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 Decidability of Presburger Array Programs
Journal of the ACM (JACM)
Uniform Derivation of Decision Procedures by Superposition
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
A Decision Procedure for an Extensional Theory of Arrays
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation
Applications of Hierarchical Reasoning in the Verification of Complex Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Memory modeling in ESL-RTL equivalence checking
Proceedings of the 44th annual Design Automation Conference
Decision procedures for extensions of the theory of arrays
Annals of Mathematics and Artificial Intelligence
Verifying C++ with STL containers via predicate abstraction
Proceedings of the twenty-second IEEE/ACM international conference on Automated software engineering
Lifting abstract interpreters to quantified logical domains
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Calysto: scalable and precise extended static checking
Proceedings of the 30th international conference on Software engineering
Discovering properties about arrays in simple programs
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
${\mathcal{T}}$-Decision by Decomposition
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Hierarchical and Modular Reasoning in Complex Theories: The Case of Local Theory Extensions
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
An SMT Approach to Bounded Reachability Analysis of Model Programs
FORTE '08 Proceedings of the 28th IFIP WG 6.1 international conference on Formal Techniques for Networked and Distributed Systems
Towards SMT Model Checking of Array-Based Systems
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
On Bounded Reachability of Programs with Set Comprehensions
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A Logic of Singly Indexed Arrays
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Deciding Extensions of the Theories of Vectors and Bags
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
Lemmas on demand for the extensional theory of arrays
SMT '08/BPR '08 Proceedings of the Joint Workshops of the 6th International Workshop on Satisfiability Modulo Theories and 1st International Workshop on Bit-Precise Reasoning
Deciding array formulas with frugal axiom instantiation
SMT '08/BPR '08 Proceedings of the Joint Workshops of the 6th International Workshop on Satisfiability Modulo Theories and 1st International Workshop on Bit-Precise Reasoning
Path Feasibility Analysis for String-Manipulating Programs
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,
Automatic Verification of Integer Array Programs
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Complete Instantiation for Quantified Formulas in Satisfiabiliby Modulo Theories
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Incremental Instance Generation in Local Reasoning
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Automated deduction for verification
ACM Computing Surveys (CSUR)
A Logic-Based Framework for Reasoning about Composite Data Structures
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Theory decision by decomposition
Journal of Symbolic Computation
Combination of convex theories: Modularity, deduction completeness, and explanation
Journal of Symbolic Computation
Symmetry and completeness in the analysis of parameterized systems
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Invariant synthesis for combined theories
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
A generic framework for reasoning about dynamic networks of infinite-state processes
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Array abstractions from proofs
CAV'07 Proceedings of the 19th international conference on Computer aided verification
On local reasoning in verification
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
What else is decidable about integer arrays?
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
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
Symbolic heap abstraction with demand-driven axiomatization of memory invariants
Proceedings of the ACM international conference on Object oriented programming systems languages and applications
What's decidable about sequences?
ATVA'10 Proceedings of the 8th international conference on Automated technology for verification and analysis
Test data generation for programs with quantified first-order logic specifications
ICTSS'10 Proceedings of the 22nd IFIP WG 6.1 international conference on Testing software and systems
Automatic verification of parametric specifications with complex topologies
IFM'10 Proceedings of the 8th international conference on Integrated formal methods
Beyond quantifier-free interpolation in extensions of Presburger arithmetic
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Towards complete reasoning about axiomatic specifications
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Satisfiability solving and model generation for quantified first-order logic formulas
FoVeOOS'10 Proceedings of the 2010 international conference on Formal verification of object-oriented software
Inferring loop invariants using postconditions
Fields of logic and computation
NFM'11 Proceedings of the Third international conference on NASA Formal methods
Encoding industrial hardware verification problems into effectively propositional logic
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
Information Processing Letters
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
On Deciding Satisfiability by Theorem Proving with Speculative Inferences
Journal of Automated Reasoning
JELIA'06 Proceedings of the 10th European conference on Logics in Artificial Intelligence
Nested refinements: a logic for duck typing
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An analysis of permutations in arrays
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
On array theory of bounded elements
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
An Instantiation Scheme for Satisfiability Modulo Theories
Journal of Automated Reasoning
Symbolic bounded conformance checking of model programs
PSI'09 Proceedings of the 7th international Andrei Ershov Memorial conference on Perspectives of Systems Informatics
On hierarchical reasoning in combinations of theories
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Bugs, moles and skeletons: symbolic reasoning for software development
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
E-Matching with free variables
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Automaton-Based array initialization analysis
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Efficient symbolic execution of value-based data structures for critical systems
NFM'12 Proceedings of the 4th international conference on NASA Formal Methods
Algorithmic analysis of array-accessing programs
ACM Transactions on Computational Logic (TOCL)
Automatic verification of real-time systems with rich data: an overview
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
EPR-based bounded model checking at word level
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Predicate abstraction of Java programs with collections
Proceedings of the ACM international conference on Object oriented programming systems languages and applications
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
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
A framework for testing first-order logic axioms in program verification
Software Quality Control
Natural proofs for structure, data, and separation
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
Inferring complete initialization of arrays
Theoretical Computer Science
Instantiation Schemes for Nested Theories
ACM Transactions on Computational Logic (TOCL)
Loop invariants: Analysis, classification, and examples
ACM Computing Surveys (CSUR)
QUIC graphs: relational invariant generation for containers
ECOOP'13 Proceedings of the 27th European conference on Object-Oriented Programming
Learning universally quantified invariants of linear data structures
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Array Theory of Bounded Elements and its Applications
Journal of Automated Reasoning
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Motivated by applications to program verification, we study a decision procedure for satisfiability in an expressive fragment of a theory of arrays, which is parameterized by the theories of the array elements. The decision procedure reduces satisfiability of a formula of the fragment to satisfiability of an equisatisfiable quantifier-free formula in the combined theory of equality with uninterpreted functions (EUF), Presburger arithmetic, and the element theories. This fragment allows a constrained use of universal quantification, so that one quantifier alternation is allowed, with some syntactic restrictions. It allows expressing, for example, that an assertion holds for all elements in a given index range, that two arrays are equal in a given range, or that an array is sorted. We demonstrate its expressiveness through applications to verification of sorting algorithms and parameterized systems. We also prove that satisfiability is undecidable for several natural extensions to the fragment. Finally, we describe our implementation in the πVC verifying compiler.