POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Constructive design of a hierarchy of semantics of a transition system by abstract interpretation
Theoretical Computer Science
Higher-Order and Symbolic Computation
Precise fixpoint computation through strategy iteration
ESOP'07 Proceedings of the 16th European conference on Programming
Computing relaxed abstract semantics w.r.t. quadratic zones precisely
SAS'10 Proceedings of the 17th international conference on Static analysis
Combining widening and acceleration in linear relation analysis
SAS'06 Proceedings of the 13th international conference on Static Analysis
An abstract interpretation framework for termination
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
A policy iteration algorithm for computing fixed points in static analysis of programs
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
Deciding conditional termination
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Precise relational invariants through strategy iteration
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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In this paper, we explore the adaptation of policy iteration techniques to compute greatest fixpoint approximations, in order to find sufficient conditions for program termination. Restricting ourselves to affine programs and the abstract domain of template constraint matrices, we show that the abstract greatest fixpoint can be computed exactly using linear programming, and that strategies are related to the template constraint matrix used. We also present a first result on the relationships between this approach and methods which use ranking functions.