Marc H. Graham

Abstraction in recovery management

There are many examples of actions on abstract data types which can be correctly implemented with nonserializable and nonrecoverable schedules of reads and writes. We examine a model of multiple layers of abstraction that explains this phenomenon and suggests an approach to building layered systems with transaction oriented synchronization and roll back. Our model may make it easier to provide the high data integrity of reliable database transaction processing in a broader class of information systems. We concentrate on the recovery aspects here, a technical report [Moss et al 85] has a more complete discussion of concurrency control.

Independent database schemas

Abstract A database schema is independent with respect to a given set of constraints if the constraints can be enforced separately in the relations. A polynomial time algorithm is presented that recognizes independent schemas, when the given constraints consist of functional dependencies and the join dependency of the database schema.

Functional dependencies on cyclic database schemes

We study how functional dependencies affect the cyclicity of a database scheme; in particular, when does a set of functional dependencies make a cyclic database scheme behave like an acyclic one.A database scheme is fd-acyclic if every pairwise-consistent database state that satisfies the fds is join-consistent. We give a simple characterization of fd-acyclicity over a restricted class of database schemes. We then give a tableau-based characterization for the general case that leads to an algorithm for testing fd-acyclicity. This algorithm actually solves the more general problem of query equivalence under functional dependencies and typed inclusion dependencies.

On the complexity and axiomatizability of consistent database states

A database is consistent with respect to a set σ of dependencies if it has a weak instance. A weak instance is a universal relation that satisfies Σ, and whose projections on the relation schemes are supersets of the relations in the database. In this paper we investigate the complexity of testing consistency and the logics that can axiomatize consistency, relative to a fixed set Σ of dependencies. If Σ is allowed to include embedded dependencies, then consistency can be non-recursive. If Σ consists only of total dependencies, then consistency can be tested in polynomial time. The degree of the polynomial can, however, be arbitrarily high. Consistency can be axiomatized but not finitely axiomatized by equality generating dependencies. If embedded dependencies are allowed then consistency cannot be finitely axiomatized by any effective logic. If, on the other hand, only total dependencies are allowed then consistency can be finitely axiomatized by fixpoint logic.

Constant time maintenance or the triumph of the FD.

Independence has been studied by many researchers in database theory. As mentioned by Beeri et. al. /BBG], independence meets the aesthetic principle of ‘separation’ or ‘one thing in one place.‘, The research presented here constitutes an attack on the desirability of independence within the context of weak instance theory. In all the contexts in which independence has been studied, it has the following essential description: Some set of ‘local’ properties is sufficient to guarantee some set of ‘global’ properties. Within weak instance theory, it takes the following form: A database state within which each relation satisfies the dependencies local to it has a weak instance, i.e., is consistent. Thii problem does not arise in practice. In practice one does not encounter states about which only this local satisfaction property is known. One encounters instead the following problem: Given a state which is known to be consistent and a suggested modification to that state, should the modification be allowed; that is, will the modified state be

Functions in databases

We discuss the objectives of including functional dependencies in the definition of a relational database. We find two distinct objectives. The appearance of a dependency in the definition of a database indicates that the states of the database are to encode a function. A method based on the chase of calculating the function encoded by a particular state is given and compared to methods utilizing derivations of the dependency. A test for deciding whether the states of a schema may encode a nonempty function is presented as is a characterization of the class of schemas which are capable of encoding nonempty functions for all the dependencies in the definition. This class is the class of dependency preserving schemas as defined by Beeri et al. and is strictly larger than the class presented by Bernstein. The second objective of including a functional dependency in the definition of a database is that the dependency be capable of constraining the states of the database; that is, capable of uncovering input errors made by the users. We show that this capability is weaker than the first objective; thus, even dependencies whose functions are everywhere empty may still act as constraints. Bounds on the requirements for a dependency to act as a constraint are derived. These results are founded on the notion of a weak instance for a database state, which replaces the universal relation instance assumption and is both intuitively and computationally more nearly acceptable.

Strong equivalence of relational expressions under dependencies

The notion of two relational database queries being quivalent over all databases satisfying a set of constraints is well understood when the databases can be thought to consist of a single relation. For multirelation databases, there has been until recently a lack of an adequate notion of what it means for a database to satisfy a set of dependencies. Honeyman [7] and Vassiliou [ 111 have proposed such a notion and argued convincingly for its appropriateness. We use their approach to define query equivalence for multi-relation databases and show that the tableau methods of [l] can be adapted to provide a test for query equivalence under our definition. Aho, Sagiv and Ullman [ 1 ] proposed tableaux as a useful representation of a large class of relational database queries. They discussed two different notions of query equivalence. Two relational algebra expressions El, El on relation variables Ra , . . . . Rk are said to be weak& equfvalent if El((rl, . . . . rk)) = E&l, a**, rk)) for any join-consistent, a database state (rl , . . . . rkh Requiring equality over all states, rather than just the join-consistent ones, gives a stricter notion called strong equivalence. For example, rr,?&AB * BC) is weakly equivalent to AB, but not strongly equivalent. AS pointed out in [ 11, when concerned with weak equivalence we can take the convenient approach of viewing expressions as defined on a single universal relation rather than on several relation variables. Following 131, they prove that two expressions are weakly equivalent if and only if there exist a pair of containment mappings between their tableaux. For strong equivalence, a similar result holds provided that a modified form of tableaux called tagged tableaux is used. When a set of depenciencies is given, certain transformations that preserve weak equivalence can be exhaustively applied to the tableau for an expression. The final tableau, called the chase of the original one, has the property that the tableau itself, viewed as a universal relation, satisfies the dependencies. If we wish to test whether two expressiorls are weakly equivalent over the set of universal relations satisfying some set of dependencies, it suffices to chase their tableaux and test for the existence of containment mappings [ 11. Thus the semantic question of equivalence of two expressions with respect to a set of dependencies is transformed to the syntactically answerable question of unrestricted weak equivalence. When strong equivalence is of interest, Aho et al.

Reliable scheduling of database transactions for unreliable systems

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Notions of dependency satisfaction

Two notions of dependency satisfaction, consistency and completeness, are introduced. Consistency is the natural generalization of weak satisfaction and seems appropriate when only equality-generating dependencies are given, but disagrees with the standard notion in the presence of tuple-generating dependencies. Completeness is based on the intuitive semantics of tuple-generating dependencies but appears unnatural for equality-generating dependencies. It is argued that neither approach is the correct one, but rather that they correspond to different policies on constraint enforcement, and each one is appropriate in different circumstances. Consistency and completeness of a state are characterized in terms of the tableau associated with the state and in terms of logical properties of a set of first-order sentences associated with the state. A close relation between the problems of testing for consistency and completeness and of testing implication of dependencies is established. The possibility of formalizing dependency satisfaction without using a universal relation scheme is examined.

Path expressions in databases

A state of a schema B is said to be consistent with a set of functional dependencies F, if there exists a weak instance for the state, an instance, W, of the scheme U such that & as a subset of the powerset of II, nlth the following two properties, [HI 11 for each relation r of the state, rcnR(W) where P 1s the scheme of r, 2) W satasfies F The chase procedure of Aho et al [ABUI, aS adapted by Honeyman [El, decades the consistency of a state