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Symbolic decision procedure for termination of linear programs

Authors:

Zhihai ZhangAuthors Info & Claims

Formal Aspects of Computing, Volume 23, Issue 2

Pages 171 - 190

https://doi.org/10.1007/s00165-009-0144-5

Published: 01 March 2011 Publication History

Abstract

Tiwari proved that the termination of a class of linear programs is decidable in Tiwari (Proceedings of CAV’04. Lecture notes in computer science, vol 3114, pp 70–82, 2004). The decision procedure proposed therein depends on the computation of Jordan forms. Thus, people may draw a wrong conclusion from this procedure, if they simply apply floating-point computation to compute Jordan forms. In this paper, we first use an example to explain this problem, and then present a symbolic implementation of the decision procedure. Thus, the rounding error problem is therefore avoided. Moreover, we also show that the symbolic decision procedure is as efficient as the numerical one given in Tiwari (Proceedings of CAV’04. Lecture notes in computer science, vol 3114, pp 70–82, 2004). The complexity of former is max{O(n⁶), O(n^m+3)}, while that of the latter is O(n^m+3), where n is the number of variables of the program and m is the number of its Boolean conditions. In addition, for the case when the characteristic polynomial of the assignment matrix is irreducible, we design a more efficient symbolic algorithm whose complexity is max(O(n⁶), O(mn³)).

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Cited By

Hark MFrohn FGiesl J(2023)Termination of triangular polynomial loopsFormal Methods in System Design10.1007/s10703-023-00440-zOnline publication date: 4-Dec-2023
https://doi.org/10.1007/s10703-023-00440-z
Lefaucheux EOuaknine JPurser DSharifi M(2023)Model Checking Linear Dynamical Systems under Floating-point RoundingTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-031-30823-9_3(47-65)Online publication date: 22-Apr-2023
https://dl.acm.org/doi/10.1007/978-3-031-30823-9_3
Xue BZhan NLi YWang Q(2018)Robust Non-termination Analysis of Numerical SoftwareDependable Software Engineering. Theories, Tools, and Applications10.1007/978-3-319-99933-3_5(69-88)Online publication date: 26-Aug-2018
https://doi.org/10.1007/978-3-319-99933-3_5
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Published In

cover image Formal Aspects of Computing

Formal Aspects of Computing Volume 23, Issue 2

Mar 2011

86 pages

ISSN:0934-5043

EISSN:1433-299X

Issue’s Table of Contents

© British Computer Society 2009.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 March 2011

Accepted: 23 November 2009

Revision received: 15 November 2009

Received: 30 September 2008

Published in FAC Volume 23, Issue 2

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Cited By

Hark MFrohn FGiesl J(2023)Termination of triangular polynomial loopsFormal Methods in System Design10.1007/s10703-023-00440-zOnline publication date: 4-Dec-2023
https://doi.org/10.1007/s10703-023-00440-z
Lefaucheux EOuaknine JPurser DSharifi M(2023)Model Checking Linear Dynamical Systems under Floating-point RoundingTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-031-30823-9_3(47-65)Online publication date: 22-Apr-2023
https://dl.acm.org/doi/10.1007/978-3-031-30823-9_3
Xue BZhan NLi YWang Q(2018)Robust Non-termination Analysis of Numerical SoftwareDependable Software Engineering. Theories, Tools, and Applications10.1007/978-3-319-99933-3_5(69-88)Online publication date: 26-Aug-2018
https://doi.org/10.1007/978-3-319-99933-3_5
Li Y(2017)Witness to non-termination of linear programsTheoretical Computer Science10.1016/j.tcs.2017.03.036681(75-100)Online publication date: Jun-2017
https://doi.org/10.1016/j.tcs.2017.03.036
Li Y(2017)Termination of Semi-algebraic Loop ProgramsDependable Software Engineering. Theories, Tools, and Applications10.1007/978-3-319-69483-2_8(131-146)Online publication date: 17-Oct-2017
https://doi.org/10.1007/978-3-319-69483-2_8
Li CLi YFeng Y(2015)Termination of initialized two variable homogeneous linear loops2015 6th IEEE International Conference on Software Engineering and Service Science (ICSESS)10.1109/ICSESS.2015.7339097(461-466)Online publication date: Sep-2015
https://doi.org/10.1109/ICSESS.2015.7339097
Li YZhi LWatt S(2014)A recursive decision method for termination of linear programsProceedings of the 2014 Symposium on Symbolic-Numeric Computation10.1145/2631948.2631966(97-106)Online publication date: 28-Jul-2014
https://dl.acm.org/doi/10.1145/2631948.2631966
Lin WWu MYang ZZeng Z(2014)Proving total correctness and generating preconditions for loop programs via symbolic-numeric computation methodsFrontiers of Computer Science10.1007/s11704-014-3150-68:2(192-202)Online publication date: 6-Mar-2014
https://doi.org/10.1007/s11704-014-3150-6
Liu JXu MZhan NZhao H(2014)Discovering non-terminating inputs for multi-path polynomial programsJournal of Systems Science and Complexity10.1007/s11424-014-2145-627:6(1286-1304)Online publication date: 30-Nov-2014
https://doi.org/10.1007/s11424-014-2145-6
Li YLi CWu WFeng Y(2013)Termination of Two Variable Homogeneous Linear LoopsProceedings of the 2013 Sixth International Conference on Business Intelligence and Financial Engineering10.1109/BIFE.2013.3(10-13)Online publication date: 14-Nov-2013
https://dl.acm.org/doi/10.1109/BIFE.2013.3
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