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204
Parametric Shape Analysis via 3Valued Logic
, 1999
"... Shape Analysis concerns the problem of determining "shape invariants"... ..."
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Cited by 539 (71 self)
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Shape Analysis concerns the problem of determining "shape invariants"...
Complexity and Expressive Power of Logic Programming
, 1997
"... 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 ..."
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Cited by 281 (57 self)
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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.
Composing Schema Mappings: SecondOrder Dependencies to the Rescue
 In PODS
, 2004
"... 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, informa ..."
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Cited by 134 (20 self)
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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.
Automatic Structures
 IN PROC. 15TH IEEE SYMP. ON LOGIC IN COMPUTER SCIENCE
, 1999
"... We study definability and complexity issues for automatic and wautomatic 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 firstorder queries. Therefore, automa ..."
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Cited by 89 (7 self)
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We study definability and complexity issues for automatic and wautomatic 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 firstorder 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 firstorder 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 modeltheoretic characterisations for automatic structures via interpretations. Finally we discuss the composition theory of automatic structures and pro...
A Formal Model for an Expressive Fragment of XSLT
, 2000
"... 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 ..."
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Cited by 64 (17 self)
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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.
Symbolically computing mostprecise abstract operations for shape analysis
 In 10th TACAS
, 2004
"... 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 3valued logical structure describing some set of concrete sto ..."
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Cited by 51 (18 self)
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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 3valued logical structure describing some set of concrete stores X) and a precondition p, and computes the mostprecise abstract value for the stores in X that satisfy p. This algorithm solves several open problems in shape analysis: (i) computing the mostprecise 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 loopfree code fragments (i.e., blocks of atomic program statements and conditions); (iv) performing interprocedural shape analysis using procedure specifications and assumeguarantee reasoning; and (v) computing the mostprecise 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 timeout 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
Constraint Satisfaction, Bounded Treewidth, and FiniteVariable Logics
, 2002
"... 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 ..."
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Cited by 44 (10 self)
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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.
Uniform ConstantDepth Threshold Circuits for Division and Iterated Multiplication
, 2002
"... this paper. 2.1. Circuit Classes We begin by formally defining the three circuit complexity classes that will concern us here. These are given by combinatorial restrictions on the circuits of the family. We will then define the uniformity restrictions we will use. Finally, we will give the equival ..."
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Cited by 38 (8 self)
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this paper. 2.1. Circuit Classes We begin by formally defining the three circuit complexity classes that will concern us here. These are given by combinatorial restrictions on the circuits of the family. We will then define the uniformity restrictions we will use. Finally, we will give the equivalent formulations of uniform circuit complexity classes in terms of descriptive complexity classes
Xpath leashed
 IN ACM COMPUTING SURVEYS
, 2007
"... This survey gives an overview of formal results on the XML query language XPath. We identify several important fragments of XPath, focusing on subsets of XPath 1.0. We then give results on the expressiveness of XPath and its fragments compared to other formalisms for querying trees, algorithms and c ..."
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Cited by 36 (3 self)
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This survey gives an overview of formal results on the XML query language XPath. We identify several important fragments of XPath, focusing on subsets of XPath 1.0. We then give results on the expressiveness of XPath and its fragments compared to other formalisms for querying trees, algorithms and complexity bounds for evaluation of XPath queries, and static analysis of XPath queries.
Modular Data Structure Verification
 EECS DEPARTMENT, MASSACHUSETTS INSTITUTE OF TECHNOLOGY
, 2007
"... 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 ..."
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Cited by 36 (21 self)
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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 higherorder 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 firstorder logic, which enables the use of existing resolutionbased theorem provers. Second, I present an approximation of HOL based on field constraint analysis, a new technique that enables