Shape Analysis concerns the problem of determining "shape invariants"...

This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.

A schema mapping is a specification that describes how data structured under one schema (the source schema) is to be transformed into data structured under a di#erent schema (the target schema). Schema mappings play a key role in numerous areas of database systems, including database design, information integration, and model management. A fundamental problem in this context is composing schema mappings: given two successive schema mappings, derive a schema mapping between the source schema of the first and the target schema of the second that has the same e#ect as applying successively the two schema mappings.

We study definability and complexity issues for automatic and w-automatic structures. These are, in general, infinite structures but they can be finitely presented by a collection of automata. Moreover, they admit effective (in fact automatic) evaluation of all first-order queries. Therefore, automatic structures provide an interesting framework for extending many algorithmic and logical methods from finite structures to infinite ones. We explain the notion of (w-)automatic structures, give examples, and discuss the relationship to automatic groups. We determine the complexity of model checking and query evaluation on automatic structures for fragments of first-order logic. Further, we study closure properties and definability issues on automatic structures and present a technique for proving that a structure is not automatic. We give model-theoretic characterisations for automatic structures via interpretations. Finally we discuss the composition theory of automatic structures and pro...

The extension of the XSL (eXtensible Style sheet Language) by variables and passing of data values between template rules has generated a powerful XML query language: XSLT (eXtensible Style sheet Language Transformations). An informal introduction to XSTL is given, on the bases of which a formal model of a fragment of XSLT is defined. This formal model is in the spirit of tree transducers, and its semantics is defined by rewrite relations. It is shown that the expressive power of the fragment is already beyond that of most other XML query languages. Finally, important properties such as termination and closure under composition are considered.

Abstract. Shape analysis concerns the problem of determining “shape invariants” for programs that perform destructive updating on dynamically allocated storage. This paper presents a new algorithm that takes as input an abstract value (a 3-valued logical structure describing some set of concrete stores X) and a precondition p, and computes the most-precise abstract value for the stores in X that satisfy p. This algorithm solves several open problems in shape analysis: (i) computing the most-precise abstract value of a set of concrete stores specified by a logical formula; (ii) computing best transformers for atomic program statements and conditions; (iii) computing best transformers for loop-free code fragments (i.e., blocks of atomic program statements and conditions); (iv) performing interprocedural shape analysis using procedure specifications and assume-guarantee reasoning; and (v) computing the most-precise overapproximation of the meet of two abstract values. The algorithm employs a decision procedure for the logic used to express properties of data structures. A decidable logic for expressing such properties is described in a companion submission [6]. The algorithm can also be used with an undecidable logic and a theorem prover; termination can be assured by using standard techniques (e.g., having the theorem prover return a safe answer if a time-out threshold is exceeded) at the cost of losing the ability to guarantee that a mostprecise result is obtained. A prototype has been implemented in TVLA, using the SPASS theorem prover. 1

We systematically investigate the connections between constraint satisfaction problems, structures of bounded treewidth, and definability in logics with a finite number of variables. We first show that constraint satisfaction problems on inputs of treewidth less than k are definable using Datalog programs with at most k variables; this provides a new explanation for the tractability of these classes of problems. After this, we investigate constraint satisfaction on inputs that are homomorphically equivalent to structures of bounded treewidth.

This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java programs with dynamically allocated data structures. Developers write Jahob specifications in classical higher-order logic (HOL); Jahob reduces the verification problem to deciding the validity of HOL formulas. I present a new method for proving HOL formulas by combining automated reasoning techniques. My method consists of 1) splitting formulas into individual HOL conjuncts, 2) soundly approximating each HOL conjunct with a formula in a more tractable fragment and 3) proving the resulting approximation using a decision procedure or a theorem prover. I present three concrete logics; for each logic I show how to use it to approximate HOL formulas, and how to decide the validity of formulas in this logic. First, I present an approximation of HOL based on a translation to first-order logic, which enables the use of existing resolution-based theorem provers. Second, I present an approximation of HOL based on field constraint analysis, a new technique that enables

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To reason effectively about programs, it is important to have some version of a transitive-closure operator so that we can describe such notions as the set of nodes reachable from a program's variables. On the other hand, with a few notable exceptions, adding transitive closure to even very tame logics makes them undecidable. In this paper, we explore...