A new polynomial-time algorithm for linear programming
Combinatorica
Verification of Real-Time Systems using Linear Relation Analysis
Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Automatic modular abstractions for linear constraints
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A Feasibility Pump for mixed integer nonlinear programs
Mathematical Programming: Series A and B
Branching and bounds tighteningtechniques for non-convex MINLP
Optimization Methods & Software - GLOBAL OPTIMIZATION
Polynomial Precise Interval Analysis Revisited
Efficient Algorithms
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
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
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
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
Modular abstractions of reactive nodes using disjunctive invariants
APLAS'11 Proceedings of the 9th Asian conference on Programming Languages and Systems
Relaxations of multilinear convex envelopes: dual is better than primal
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
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Static analysis of a computer program by abstract interpretation helps prove behavioural properties of the program. Programs are defined by means of a forward collecting semantics function relating the values of the program variables during the execution of the program. The least fixed point of the semantics function is a program invariants providing useful information about the program's behaviour. Mathematical Programming is a formal language for describing and solving optimization problems expressed in very general terms. This paper establishes a link between the two disciplines by providing a mathematical program that models the problem of finding the least fixed point of a semantics function. Although we limit the discussion to integer affine arithmetic semantics in the interval domain, the flexibility and power of mathematical programming tools have the potential for enriching static analysis considerably.