Theory of linear and integer programming
Theory of linear and integer programming
POPL '87 Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
The complexity of linear problems in fields
Journal of Symbolic Computation
Information Sciences: an International Journal
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
An algorithm for solving parametric linear systems
Journal of Symbolic Computation
Journal of Symbolic Computation
Quantifier elimination for real algebra—the cubic case
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Temporal verification of reactive systems: safety
Temporal verification of reactive systems: safety
Automatic generation of invariants and intermediate assertions
Theoretical Computer Science - Special issue: principles and practice of constraint programming
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Term rewriting and all that
An axiomatic basis for computer programming
Communications of the ACM
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
Introduction to Mathematical Theory of Computation
Introduction to Mathematical Theory of Computation
A Technique for Invariant Generation
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
HYTECH: The Cornell HYbrid TECHnology Tool
Hybrid Systems II
Polynomial Constants Are Decidable
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
A Transformational Approach for Generating Non-linear Invariants
SAS '00 Proceedings of the 7th International Symposium on Static Analysis
Powerful Techniques for the Automatic Generation of Invariants
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Symbolic Model Checking of Infinite State Systems Using Presburger Arithmetic
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Automatic Generation of Polynomial Loop Invariants: Algebraic Foundations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Computing polynomial program invariants
Information Processing Letters
Automatic generation of polynomial invariants of bounded degree using abstract interpretation
Science of Computer Programming
Polynomial approximations of the relational semantics of imperative programs
Science of Computer Programming
Generating all polynomial invariants in simple loops
Journal of Symbolic Computation
Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation
Guarded models for intrusion detection
Proceedings of the 2007 workshop on Programming languages and analysis for security
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Constructing invariants for hybrid systems
Formal Methods in System Design
Using SMT solvers to verify high-integrity programs
Proceedings of the second workshop on Automated formal methods
Program analysis as constraint solving
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
Program Verification by Using DISCOVERER
Verified Software: Theories, Tools, Experiments
Analysing All Polynomial Equations in ${\mathbb Z_{2^w}}$
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
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Endomorphisms for Non-trivial Non-linear Loop Invariant Generation
Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
Constraint-Based Invariant Inference over Predicate Abstraction
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,
Program verification using templates over predicate abstraction
Proceedings of the 2009 ACM SIGPLAN conference on Programming language design and implementation
Finding positively invariant sets of a class of nonlinear loops via curve fitting
Proceedings of the 2009 conference on Symbolic numeric computation
Harnessing a Refinement Theory to Compute Loop Functions
Electronic Notes in Theoretical Computer Science (ENTCS)
Mathematics for reasoning about loop functions
Science of Computer Programming
Relational Methods in the Analysis of While Loops: Observations of Versatility
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Computing procedure summaries for interprocedural analysis
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
Generating representation invariants of structurally complex data
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Discovering non-linear ranking functions by solving semi-algebraic systems
ICTAC'07 Proceedings of the 4th international conference on Theoretical aspects of computing
Reasoning algebraically about P-solvable loops
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
Generating polynomial invariants with DISCOVERER and QEPCAD
Formal methods and hybrid real-time systems
Invariant generation for P-solvable loops with assignments
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Polynomial invariants for linear loops
Cybernetics and Systems Analysis
Journal of Symbolic Computation
Mechanical inference of invariants for FOR-loops
Journal of Symbolic Computation
Reflexive transitive invariant relations: A basis for computing loop functions
Journal of Symbolic Computation
Linear-invariant generation for probabilistic programs: automated support for proof-based methods
SAS'10 Proceedings of the 17th international conference on Static analysis
Inferring loop invariants using postconditions
Fields of logic and computation
An iterative method for generating loop invariants
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
SAT Modulo Linear Arithmetic for Solving Polynomial Constraints
Journal of Automated Reasoning
Interprocedurally analyzing polynomial identities
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Calculating polynomial runtime properties
APLAS'05 Proceedings of the Third Asian conference on Programming Languages and Systems
Program verification using automatic generation of invariants
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
Verification constraint problems with strengthening
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
Invariant and type inference for matrices
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Schema-guided synthesis of imperative programs by constraint solving
LOPSTR'04 Proceedings of the 14th international conference on Logic Based Program Synthesis and Transformation
Generation of basic semi-algebraic invariants using convex polyhedra
SAS'05 Proceedings of the 12th international conference on Static Analysis
A complete invariant generation approach for p-solvable loops
PSI'09 Proceedings of the 7th international Andrei Ershov Memorial conference on Perspectives of Systems Informatics
Invariant relations: an automated tool to analyze loops
VECoS'11 Proceedings of the Fifth international conference on Verification and Evaluation of Computer and Communication Systems
Program analysis using quantifier-elimination heuristics
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Exercises in nonstandard static analysis of hybrid systems
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Invariant functions and invariant relations: An alternative to invariant assertions
Journal of Symbolic Computation
Invariant relations, invariant functions, and loop functions
Innovations in Systems and Software Engineering
Optimal abstraction on real-valued programs
SAS'07 Proceedings of the 14th international conference on Static Analysis
Triangular decomposition of semi-algebraic systems
Journal of Symbolic Computation
Inference of polynomial invariants for imperative programs: a farewell to gröbner bases
SAS'12 Proceedings of the 19th international conference on Static Analysis
ICFEM'12 Proceedings of the 14th international conference on Formal Engineering Methods: formal methods and software engineering
A data driven approach for algebraic loop invariants
ESOP'13 Proceedings of the 22nd European conference on Programming Languages and Systems
Generating concise assertions with complete coverage
Proceedings of the 23rd ACM international conference on Great lakes symposium on VLSI
Loop invariants: Analysis, classification, and examples
ACM Computing Surveys (CSUR)
Probabilistic program analysis with martingales
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
PRINSYS: on a quest for probabilistic loop invariants
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
Automated Reasoning and Mathematics
Synthesizing switching controllers for hybrid systems by generating invariants
Theories of Programming and Formal Methods
Verifying while loops with invariant relations
International Journal of Critical Computer-Based Systems
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We present a new technique for the generation of non-linear (algebraic) invariants of a program. Our technique uses the theory of ideals over polynomial rings to reduce the non-linear invariant generation problem to a numerical constraint solving problem. So far, the literature on invariant generation has been focussed on the construction of linear invariants for linear programs. Consequently, there has been little progress toward non-linear invariant generation. In this paper, we demonstrate a technique that encodes the conditions for a given template assertion being an invariant into a set of constraints, such that all the solutions to these constraints correspond to non-linear (algebraic) loop invariants of the program. We discuss some trade-offs between the completeness of the technique and the tractability of the constraint-solving problem generated. The application of the technique is demonstrated on a few examples.