On the relationship of congruence closureand unification

Congruence closure is a fundamental operation for symbolic computation. Unification closureis defined as its directional dual, i.e., on the same inputs but top-down as opposed to bottom-up. Unifying terms is another fundamental operation for symbolic computation and is commonly computed using unification closure. We clarify the directional duality by reducing unification closure to a special form of congruence closure. This reduction reveals a correspondence between repeated variables in terms to be unified and equalities of monadic ground terms. We then show that: (1) single equality congruence closure on a directed acyclic graph, and (2) acyclic congruence closure of a fixed number of equalities, are in the parallel complexity class NC. The directional dual unification closures in these two cases are known to be log-space complete for PTIME. As a consequence of our reductions we show that if the number of repeated variables in the input terms is fixed, then term unification can be performed in NC; this extends the known parallelizable cases of term unification. Using parallel complexity we also clarify the relationship of unification closure and the testing of deterministic finite automata for equivalence

The Complexity of Concurrency Control for Distributed Databases

This study is an analysis of the distributed version of data base concurrency control. It provides concrete mathematical evidence that the distributed problem is an inherently more complex task than the centralized one. The notions of transaction, concurrency, history, serializability, scheduler, etc, for centralized databases are now well-understood both from a theoretical and a practical point of view

Algorithms for a scheduling application of the Asymmetric Traveling Salesman Problem.

Thesis. 1978. M.S.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERINGIncludes bibliographical references.M.S

On the Computational Complexity of Cardinality Constraints in Relational Databases

We show that the problem of determining whether of not a lossless join property holds for a database, in the presence of key dependencies and cardinality constraints on the domains of the attributes is NP-complete

Functional Database Query Languages as Typed Lambda Calculi of Fixed Order

We present functional database query languages expressing the FO- and PTIME-queries. This framework is a functional analogue of the logical languages of first-order and fixpoint formulas over finite structures, and its formulas consist of: atomic constants of order 0, equality among these constants, variables, application, lambda and let abstraction; all typable in 4 functionality order. In this framework, proposed in [25] for arbitrary functionality order, typed lambda terms are used for input-output databases and for query program syntax, and reduction is used for query program semantics. We define two families of languages: TLI = i or simply-typed list iteration of order i + 3 with equality and MLI = i or ML-typed list iteration of order i + 3 with equality; we use i + 3 since our list representation of input-output databases requires at least order 3. We show that, over list-represented databases, both TLI = 0 and MLI = 0 exactly express the FO-queries and both TLI = 1 and ..