Abstract interpretation and application to logic programs
Journal of Logic Programming
The formal semantics of programming languages: an introduction
The formal semantics of programming languages: an introduction
Computable analysis: an introduction
Computable analysis: an introduction
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
Non-linear loop invariant generation using Gröbner bases
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Automatic Generation of Polynomial Loop Invariants: Algebraic Foundations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Automatic modular abstractions for linear constraints
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A Quantifier Elimination Algorithm for Linear Real Arithmetic
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A minimalistic look at widening operators
Higher-Order and Symbolic Computation
Quantifier elimination by lazy model enumeration
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
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In this paper, we show that it is possible to abstract program fragments using real variables using formulas in the theory of real closed fields. This abstraction is compositional and modular. We first propose an exact abstraction for programs without loops. Given an abstract domain (in a wide class including intervals and octagons), we then show how to obtain an optimal abstraction of program fragments with respect to that domain. This abstraction allows computing optimal fixed points inside that abstract domain, without the need for a widening operator.