Discovering non-linear ranking functions by solving semi-algebraic systems

Authors:
Yinghua Chen;Bican Xia;Lu Yang;Naijun Zhan;Chaochen Zhou
Affiliations:
LMAM & School of Mathematical Sciences, Peking University;LMAM & School of Mathematical Sciences, Peking University;Institute of Theoretical Computing, East China Normal University;Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, P.R. China;Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences
Venue:
ICTAC'07 Proceedings of the 4th international conference on Theoretical aspects of computing
Year:
2007

Citing 14
Cited 8

Partial Cylindrical Algebraic Decomposition for quantifier elimination

Journal of Symbolic Computation
Temporal verification of reactive systems: safety

Temporal verification of reactive systems: safety
REDLOG: computer algebra meets computer logic

ACM SIGSAM Bulletin
Recent advances on determining the number of real roots of parametric polynomials

Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
An axiomatic basis for computer programming

Communications of the ACM
A Discipline of Programming

A Discipline of Programming
An algorithm for isolating the real solutions of semi-algebraic systems

Journal of Symbolic Computation
Synthesis of Linear Ranking Functions

TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Non-linear loop invariant generation using Gröbner bases

Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Real solution isolation using interval arithmetic

Computers & Mathematics with Applications
Proving program invariance and termination by parametric abstraction, lagrangian relaxation and semidefinite programming

VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Termination of polynomial programs

VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Termination of integer linear programs

CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
TERMINATOR: beyond safety

CAV'06 Proceedings of the 18th international conference on Computer Aided Verification

Finding positively invariant sets of a class of nonlinear loops via curve fitting

Proceedings of the 2009 conference on Symbolic numeric computation
Generating polynomial invariants with DISCOVERER and QEPCAD

Formal methods and hybrid real-time systems
Termination of linear programs with nonlinear constraints

Journal of Symbolic Computation
Termination of loop programs with polynomial guards

ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part IV
Symbolic termination analysis of solvable loops

Journal of Symbolic Computation
Non-termination sets of simple linear loops

ICTAC'12 Proceedings of the 9th international conference on Theoretical Aspects of Computing
On the limits of the classical approach to cost analysis

SAS'12 Proceedings of the 19th international conference on Static Analysis
Word-length optimization beyond straight line code

Proceedings of the ACM/SIGDA international symposium on Field programmable gate arrays

Quantified Score

Hi-index	0.00

Visualization

Abstract

Differing from [6] this paper reduces non-linear ranking function discovering for polynomial programs to semi-algebraic system solving, and demonstrates how to apply the symbolic computation tools, DISCOVERER and QEPCAD, to some interesting examples.