Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 18
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Duan, Zhenhua Tian, Cong and Zhang, Nan 2016. A canonical form based decision procedure and model checking approach for propositional projection temporal logic. Theoretical Computer Science, Vol. 609, p. 544.


    Zhang, Nan Yang, Mengfei Gu, Bin Duan, Zhenhua and Tian, Cong 2016. Verifying safety critical task scheduling systems in PPTL axiom system. Journal of Combinatorial Optimization, Vol. 31, Issue. 2, p. 577.


    Yang, Xiaoxiao Zhang, Yu Fu, Ming and Feng, Xinyu 2014. A temporal programming model with atomic blocks based on projection temporal logic. Frontiers of Computer Science, Vol. 8, Issue. 6, p. 958.


    Zhang, Nan Duan, Zhenhua Tian, Cong and Du, Dingzhu 2014. A formal proof of the deadline driven scheduler in PPTL axiomatic system. Theoretical Computer Science, Vol. 554, p. 229.


    Duan, Zhenhua Zhang, Nan and Koutny, Maciej 2013. A complete proof system for propositional projection temporal logic. Theoretical Computer Science, Vol. 497, p. 84.


    Xiaorui Wang, Qingxian Wang, Yudong Guo, and Jianping Lu, 2013. 2013 IEEE 4th International Conference on Software Engineering and Service Science. p. 639.

    Zhang, Nan Duan, Zhenhua and Tian, Cong 2013. A cylinder computation model for many-core parallel computing. Theoretical Computer Science, Vol. 497, p. 68.


    Zhu, Weijun Zhou, Qinglei Yang, Weidong and Zhang, Haibin 2013. A Novel Algorithm for Intrusion Detection Based on RASL Model Checking. Mathematical Problems in Engineering, Vol. 2013, p. 1.


    Duan, Zhenhua and Tian, Cong 2012. Handbook of Finite State Based Models and Applications.


    Tilly, Marcel Reiff-Marganiec, Stephan and Janicke, Helge 2012. 2012 IEEE Eighth World Congress on Services. p. 242.

    Mat, A.Rahman and Liu, Shaoying 2011. 2011 3rd International Conference on Computer Research and Development. p. 65.

    Schewe, Sven and Tian, Cong 2011. 2011 Eighteenth International Symposium on Temporal Representation and Reasoning. p. 64.

    Tian, Cong and Duan, Zhenhua 2011. 2011 Fifth International Conference on Theoretical Aspects of Software Engineering. p. 45.

    TIAN, Cong and DUAN, Zhen-Hua 2011. Model Checking Rate Monotonic Scheduling Algorithm Based on Propositional Projection Temporal Logic. Journal of Software, Vol. 22, Issue. 2, p. 211.


    WEN, Jing WANG, Huai-Min YING, Shi NI, You-Cong and WANG, Tao 2011. Toward a Software Architectural Design Approach for Trusted Software Based on Monitoring. Chinese Journal of Computers, Vol. 33, Issue. 12, p. 2321.


    Zhang, Nan and Duan, Zhenhua 2011. 2011 First ACIS/JNU International Conference on Computers, Networks, Systems and Industrial Engineering. p. 198.

    Pengfei Zhang, 2009. 2009 Asia-Pacific Conference on Computational Intelligence and Industrial Applications (PACIIA). p. 312.

    Tian, Cong and Duan, Zhenhua 2009. A note on stutter-invariant PLTL. Information Processing Letters, Vol. 109, Issue. 13, p. 663.


    ×

Complexity of propositional projection temporal logic with star

  • CONG TIAN (a1) and ZHENHUA DUAN (a1)
  • DOI: http://dx.doi.org/10.1017/S096012950800738X
  • Published online: 01 February 2009
Abstract

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.

Copyright
Corresponding author
Corresponding author.
Footnotes
Hide All

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.

Footnotes
Linked references
Hide All

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.

H. Bowman and S. Thompson (2003) A decision procedure and complete axiomatization of interval temporal logic with projection. Journal of logic and Computation 13 (2) 195239.

Z. Duan and M. Koutny (2004) A Framed Temporal Logic Programming Language. Journal of Computer Science and Technology 19 (3) 341351.

Z. Duan and C. Tian (2007) Decidability of Propositional Projection Temporal Logic with Infinite Models. In: Proceedings, Theory and Applications of Models of Computation 2007. Springer-Verlag Lecture Notes in Computer Science 4484 521532.

Z. Duan , X. Yang and M. Koutny (2008a) Framed Temporal Logic Programming. Science of Computer Programming 70 3161.

Z. Duan , C. Tian and L. Zhang (2008b) A Decision Procedure for Propositional Projection Temporal Logic with Infinite Models. Acta Informatica 45 (1) 4378.

D. Harel , D. Kozen and R. Parikh (1982) Process logic: Expressiveness, decidability, completeness. J. Comput. System Sci. 25 144170.

J. Holzmann (2003) The Model Checker Spin. IEEE Trans. on Software Engineering 23 (5) 279295.

S. Kripke (1963) Semantical analysis of modal logic I: normal propositional calculi. Z. Math. Logik Grund. Math 9 6796.

S. Liu and H. Wang (2007) An automated approach to specification animation for validation. The Journal of Systems and Software 80 (8) 12711285.

S. Liu and Y. Chen (2008) A relation-based method combining functional and structural testing for test case generation. The Journal of Systems and Software 81 (2) 234248.

Z. Manna and A. Pnueli (1992) The temporal logic of reactive and concurrent systems, Springer-Verlag.

B. Moszkowski (2004) A hierarchical completeness proof for propositional temporal logic. In: N. Dershowitz (ed.) Verification: Theory and Practice: Essays Dedicated to Zohar Manna on the Occasion of his 64th Birthday. Springer-Verlag Lecture Notes in Computer Science 2772 480523.

A. Tarski (1955) A Lattice-Theoretical Fixpoint Theorem and its Applications. Pacific J. Math 5 285309.

C. Tian and Z. Duan (2007) Model Checking Propositional Projection Temporal Logic Based on SPIN. In: ICFEM 2007. Springer-Verlag Lecture Notes in Computer Science 4789 246265.

H. Wang and Q. Xu (2004) Completeness of Temporal Logics over Infinite Models. Discrete Applied Mathematics 136 87103.

P. Wolper (1983) Temporal logic can be more expressive. Information and Control 56 7299.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×