Abstract not found

Abstract not found

This paper provides an overview of the STATEMATE system, constructed over the past several years by the authors and their colleagues at Ad Cad Ltd., the R&D subsidiary of i-Logix, Inc. STATEMATE is a set of tools, with a heavy graphical orientation, in- tended for the specification, analysis, design, and documentation of large and complex reactive systems, such as real-time embedded sys- tems, control and communication systems, and interactive software or hardware. It enables a user to prepare, analyze, and debug diagram- matic, yet precise, descriptions of the system under development from three interrelated points of view, capturing structure, functionality, and behavior. These views are represented by three graphical languages, the most intricate of which is the language of statecharts [4], used to depict reactive behavior over time. In addition to the use of statecharts, the main novelty of STATEMATE is in the fact that it "understands " the entire descriptions perfectly, to the point of being able to analyze them for crucial dynamic properties, to carry out rigorous ex- ecutions and simulations of the described system, and to create run- ning code automatically. These features are invaluable when it comes to the quality and reliability of the final outcome.

We investigate the relationship between programming with constraints and database query languages. We show that efficient, declarative database programming can be combined with efficient constraint solving. The key intuition is that the generalization of a ground fact, or tuple, is a conjunction of constraints over a small number of variables. We describe the basic Constraint Query Language design principles and illustrate them with four classes of constraints: real polynomial inequalities, dense linear order inequalities, equalities over an infinite domain, and boolean equalities. For the analysis, we use quantifier elimination techniques from logic and the concept of data complexity from database theory. This framework is applicable to managing spatial data and can be combined with existing multidimensional searching algorithms and data structures.

We characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe. We also show that even without the ordering one application of fixed point suffices to express any query expressible with several alternations of fixed point and negation. This proves that the fixed point query hierarchy suggested by Chandra and Harel collapses at the first fixed point level. It is also a general result showing that in finite model theory one application of fixed point suffices. Introduction and Summary Query languages for relational databases have received considerable attention. In 1972 Codd showed that two natural languages for queries -- one algebraic and the other a version of first order predicate calculus -- have identical powers of expressibility, [Cod72]. Query languages which are as expressive as Codd's Relational Calculus are sometimes called complete. This term is misleading however becau...

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.

this paper a series of languages adequate for expressing exactly those properties checkable in a series of computational complexity classes. For example, we show that a property of graphs (respectively groups, binary strings, etc.) is in polynomial time if and only if it is expressible in the first order language of graphs (respectively groups, binary strings, etc.) together with a least fixed point operator. As another example, a property is in logspace if and only if it is expressible in first order logic together with a deterministic transitive closure operator. The roots of our approach to complexity theory go back to 1974 when Fagin showed that the NP properties are exactly those expressible in second order existential sentences. It follows that second order logic expresses exactly those properties which are in the polynomial time hierarchy. We show that adding suitable transitive closure operators to second order logic results in languages capturing polynomial space and exponential time, respectively. The existence of such natural languages for each important complexity class sheds a new light on complexity theory. These languages reaffirm the importance of the complexity classes as much more than machine dependent issues. Furthermore a whole new approach is suggested. Upper bounds (algorithms) can be produced by expressing the property of interest in one of our languages. Lower bounds may be demonstrated by showing that such expression is impossible.

Efficient methods of processing unanticipated queries are a crucial prerequisite for the success of generalized database management systems. A wide variety of approaches to improve the performance of query evaluation algorithms have been proposed: logic-based and semantic transformations, fast implementations of basic operations, and combinatorial or heuristic algorithms for generating alternative access plans and choosing among them. These methods are presented in the framework of a general query evaluation procedure using the relational calculus representation of queries. In addition, nonstandard query optimization issues such as higher level query evaluation, query optimization in distributed databases, and use of database machines are addressed. The focus, however, is on query optimization in centralized database systems.

The alternating fixpoint of a logic program with negation is defined constructively. The underlying idea is monotonically to build up a set of negative conclusions until the least fixpoint is reached, using a transformation related to the one that defines stable models. From a fixed set of negative conclusions, the positive conclusions follow (without deriving any further negative ones), by traditional Horn clause semantics. The union of positive and negative conclusions is called the alternating xpoint partial model. The name "alternating" was chosen because the transformation runs in two passes; the first pass transforms an underestimate of the set of negative conclusions into an (intermediate) overestimate; the second pass transforms the overestimate into a new underestimate; the composition of the two passes is monotonic. The principal contributions of this work are (1) that the alternating fixpoint partial model is identical to the well-founded partial model, and (2) that alternating xpoint logic is at least as expressive as xpoint logic on all structures. Also, on finite structures, fixpoint logic is as expressive as alternating fixpoint logic.

Abstract not found