A minimal and complete unification procedure for a theory with individual and sequence variables, free constants and free fixed and flexible arity function symbols is described and a brief overview of an extension with pattern-terms is given.

We study analogs of classical relational calculus in the context of strings. We start by studying string logics. Taking a classical model-theoretic approach, we fix a set of string operations and look at the resulting collection of definable relations. These form an algebra - a class of n-ary relations for every n, closed under projection and Boolean operations. We show that by choosing the string vocabulary carefully, we get string logics that have desirable properties: computable evaluation and normal forms. We identify five distinct models and study the differences in their model-theory and complexity of evaluation. We identify a subset of these models which have additional attractive properties, such as finite VC dimension and quantifier elimination. Once you have a logic,

We study relational calculi with support for string operations. Most prior proposals were based on adding the operation of concatenation to rst-order logic. Such an extension is problematic as the relational calculus becomes computationally complete, which in turn implies strong limits on the ability to perform optimization and static analysis of properties such as query safety. In contrast, we look at extensions of relational calculus that have nice expressiveness, decidability, and safety properties, while corresponding to sets of string operations used in SQL. We start with an extension based on the string ordering and LIKE predicates. We then extend this basic model to include string length comparison. While both of these share some of the attractive properties of relational calculus (low data complexity for generic queries, eective syntax for safe queries, correspondence with an algebra), there is a large gap between these calculi in expressive power and complexity. The smaller...

This paper develops a query language for sequence databases, such as genome databases and text databases. Unlike relational data, queries over sequential data can easily produce infinite answer sets, since the universe of sequences is infinite, even for a finite alphabet. The challenge is to develop query languages that are both highly expressive and finite. This paper develops such a language as a subset of a logic for string databases called Sequence Datalog. The main idea is to use safe recursion to control and limit unsafe recursion. The main results are the definition of a finite form of recursion, called domain--bounded recursion, and a characterization of its complexity and expressive power. Although finite, the resulting class of programs is highly expressive, since its data complexity is complete for the elementary functions. 1 Introduction It is widely accepted that relational databases do not provide enough support for many of today's advanced applications. In some...