We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base T , an update p, and a formula q, decide whether q is derivable from T p, the updated (or revised) knowledge base. This problem amounts to evaluating the counterfactual p > q over T . Besides the general case, also subcases are considered, in particular where T is a conjunction of Horn clauses, or where the size of p is bounded by a constant.

Several languages, such as LOREL and UnQL, support querying of semi-structured data. Others, such as WebSQL and WebLog, query Web sites. All these languages model data as labeled graphs and use regular path expressions to express queries that traverse arbitrary paths in graphs. Naive execution of path expressions is inefficient, however, because it often requires exhaustive graph search. We describe two optimization techniques for queries with regular path expressions, which we call regular queries. Both rely on graph schemas, which specify partial knowledge of a graph's structure. Query pruning restricts search to a fragment of the graph; we give an efficient algorithm for rewriting any regular query into a pruned one. Query rewriting using state extents can entirely eliminate or substantially reduce graph traversal; it is reminiscent of optimizing relational queries using indices. There may be several ways to optimize a query using state extents; we give an exponential-time algorith...

Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logic-based abduction. Candidates for abductive explanations are usually subjected to minimality criteria such as subsetminimality, minimal cardinality, minimal weight, or minimality under prioritization of individual hypotheses. This paper presents a comprehensive complexity analysis of relevant decision and search problems related to abduction on propositional theories. Our results indicate that abduction is harder than deduction. In particular, we show that with the most basic forms of abduction the relevant decision problems are complete for complexity classes at the second level of the polynomial hierarchy, while the use of prioritization raises the complexity to the third level in certain cases.

The high computational complexity of advanced reasoning tasks such as reasoning about knowledge and planning calls for efficient and reliable algorithms for reasoning problems harder than NP. In this paper we propose Evaluate, an algorithm for evaluating Quantified Boolean Formulae, a language that extends propositional logic in a way such that many advanced forms of propositional reasoning, e.g., circumscription, can be easily formulated as evaluation of a QBF. Algorithms for evaluation of QBFs are suitable for the experimental analysis on a wide range of complexity classes, a property not easily found in other formalisms. Evaluate is based on a generalization of the Davis-Putnam procedure for SAT, and is guaranteed to work in polynomial space. Before presenting the algorithm, we discuss several abstract properties of QBFs that we singled out to make it more efficient. We also discuss various options that were investigated about heuristics and data structures, and report the main res...

. We present algorithms for computing similarity relations of labeled graphs. Similarity relations have applications for the refinement and verification of reactive systems. For finite graphs, we present an O(mn) algorithm for computing the similarity relation of a graph with n vertices and m edges (assuming m n). For effectively presented infinite graphs, we present a symbolic similarity-checking procedure that terminates if a finite similarity relation exists. We show that 2D rectangular automata, which model discrete reactive systems with continuous environments, define effectively presented infinite graphs with finite similarity relations. It follows that the refinement problem and the 8CTL model-checking problem are decidable for 2D rectangular automata. 1 Introduction A labeled graph G = (V; E;A; hh\Deltaii) consist of a (possibly infinite) set V of vertices, a set E ` V 2 of edges, a set A of labels, and a function hh\Deltaii : V ! A that maps each vertex v to a label hh...

Noncooperative game theory provides a normative framework for analyzing strategic interactions.

In this paper, we ask if the traditional relational query acceleration techniques of summary tables and covering indexes have analogs for branching path expression queries over tree- or graph-structured XML data. Our answer is yes --- the forward-and-backward index already proposed in the literature can be viewed as a structure analogous to a summary table or covering index. We also show that it is the smallest such index that covers all branching path expression queries. While this index is very general, our experiments show that it can be so large in practice as to o#er little performance improvement over evaluating queries directly on the data. Likening the forward-and-backward index to a covering index on all the attributes of several tables, we devise an index definition scheme to restrict the class of branching path expressions being indexed. The resulting index structures are dramatically smaller and perform better than the full forward-and-backward index for these classes of branching path expressions. This is roughly analogous to the situation in multidimensional or OLAP workloads, in which more highly aggregated summary tables can service a smaller subset of queries but can do so at increased performance. We evaluate the performance of our indexes on both relational decompositions of XML and a native storage technique. As expected, the performance benefit of an index is maximized when the query matches the index definition.

This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of well-known semantics, as well as the complexity of deciding whether a propositional formula is satised by all models according to a given semantics. We concentrate on nite propositional disjunctive programs with as wells as without integrity constraints, i.e., clauses with empty heads; the problems are located in appropriate slots of the polynomial hierarchy. In particular, we show that the consistency check is P 2 -complete for the disjunctive stable model semantics (in the total as well as partial version), the iterated closed world assumption, and the perfect model semantics, and we show that the inference problem for these semantics is P 2 -complete; analogous results are derived for the an

Circumscription and the closed world assumption with its variants are well-known nonmonotonic techniques for reasoning with incomplete knowledge. Their complexity in the propositional case has been studied in detail for fragments of propositional logic. One open problem is whether the deduction problem for arbitrary propositional theories under the extended closed world assumption or under circumscription is $\Pi^P_2$-complete, i.e., complete for a class of the second level of the polynomial hierarchy. We answer this question by proving these problems $\Pi^P_2$-complete, and we show how this result applies to other variants of closed world reasoning.

We consider the following problem: given a labelled directed graph G and a regular expression R, find all pairs of nodes connected by a simple path such that the concatenation of the labels along the path satisfies R. The problem is motivated by the observation that many recursive queries in relational databases can be expressed in this form, and by the implementation of a query language, G+ , based on this observation. We show that the problem is in general intractable, but present an algorithm than runs in polynomial time in the size of the graph when the regular expression and the graph are free of conflicts. We also present a class of languages whose expressions can always be evaluated in time polynomial in the size of both the graph and the expression, and characterize syntactically the expressions for such languages. Key words. Labelled directed graphs, NP-completeness, polynomial-time algorithms, regular expressions, simple paths AMS(MOS) subject classifications. 68P, 6...