Related papers: Descriptive complexity for pictures languages (ext…
Recent progress on image captioning has made it possible to generate novel sentences describing images in natural language, but compressing an image into a single sentence can describe visual content in only coarse detail. While one new…
Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…
This paper introduces an abstract notion of fragments of monadic second-order logic. This concept is based on purely syntactic closure properties. We show that over finite words, every logical fragment defines a lattice of languages with…
We propose a computationally efficient and high-performance classification algorithm by incorporating class structural information in analysis dictionary learning. To achieve more consistent classification, we associate a class…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
In this paper we consider the class of lambda-nondeterministic linear automata as a model of the class of linear languages. As usual in other automata models, lambda-moves do not increase the acceptance power. The main contribution of this…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…
We study the question of whether, for a given class of finite graphs, one can define, for each graph of the class, a linear ordering in monadic second-order logic, possibly with the help of monadic parameters. We consider two variants of…
Descriptive Complexity has been very successful in characterizing complexity classes of decision problems in terms of the properties definable in some logics. However, descriptive complexity for counting complexity classes, such as FP and…
We present a general theory and corresponding declarative model for the embodied grounding and natural language based analytical summarisation of dynamic visuo-spatial imagery. The declarative model ---ecompassing spatio-linguistic…
By virtue of linguistic compositionality, few syntactic rules and a finite lexicon can generate an unbounded number of sentences. That is, language, though seemingly high-dimensional, can be explained using relatively few degrees of…
We give in this paper a logical characterization for unambiguous Context Free Languages, in the vein of descriptive complexity. A fragment of the logic characterizing context free languages given by Lautemann, Schwentick and Th\'erien [18]…
We discuss the definability of finite graphs in first-order logic with two relation symbols for adjacency and equality of vertices. The logical depth $D(G)$ of a graph $G$ is equal to the minimum quantifier depth of a sentence defining $G$…
Altenbernd, Thomas and W\"ohrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with usual acceptance conditions, such as the B\"uchi and Muller ones [1]. It was proved…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
Descriptive complexity theory aims at inferring a problem's computational complexity from the syntactic complexity of its description. A cornerstone of this theory is Fagin's Theorem, by which a graph property is expressible in existential…
Descriptive complexity theory is an important area in the study of computational complexity. In this direction, it is possible to describe combinatorial problems exclusively by logical methods, without resorting to the use of complicated…
Description logics are knowledge representation languages that have been designed to strike a balance between expressivity and computational tractability. Many different description logics have been developed, and numerous computational…
We develop a unified second-order parameterized complexity theory for spaces of integrable functions. This generalizes the well-established case of second-order parameterized complexity theory for spaces of continuous functions.…