Predicate abstraction for software verification
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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 framework for numeric analysis of array operations
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Combining abstract interpreters
Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation
Logic-flow analysis of higher-order programs
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation
Array abstractions from proofs
CAV'07 Proceedings of the 19th international conference on Computer aided verification
A logic and decision procedure for predicate abstraction of heap-manipulating programs
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
What's decidable about arrays?
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Discovering properties about arrays in simple programs
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
Logical foundation for static analysis: application to binary static analysis for security
ACM SIGAda Ada Letters
Thread Quantification for Concurrent Shape Analysis
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Quantitative Separation Logic and Programs with Lists
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Compositional shape analysis by means of bi-abduction
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Symbolic String Verification: Combining String Analysis and Size Analysis
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,
Finding Loop Invariants for Programs over Arrays Using a Theorem Prover
FASE '09 Proceedings of the 12th International Conference on Fundamental Approaches to Software Engineering: 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
Type-based data structure verification
Proceedings of the 2009 ACM SIGPLAN conference on Programming language design and implementation
Automatic Verification of Integer Array Programs
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
ACM Computing Surveys (CSUR)
Abstraction Refinement for Quantified Array Assertions
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
Inferring Dataflow Properties of User Defined Table Processors
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
Abstract Transformers for Thread Correlation Analysis
APLAS '09 Proceedings of the 7th Asian Symposium on Programming Languages and Systems
Refining Abstract Interpretation-Based Static Analyses with Hints
APLAS '09 Proceedings of the 7th Asian Symposium on Programming Languages and Systems
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Non-disjunctive numerical domain for array predicate abstraction
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
Algorithmic analysis of array-accessing programs
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Range analysis of microcontroller code using bit-level congruences
FMICS'10 Proceedings of the 15th international conference on Formal methods for industrial critical systems
A parametric segmentation functor for fully automatic and scalable array content analysis
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Precise reasoning for programs using containers
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An assume guarantee approach for checking quantified array assertions
AMAST'10 Proceedings of the 13th international conference on Algebraic methodology and software technology
Automatically inferring quantified loop invariants by algorithmic learning from simple templates
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Static contract checking with abstract interpretation
FoVeOOS'10 Proceedings of the 2010 international conference on Formal verification of object-oriented software
The reduced product of abstract domains and the combination of decision procedures
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
On inter-procedural analysis of programs with lists and data
Proceedings of the 32nd ACM SIGPLAN conference on Programming language design and implementation
The complexity of abduction for separated heap abstractions
SAS'11 Proceedings of the 18th international conference on Static analysis
Compositional Shape Analysis by Means of Bi-Abduction
Journal of the ACM (JACM)
Invariant and type inference for matrices
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Deriving invariants by algorithmic learning, decision procedures, and predicate abstraction
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Shape analysis in the absence of pointers and structure
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
An analysis of permutations in arrays
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Invariant synthesis for programs manipulating lists with unbounded data
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Fluid updates: beyond strong vs. weak updates
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
Case studies on invariant generation using a saturation theorem prover
MICAI'11 Proceedings of the 10th Mexican international conference on Advances in Artificial Intelligence - Volume Part I
Abstract domains for automated reasoning about list-manipulating programs with infinite data
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
Algorithmic analysis of array-accessing programs
ACM Transactions on Computational Logic (TOCL)
Invariant relations, invariant functions, and loop functions
Innovations in Systems and Software Engineering
Theories, solvers and static analysis by abstract interpretation
Journal of the ACM (JACM)
Accurate invariant checking for programs manipulating lists and arrays with infinite data
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
An abstract domain to infer types over zones in spreadsheets
SAS'12 Proceedings of the 19th international conference on Static Analysis
Synthesis of circular compositional program proofs via abduction
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Finding optimum abstractions in parametric dataflow analysis
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
Abstract interpretation of microcontroller code: Intervals meet congruences
Science of Computer Programming
Inductive invariant generation via abductive inference
Proceedings of the 2013 ACM SIGPLAN international conference on Object oriented programming systems languages & applications
QUIC graphs: relational invariant generation for containers
ECOOP'13 Proceedings of the 27th European conference on Object-Oriented Programming
Explain: a tool for performing abductive inference
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Verifying while loops with invariant relations
International Journal of Critical Computer-Based Systems
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We describe a general technique for building abstract interpreters over powerful universally quantified abstract domains that leverage existing quantifier-free domains. Our quantified abstract domain can represent universally quantified facts like ∀i(0 ≤ i n ⇒ α[i] = 0). The principal challenge in this effort is that, while most domains supply over-approximations of operations like join, meet, and variable elimination, working with the guards of quantified facts requires under-approximation. We present an automatic technique to convert the standard over-approximation operations provided with all domains into sound under-approximations. We establish the correctness of our abstract interpreters by identifying two lattices---one that establishes the soundness of the abstract interpreter and another that defines its precision, or completeness. Our experiments on a variety of programs using arrays and pointers (including several sorting algorithms) demonstrate the feasibility of the approach on challenging examples.