Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Computing polynomial program invariants
Information Processing Letters
Automatic generation of polynomial invariants of bounded degree using abstract interpretation
Science of Computer Programming
Rigorous Error Bounds for the Optimal Value in Semidefinite Programming
SIAM Journal on Numerical Analysis
Static analysis by policy iteration on relational domains
ESOP'07 Proceedings of the 16th European conference on Programming
Precise fixpoint computation through strategy iteration
ESOP'07 Proceedings of the 16th European conference on Programming
Static analysis of the accuracy in control systems: principles and experiments
FMICS'07 Proceedings of the 12th international conference on Formal methods for industrial critical systems
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Efficient strongly relational polyhedral analysis
VMCAI'06 Proceedings of the 7th 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
Generation of basic semi-algebraic invariants using convex polyhedra
SAS'05 Proceedings of the 12th international conference on Static Analysis
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
Static Analysis by Abstract Interpretation: A Mathematical Programming Approach
Electronic Notes in Theoretical Computer Science (ENTCS)
Solving systems of rational equations through strategy iteration
ACM Transactions on Programming Languages and Systems (TOPLAS)
Generalizing the template polyhedral domain
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
Improving strategies via SMT solving
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
Policy iteration within logico-numerical abstract domains
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
A logical product approach to zonotope intersection
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Template-Based unbounded time verification of affine hybrid automata
APLAS'11 Proceedings of the 9th Asian conference on Programming Languages and Systems
Donut domains: efficient non-convex domains for abstract interpretation
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
PVS linear algebra libraries for verification of control software algorithms in C/ACSL
NFM'12 Proceedings of the 4th international conference on NASA Formal Methods
Abstract interpretation meets convex optimization
Journal of Symbolic Computation
Tropical linear-fractional programming and parametric mean payoff games
Journal of Symbolic Computation
Proving Termination by Policy Iteration
Electronic Notes in Theoretical Computer Science (ENTCS)
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We introduce a new domain for finding precise numerical invariants of programs by abstract interpretation. This domain, which consists of level sets of non-linear functions, generalizes the domain of linear “templates” introduced by Manna, Sankaranarayanan, and Sipma. In the case of quadratic templates, we use Shor's semi-definite relaxation to derive computable yet precise abstractions of semantic functionals, and we show that the abstract fixpoint equation can be solved accurately by coupling policy iteration and semi-definite programming. We demonstrate the interest of our approach on a series of examples (filters, integration schemes) including a degenerate one (symplectic scheme).