A practical algorithm for exact array dependence analysis
Communications of the ACM
The theory of N,+,Vk,Vl is undecidable
Theoretical Computer Science
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Mona: Monadic Second-Order Logic in Practice
TACAS '95 Proceedings of the First International Workshop on Tools and Algorithms for Construction and Analysis of Systems
The Power of QDDs (Extended Abstract)
SAS '97 Proceedings of the 4th International Symposium on Static Analysis
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
An Improved Reachability Analysis Method for Strongly Linear Hybrid Systems (Extended Abstract)
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Diophantine Equations, Presburger Arithmetic and Finite Automata
CAAP '96 Proceedings of the 21st International Colloquium on Trees in Algebra and Programming
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Flat Parametric Counter Automata
Fundamenta Informaticae - Machines, Computations and Universality, Part II
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Accelerating interpolation-based model-checking
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Synthesizing geometry constructions
Proceedings of the 32nd ACM SIGPLAN conference on Programming language design and implementation
Flat parametric counter automata
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Flat counter automata almost everywhere!
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
MERIT: an interpolating model-checker
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Flat Parametric Counter Automata
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Fixpoint-guided abstraction refinements
SAS'07 Proceedings of the 14th international conference on Static Analysis
Computable fixpoints in well-structured symbolic model checking
Formal Methods in System Design
Hi-index | 5.23 |
It has been known for a long time that the sets of integer vectors that are recognizable by finite-state automata are those that can be defined in an extension of Presburger arithmetic. In this paper, we address the problem of deciding whether the closure of a linear transformation preserves the recognizable nature of sets of integer vectors. We solve this problem by introducing an original extension of the concept of recognizability to sets of vectors with complex components. This generalization allows to obtain a simple necessary and sufficient condition over linear transformations, in terms of the eigenvalues of the transformation matrix. We then show that these eigenvalues do not need to be computed explicitly in order to evaluate the condition, and we give a full decision procedure based on simple integer arithmetic. The proof of this result is constructive, and can be turned into an algorithm for applying the closure of a linear transformation that satisfies the condition to a finite-state representation of a set. Finally, we show that the necessary and sufficient condition that we have obtained can straightforwardly be turned into a sufficient condition for linear transformations with linear guards.