Theory of linear and integer programming
Theory of linear and integer programming
Temporal verification of reactive systems: safety
Temporal verification of reactive systems: safety
Verification of Real-Time Systems using Linear Relation Analysis
Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A New Numerical Abstract Domain Based on Difference-Bound Matrices
PADO '01 Proceedings of the Second Symposium on Programs as Data Objects
Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
A static analyzer for large safety-critical software
PLDI '03 Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
The octahedron abstract domain
Science of Computer Programming
Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation
Verification of Concurrent Systems with Parametric Delays Using Octahedra
Fundamenta Informaticae - The Fourth Special Issue on Applications of Concurrency to System Design (ACSD05)
Program analysis as constraint solving
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
Inferring Min and Max Invariants Using Max-Plus Polyhedra
SAS '08 Proceedings of the 15th international symposium on Static Analysis
Constraint-Based Approach for Analysis of Hybrid Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Automatic modular abstractions for linear constraints
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A Sound Floating-Point Polyhedra Abstract Domain
APLAS '08 Proceedings of the 6th Asian Symposium on Programming Languages and Systems
Constraint-Based Invariant Inference over Predicate Abstraction
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
SubPolyhedra: A (More) Scalable Approach to Infer Linear Inequalities
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
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,
Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Generating and Analyzing Symbolic Traces of Simulink/Stateflow Models
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
ACM Computing Surveys (CSUR)
Complexity and Algorithms for Monomial and Clausal Predicate Abstraction
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Theoretical Computer Science
Logahedra: A New Weakly Relational Domain
ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
Weakly-relational shapes for numeric abstractions: improved algorithms and proofs of correctness
Formal Methods in System Design
A minimalistic look at widening operators
Higher-Order and Symbolic Computation
Static analysis by policy iteration on relational domains
ESOP'07 Proceedings of the 16th European conference on Programming
Invariant synthesis for combined theories
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Array abstractions from proofs
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Symbolic model checking of hybrid systems using template polyhedra
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
Pentagons: A weakly relational abstract domain for the efficient validation of array accesses
Science of Computer Programming
Abstract Fixpoint Computations with Numerical Acceleration Methods
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
Static Analysis by Abstract Interpretation: A Mathematical Programming Approach
Electronic Notes in Theoretical Computer Science (ENTCS)
A Note on the Inversion Join for Polyhedral Analysis
Electronic Notes in Theoretical Computer Science (ENTCS)
Deriving numerical abstract domains via principal component analysis
SAS'10 Proceedings of the 17th international conference on Static analysis
Computing relaxed abstract semantics w.r.t. quadratic zones precisely
SAS'10 Proceedings of the 17th international conference on Static analysis
Solving systems of rational equations through strategy iteration
ACM Transactions on Programming Languages and Systems (TOPLAS)
Linear absolute value relation analysis
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
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
Fast interprocedural linear two-variable equalities
ACM Transactions on Programming Languages and Systems (TOPLAS)
Policy iteration within logico-numerical abstract domains
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
A lightweight approach for loop summarization
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Discretizing affine hybrid automata with uncertainty
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Static analysis in disjunctive numerical domains
SAS'06 Proceedings of the 13th international conference on Static Analysis
Verification constraint problems with strengthening
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
An abstract domain to discover interval linear equalities
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Automatic abstraction for congruences
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
A logical product approach to zonotope intersection
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Efficient strongly relational polyhedral analysis
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Linear ranking with reachability
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Widening operators for weakly-relational numeric abstractions
SAS'05 Proceedings of the 12th international conference on Static Analysis
Generation of basic semi-algebraic invariants using convex polyhedra
SAS'05 Proceedings of the 12th international conference on Static Analysis
Finding relations among linear constraints
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
Template-Based unbounded time verification of affine hybrid automata
APLAS'11 Proceedings of the 9th Asian conference on Programming Languages and Systems
Random: r-based analyzer for numerical domains
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Abstract interpretation meets convex optimization
Journal of Symbolic Computation
Tropical linear-fractional programming and parametric mean payoff games
Journal of Symbolic Computation
Acceleration of the abstract fixpoint computation in numerical program analysis
Journal of Symbolic Computation
Discovering invariants via simple component analysis
Journal of Symbolic Computation
Using dynamic analysis to discover polynomial and array invariants
Proceedings of the 34th International Conference on Software Engineering
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
The gauge domain: scalable analysis of linear inequality invariants
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
A method for symbolic computation of abstract operations
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Verification of Concurrent Systems with Parametric Delays Using Octahedra
Fundamenta Informaticae - The Fourth Special Issue on Applications of Concurrency to System Design (ACSD05)
Optimal abstraction on real-valued programs
SAS'07 Proceedings of the 14th 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
The Abstract Domain of Parallelotopes
Electronic Notes in Theoretical Computer Science (ENTCS)
TreeKs: A Functor to Make Numerical Abstract Domains Scalable
Electronic Notes in Theoretical Computer Science (ENTCS)
An Accurate Join for Zonotopes, Preserving Affine Input/Output Relations
Electronic Notes in Theoretical Computer Science (ENTCS)
Proving Termination by Policy Iteration
Electronic Notes in Theoretical Computer Science (ENTCS)
Computing minimal separating DFAs and regular invariants using SAT and SMT solvers
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Modular static analysis with zonotopes
SAS'12 Proceedings of the 19th international conference on Static Analysis
Bilateral algorithms for symbolic abstraction
SAS'12 Proceedings of the 19th international conference on Static Analysis
When the decreasing sequence fails
SAS'12 Proceedings of the 19th international conference on Static Analysis
Certification of bounds of non-linear functions: the templates method
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
Abstract acceleration of general linear loops
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Bias-variance tradeoffs in program analysis
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Symbolic optimization with SMT solvers
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Synthesizing switching controllers for hybrid systems by generating invariants
Theories of Programming and Formal Methods
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We present a method for generating linear invariants for large systems. The method performs forward propagation in an abstract domain consisting of arbitrary polyhedra of a predefined fixed shape. The basic operations on the domain like abstraction, intersection, join and inclusion tests are all posed as linear optimization queries, which can be solved efficiently by existing LP solvers. The number and dimensionality of the LP queries are polynomial in the program dimensionality, size and the number of target invariants. The method generalizes similar analyses in the interval, octagon, and octahedra domains, without resorting to polyhedral manipulations. We demonstrate the performance of our method on some benchmark programs.