This is to advocate the approach to reducing program verification to the algebraic symbolic computation. Recent advances indicate that various verification problems can be reduced to semi-algebraic systems (SAS for short), and resolved through computer algebra tools. In this talk, we report our encouraging attempts at applying DISCOVERER to program termination analysis and state reachability computation. DISCOVERER is a Maple program implementing an algorithm of real solution classification and isolation for SAS, which is based on the discovery of complete discrimination systems of parametric polynomials. The talk also concludes that this approach deserves further attention from the program verification community. For theoretical and technical details of the work, we refer the reader to [1,2,3,4,5].
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Lu Yang,et al.
Recent Advances on Determining the Number of Real Roots of Parametric Polynomials
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1999,
J. Symb. Comput..
[2]
Lu Yang,et al.
A complete discrimination system for polynomials
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1996
.
[3]
Chaochen Zhou,et al.
Program Verification by Using DISCOVERER
,
2005,
VSTTE.
[4]
Bican Xia,et al.
Real Solution Classification for Parametric Semi-Algebraic Systems
,
2005,
Algorithmic Algebra and Logic.
[5]
Bican Xia,et al.
An Algorithm for Isolating the Real Solutions of Semi-algebraic Systems
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2002,
J. Symb. Comput..