Showing papers in "Acta Cybernetica in 1992"

Normal form relation schemes: a new characterization

Abstract: A new characterization of relational database schemes in normal forms is given. This characterization is based on the properties of the semilattice of closed sets of attributes. For the problems testing third and Boyce -Codd normal forma, which are known to be ^/ / ' -complete for relation schemes, this new characterization helps establish polynomial algorithms if the input is a relation (matrix) rather than a relation scheme. The problem of approximation of an arbitrary family of functional dependencies by one in a normal form is also addressed.

Computing Maximum Valued Regions.

Abstract: We consider the problem of finding optimum connected configurations in the plane and in undirected graphs. First, we show that a special case concerning rectilinear grids in the plane and arising in oil business is NPcomplete, and we present a fast approximation algorithm for it. Secondly, we identify a number of polynomial time solvable special cases for the corresponding problem in graphs. The special cases include trees, interval graphs, cographs and split graphs.

The Boolean Closure of DR-Recognizable Tree Languages.

Abstract: The family DRec of tree languages recognized by deterministic root-tofrontier (top-down) tree automata is not closed under unions or complements. Hence, it is not a variety of tree languages in the sense of Steinby. However, we show that the Boolean closure of DRec is a variety which is properly included in the variety Rec of all recognizable tree languages. This Boolean closure is also compared with some other tree language varieties.

Regularizing Context-Free Languages by AFL Operations: Concatenation and Kleene Closure.

Abstract: We consider the possibility to obtain a regular language by applying a given operation to a context-free language. Properties of the family of context-free languages which can be \"regularized'1 by concatenation with a regular set or by Kleene closure are investigated here: size, hierarchies, characterizations, closure, decidability.

The Self-organizing List and Processor Problems under Randomized Policies.

Abstract: We consider the self-organizing list problem in the case that only one item has a different request probability and show that transposition has a steady state cost stochastically smaller than any randomized policy that moves the requested item, found in position t, to position j with some probability dij, i > j. A random variable X is said to be stochastically smaller than another random variable Y, written X <„ Y if Pr{X > Jfc} < Pr{Y > k}, for any k. This is a stronger statement than E[X] < E[Y|. We also show that the steady state cost under the policy that moves the requested item i positions forward is stochastically increasing in t. Sufficient conditions are given for the steady state cost under a randomized policy A to be stochastically smaller than that under another randomized policy B. Similar results are obtained for the processor problem, where a list of processors is considered. OPTIMAL LIST ORDER; MEMORY CONSTRAINTS; TRANSPOSITION RULE; RAMDOMIZATION 0 Introduction A self-organizing list problem is characterized by a sequential list of n items subject to a reordering policy. At the beginning of each time period, an item is requested and the list is searched sequentially from the first position until the requested item is found. Each of these n items has an unknown probability of being requested. Let p = (pi,p2, • • • ,Pn) be the request probability vector, where p,is the request probability of item t,i = 1 , . . . , n, and 0 < p,< 1, Pi — 1. At the end of each period, the items on the list are reordered according to the reordering policy. The cost of each period is taken to be the position where the requested item is found. We are interested in the steady state costs under various policies. A reordering policy is called optimal if it minimizes the expected steady state cost for any given request probability vector p. The self-organizing list problem will now be called the list problem and the policy will mean the reordering policy. Kan and Ross [6] define a no-memory policy as a reordering policy that depends only on the position of the requested item and the current ordering. Some of the most studied examples of the no-memory policies are the transposition, moveto-front, and move-i-position policies. Keeping the relative positions of all other 'Department of Economics, Thammasat University, Bangkok, Thailand 10200