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International Conference on Combinatorial Optimization and Applications

COCOA 2010: Combinatorial Optimization and Applications pp 374–386Cite as

A Transformation from PPTL to S1S

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6509))

Abstract

A transformation from Propositional Projection Temporal Logic (PPTL) as well as Propositional Interval Temporal Logic (PITL) with infinite models to monadic second order logic with one successor (S1S) is presented in this paper. To this end, intervals where PPTL and PITL formulas are interpreted over are represented as \(\mathfrak{T}\)-structures. Further, the semantics of PPTL and PITL formulas are redefined over \(\mathfrak{T}\)-structures. Moreover, according to \(\mathfrak{T}\)-structure semantics, a PPTL or PITL formula is translated to a formula in S1S. As a result, many mature theoretical and technical results, such as decidability etc. for S1S can be easily inherited by PPTL and PITL.

This research is supported by the NSFC Grant No. 61003078, 60873018, 60910004, 60433010 and 61003079, 973 Program Grant No. 2010CB328102 and SRFDP Grant No. 200807010012.

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Author information

Authors and Affiliations

  1. Institute of Computing Theory and Technology, and ISN Laboratory, Xidian University, Xi’an, 710071, P.R. China

    Cong Tian & Zhenhua Duan

Authors
  1. Cong Tian
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  2. Zhenhua Duan
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, 75080, Richardson, TX, USA

    Weili Wu  & Ovidiu Daescu  & 

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Tian, C., Duan, Z. (2010). A Transformation from PPTL to S1S. In: Wu, W., Daescu, O. (eds) Combinatorial Optimization and Applications. COCOA 2010. Lecture Notes in Computer Science, vol 6509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17461-2_30

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  • DOI: https://doi.org/10.1007/978-3-642-17461-2_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17460-5

  • Online ISBN: 978-3-642-17461-2

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