Current object-oriented data models lack several important features that would allow one to express relevant knowledge about the classes of a schema. In particular, there is no data model supporting simultaneously the inverse of the functions represented by attributes, the union, the intersection and the complement of classes, the possibility of using nonbinary relations, and the possibility of expressing cardinality constraints on attributes and relations. In this paper we define a new data model, called CAR, which extends the basic core of current object-oriented data models with all the above mentioned features. A technique is then presented both for checking the consistency of class definitions, and for computing the logical consequences of the knowledge represented in the schema. Finally, the inherent complexity of reasoning in CAR is investigated, and the complexity of our inferencing technique is studied, depending on various assumptions on the schema. 1 Introduction Many recen...

1 Introduction This paper considers the satisfiability problem for a logic that allows reason-ing about sets and their cardinalities. We call this logic quantifier-free Boolean Algebra with Presburger Arithmetic and denote it QFBAPA. Our motivationfor QFBAPA is proving the validity of formulas arising from program verifica-tion [12,13,14], but

In [22], it was shown that MSO logic for ordered unranked trees becomes undecidable if Presburger constraints are allowed at children of nodes. We now show that a decidable logic is obtained if we use a a modal fixpoint logic instead. We present an automata theoretic characterization of this logic by means of deterministic Presburger tree automata (PTA) and show how it can be used to express numerical document queries. Surprisingly, the complexity of satisfiability for the extended logic is asymptotically the same as for the original logic. The non-emptiness for PTAs is in general pspace-complete which is moderate given that it is already pspace-hard to test whether the complement of a regular expression is non-empty. We also identify a subclass of PTAs with a tractable non-emptiness problem. Further, to decide whether a tree t satisfies a formula # is polynomial in the size of # and linear in the size of t.

The Hamming center problem for a set S of k binary strings, each of length n, asks for a binary string of length n that minimizes the maximum Hamming distance between and any string in S. The decision version of this problem is known to be NP-complete [6]. We provide several approximation algorithms for the Hamming center problem. Our main result is a randomized ( 4 3 + ")-approximation algorithm running in polynomial time if the Hamming radius of S is at least superlogarithmic in k. Furthermore, we show how to nd in polynomial time a set B of O(log k) strings of length n such that for each string in S there is at least one string in B within Hamming distance not exceeding the radius of S. 1 Introduction Let Z n 2 be the set of all strings of length n over the alphabet f0; 1g. For any 2 Z n 2 we use the notation [i] to refer to the symbol placed at the ith position of , where i = 1; ::; n, and we let [i::j] represent the substring of starting at position i and endin...

Graphs are an intuitive model for states of a (software) system that include pointer structures --- for instance, object-oriented programs.

A new algorithm for computing a complete set of unifiers for two terms involving associative-commutative function symbols is presented. The algorithm is based on a non-deterministic algorithm given by the authors in 1986 to show the NP-completeness of associative-commutative unifiability. The algorithm is easy to understand, its termination can be easily established. More importantly, its complexity can be easily analyzed and is shown to be doubly exponential in the size of the input terms. The analysis also shows that there is a double-exponential upper bound on the size of a complete set of unifiers of two input terms. Since there is a family of simple associative-commutative unification problems which have complete sets of unifiers whose size is doubly exponential, the algorithm is optimal in its order of complexity in this sense. This is the first associative-commutative unification algorithm whose complexity has been completely analyzed. The approach can also be used to show a singl...

A new branch-and-bound algorithm for the exact solution of the 0-1 Knapsack Problem is presented. The algorithm is based on solving an "expanding core", which initially only contains the break item, but which is expanded each time the branch-and-bound algorithm reaches the border of the core. Computational experiments show that most data instances are optimally solved without sorting or preprocessing a great majority of the items. Detailed program sketches are provided, and computational experiments are reported, indicating that the algorithm presented not only is shorter, but also faster and more stable than any other algorithm hitherto proposed.

Abstract. We present a new abstraction-based framework for deciding satisfiability of quantifier-free Presburger arithmetic formulas. Given a Presburger formula φ, our algorithm invokes a SAT solver to produce proofs of unsatisfiability of approximations of φ. These proofs are in turn used to generate abstractions of φ as inputs to a theorem prover. The SAT-encodings of the approximations of φ are obtained by instantiating the variables of the formula over finite domains. The satisfying integer assignments provided by the theorem prover are then used to selectively increase domain sizes and generate fresh SAT-encodings of φ. The efficiency of this approach derives from the ability of SAT solvers to extract small unsatisfiable cores, leading to small abstracted formulas. We present experimental results which suggest that our algorithm is considerably more efficient than directly invoking the theorem prover on the original formula. 1

We describe a family of decision procedures that extend the decision procedure for quantifier-free constraints on recursive algebraic data types (term algebras) to support recursive abstraction functions. Our abstraction functions are catamorphisms (term algebra homomorphisms) mapping algebraic data type values into values in other decidable theories (e.g. sets, multisets, lists, integers, booleans). Each instance of our decision procedure family is sound; we identify a widely applicable many-to-one condition on abstraction functions that implies the completeness. Complete instances of our decision procedure include the following correctness statements: 1) a functional data structure implementation satisfies a recursively specified invariant, 2) such data structure conforms to a contract given in terms of sets, multisets, lists, sizes, or heights, 3) a transformation of a formula (or lambda term) abstract syntax tree changes the set of free variables in the specified way.

We present a decision procedure for a constraint language combining multisets of ur-elements, the integers, and an arbitrary rstorder theory T of the ur-elements. Our decision procedure is an extension of the Nelson-Oppen combination method speci cally tailored to the combination domain of multisets, integers, and ur-elements.