Journal of Symbolic Computation
Object-oriented software construction (2nd ed.)
Object-oriented software construction (2nd ed.)
Quantifier Hierarchies over Word Relations
CSL '91 Proceedings of the 5th Workshop on Computer Science Logic
Satisfiability of word equations with constants is in PSPACE
Journal of the ACM (JACM)
Decision procedures for extensions of the theory of arrays
Annals of Mathematics and Artificial Intelligence
Full functional verification of linked data structures
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
A Logic of Singly Indexed Arrays
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Automatic Verification of Integer Array Programs
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Decision procedures for multisets with cardinality constraints
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
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
Building a calculus of data structures
VMCAI'10 Proceedings of the 11th 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
Deciding functional lists with sublist sets
VSTTE'12 Proceedings of the 4th international conference on Verified Software: theories, tools, experiments
Predicate abstraction of Java programs with collections
Proceedings of the ACM international conference on Object oriented programming systems languages and applications
A verifier for functional properties of sequence-manipulating programs
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Array Theory of Bounded Elements and its Applications
Journal of Automated Reasoning
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We present a first-order theory of (finite) sequences with integer elements, Presburger arithmetic, and regularity constraints, which can model significant properties of data structures such as lists and queues. We give a decision procedure for the quantifier-free fragment, based on an encoding into the first-order theory of concatenation; the procedure has PSPACE complexity. The quantifier-free fragment of the theory of sequences can express properties such as sortedness and injectivity, as well as Boolean combinations of periodic and arithmetic facts relating the elements of the sequence and their positions (e.g., "for all even i's, the element at position i has value i + 3 or 2i"). The resulting expressive power is orthogonal to that of the most expressive decidable logics for arrays. Some examples demonstrate that the fragment is also suitable to reason about sequence-manipulating programs within the standard framework of axiomatic semantics.