Model checking and abstraction
ACM Transactions on Programming Languages and Systems (TOPLAS)
Property preserving abstractions for the verification of concurrent systems
Formal Methods in System Design - Special issue on computer-aided verification (based on CAV'92 workshop)
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
Automatic Generation of Invariants
Formal Methods in System Design - Special issue on The First Federated Logic Conference (FLOC'96), part II
Communications of the ACM
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Comparing the Galois Connection and Widening/Narrowing Approaches to Abstract Interpretation
PLILP '92 Proceedings of the 4th International Symposium on Programming Language Implementation and Logic Programming
Computing Abstractions of Infinite State Systems Compositionally and Automatically
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Abstract and Model Check While You Prove
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
Powerful Techniques for the Automatic Generation of Invariants
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Verifying Invariants Using theorem Proving
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Counter-Example Based Predicate Discovery in Predicate Abstraction
FMCAD '02 Proceedings of the 4th International Conference on Formal Methods in Computer-Aided Design
An Overview of Formal Verification for the Time-Triggered Architecture
FTRTFT '02 Proceedings of the 7th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems: Co-sponsored by IFIP WG 2.2
Non-linear loop invariant generation using Gröbner bases
Proceedings of the 31st 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
Simulation-directed invariant mining for software verification
Proceedings of the conference on Design, automation and test in Europe
Endomorphisms for Non-trivial Non-linear Loop Invariant Generation
Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
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
A pattern-based approach for modeling and analyzing error recovery
Architecting dependable systems IV
Automatic refinement of split binary semaphore
ICTAC'07 Proceedings of the 4th international conference on Theoretical aspects of computing
Instantiation-based invariant discovery
NFM'11 Proceedings of the Third international conference on NASA Formal methods
Proving safety properties of rewrite theories
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Formal verification of pentium ® 4 components with symbolic simulation and inductive invariants
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Counterexample guided invariant discovery for parameterized cache coherence verification
CHARME'05 Proceedings of the 13 IFIP WG 10.5 international conference on Correct Hardware Design and Verification Methods
Generation of basic semi-algebraic invariants using convex polyhedra
SAS'05 Proceedings of the 12th international conference on Static Analysis
Anti-unification algorithms and their applications in program analysis
PSI'09 Proceedings of the 7th international Andrei Ershov Memorial conference on Perspectives of Systems Informatics
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Generating concise assertions with complete coverage
Proceedings of the 23rd ACM international conference on Great lakes symposium on VLSI
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Most of the properties established during verification are either invariants or depend crucially on invariants. The effectiveness of automated formal verification is therefore sensitive to the ease with which invariants, even trivial ones, can be automatically deduced. While the strongest invariant can be defined as the least fixed point of the strongest post-condition of a transition system starting with the set of initial states, this symbolic computation rarely converges. We present a method for invariant generation and strengthening that relies on the simultaneous construction of least and greatest fixed points, restricted widening and narrowing, and quantifier elimination. The effectiveness of the method is demonstrated on a number of examples.