory and Technology, Xidian University, Xi'an, 710071, P. R. China
ZHENHUA DUAN*
Affiliation:
Institute of Computing Theory and Technology, Xidian University, Xi'an, 710071, P. R. China
*
‡Corresponding author.
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Abstract

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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.

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 19 , Special Issue 1: Theory and Applications of Models of Computation (TAMC) , February 2009 , pp. 73 - 100
Copyright
Copyright © Cambridge University Press 2009

Footnotes

†

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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