Verification Decidability of Presburger Array Programs
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Combining Multisets with Integers
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Decision procedures for extensions of the theory of arrays
Annals of Mathematics and Artificial Intelligence
Monitoring External Resources in Java MIDP
Electronic Notes in Theoretical Computer Science (ENTCS)
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Safety Guarantees from Explicit Resource Management
Formal Methods for Components and Objects
Decision procedures for multisets with cardinality constraints
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
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's decidable about arrays?
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Hierarchic reasoning in local theory extensions
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Path- and index-sensitive string analysis based on monadic second-order logic
ACM Transactions on Software Engineering and Methodology (TOSEM) - Testing, debugging, and error handling, formal methods, lifecycle concerns, evolution and maintenance
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Vectors and bags are basic collection data structures, which are used frequently in programs and specifications. Reasoning about these data structures is supported by established algorithms for deciding ground satisfiability in the theories of arrays (for vectors) and multisets (for bags), respectively. Yet, these decision procedures are only able to reason about vectors and bags in isolation, not about their combination. This paper presents a decision procedure for the combination of the theories of vectors and bags, even when extended with a function bagof bridging between vectors and bags. The function bagof converts vectors into the bags of their elements, thus admitting vector/bag comparisons. Moreover, for certain syntactically restricted classes of ground formulae decidability is retained if the theory of vectors is extended further with a map function which applies uninterpreted functions to all elements of a vector.