Modelling Garbage Collection Algorithms --- Extend abstract

We show how abstract requirements of garbage collection can be captured using temporal logic. The temporal logic specification can then be used as a basis for process algebra specifications which can involve varying amounts of parallelism. We present two simple CCS specifications as an example, followed by a more complex specification of the cyclic reference counting algorithm. The verification of such algorithms is then briefly discussed

Matching Dependencies with Arbitrary Attribute Values: Semantics, Query Answering and Integrity Constraints

Matching dependencies (MDs) were introduced to specify the identification or matching of certain attribute values in pairs of database tuples when some similarity conditions are satisfied. Their enforcement can be seen as a natural generalization of entity resolution. In what we call the "pure case" of MDs, any value from the underlying data domain can be used for the value in common that does the matching. We investigate the semantics and properties of data cleaning through the enforcement of matching dependencies for the pure case. We characterize the intended clean instances and also the "clean answers" to queries as those that are invariant under the cleaning process. The complexity of computing clean instances and clean answers to queries is investigated. Tractable and intractable cases depending on the MDs and queries are identified. Finally, we establish connections with database "repairs" under integrity constraints.Comment: 13 pages, double column, 2 figure

Deterministic Polynomial Time Algorithms for Matrix Completion Problems

We present new deterministic algorithms for several cases of the maximum rank matrix completion problem (for short matrix completion), i.e. the problem of assigning values to the variables in a given symbolic matrix as to maximize the resulting matrix rank. Matrix completion belongs to the fundamental problems in computational complexity with numerous important algorithmic applications, among others, in computing dynamic transitive closures or multicast network codings (Harvey et al SODA 2005, Harvey et al SODA 2006). We design efficient deterministic algorithms for common generalizations of the results of Lovasz and Geelen on this problem by allowing linear functions in the entries of the input matrix such that the submatrices corresponding to each variable have rank one. We present also a deterministic polynomial time algorithm for finding the minimal number of generators of a given module structure given by matrices. We establish further several hardness results related to matrix algebras and modules. As a result we connect the classical problem of polynomial identity testing with checking surjectivity (or injectivity) between two given modules. One of the elements of our algorithm is a construction of a greedy algorithm for finding a maximum rank element in the more general setting of the problem. The proof methods used in this paper could be also of independent interest.Comment: 14 pages, preliminar

A threshold for majority in the context of aggregating partial order relations

We consider a voting problem where voters have expressed their preferences on a single set of objects. These preferences take the shape of strict partial order relations. In order to allow extraction of a unique strict partial order relation corresponding to a social set of preferences, we determine the minimum number of votes a pairwise preference should receive in order to qualify as a social pairwise preference. Transitive closure of the social pairwise preferences will result in the social set of preferences. At the same time, the social set of preferences needs to be cycle-free, and the minimum number of votes should be determined with this constraint in mind. We provide an example application

Deciding Conditional Termination

We address the problem of conditional termination, which is that of defining the set of initial configurations from which a given program always terminates. First we define the dual set, of initial configurations from which a non-terminating execution exists, as the greatest fixpoint of the function that maps a set of states into its pre-image with respect to the transition relation. This definition allows to compute the weakest non-termination precondition if at least one of the following holds: (i) the transition relation is deterministic, (ii) the descending Kleene sequence overapproximating the greatest fixpoint converges in finitely many steps, or (iii) the transition relation is well founded. We show that this is the case for two classes of relations, namely octagonal and finite monoid affine relations. Moreover, since the closed forms of these relations can be defined in Presburger arithmetic, we obtain the decidability of the termination problem for such loops.Comment: 61 pages, 6 figures, 2 table