Search results for "expressive power"
showing 6 items of 6 documents
The expressive power of the shuffle product
2010
International audience; There is an increasing interest in the shuffle product on formal languages, mainly because it is a standard tool for modeling process algebras. It still remains a mysterious operation on regular languages.Antonio Restivo proposed as a challenge to characterize the smallest class of languages containing the singletons and closed under Boolean operations, product and shuffle. This problem is still widely open, but we present some partial results on it. We also study some other smaller classes, including the smallest class containing the languages composed of a single word of length 2 which is closed under Boolean operations and shuffle by a letter (resp. shuffle by a l…
Padding and the expressive power of existential second-order logics
1998
Padding techniques are well-known from Computational Complexity Theory. Here, an analogous concept is considered in the context of existential second-order logics. Informally, a graph H is a padded version of a graph G, if H consists of an isomorphic copy of G and some isolated vertices. A set A of graphs is called weakly expressible by a formula ϕ in the presence of padding, if ϕ is able to distinguish between (sufficiently) padded versions of graphs from A and padded versions of graphs that are not in A.
New Encodings of Pseudo-Boolean Constraints into CNF
2009
International audience; This paper answers affirmatively the open question of the existence of a polynomial size CNF encoding of pseudo-Boolean (PB) constraints such that generalized arc consistency (GAC) is maintained through unit propagation (UP). All previous encodings of PB constraints either did not allow UP to maintain GAC, or were of exponential size in the worst case. This paper presents an encoding that realizes both of the desired properties. From a theoretical point of view, this narrows the gap between the expressive power of clauses and the one of pseudo-Boolean constraints.
Functions definable by numerical set-expressions
2011
A "numerical set-expression" is a term specifying a cascade of arithmetic and logical operations to be performed on sets of non-negative integers. If these operations are confined to the usual Boolean operations together with the result of lifting addition to the level of sets, we speak of "additive circuits". If they are confined to the usual Boolean operations together with the result of lifting addition and multiplication to the level of sets, we speak of "arithmetic circuits". In this paper, we investigate the definability of sets and functions by means of additive and arithmetic circuits, occasionally augmented with additional operations.
Novel Indexing Method of Relations Between Salient Objects
2011
Since the last decade, images have been integrated into several application domains such as GIS, medicine, etc. This integration necessitates new managing methods particularly in image retrieval. Queries should be formulated using different types of features such as low-level features of images (histograms, color distribution, etc.), spatial and temporal relations between salient objects, semantic features, etc. In this chapter, we propose a novel method for identifying and indexing several types of relations between salient objects. Spatial relations are used here to show how our method can provide high expressive power to relations in comparison to the traditional methods.
On Diving in Trees Thomas Schwentick
2000
The paper is concerned with queries on tree-structured data. It defines fragments of first-order logic (FO) and FO extended by regular expressions along paths. These fragments have the same expressive power as the full logics themselves. On the other hand, they can be evaluated reasonably efficient, even if the formula which represents the query is considered as part of the input.