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The authors 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. They 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").
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