When Can Matrix Query Languages Discern Matrices?

We investigate when two graphs, represented by their adjacency matrices, can be distinguished by means of sentences formed in MATLANG, a matrix query language which supports a number of elementary linear algebra operators. When undirected graphs are concerned, and hence the adjacency matrices are real and symmetric, precise characterisations are in place when two graphs (i.e., their adjacency matrices) can be distinguished. Turning to directed graphs, one has to deal with asymmetric adjacency matrices. This complicates matters. Indeed, it requires to understand the more general problem of when two arbitrary matrices can be distinguished in MATLANG. We provide characterisations of the distinguishing power of MATLANG on real and complex matrices, and on adjacency matrices of directed graphs in particular. The proof techniques are a combination of insights from the symmetric matrix case and results from linear algebra and linear control theory

Towards an implementable dependency grammar

The aim of this paper is to define a dependency grammar framework which is both linguistically motivated and computationally parsable. See the demo at http://www.conexor.fi/analysers.html#testingComment: 10 page

An Automata Theoretic Approach to the Zero-One Law for Regular Languages: Algorithmic and Logical Aspects

A zero-one language L is a regular language whose asymptotic probability converges to either zero or one. In this case, we say that L obeys the zero-one law. We prove that a regular language obeys the zero-one law if and only if its syntactic monoid has a zero element, by means of Eilenberg's variety theoretic approach. Our proof gives an effective automata characterisation of the zero-one law for regular languages, and it leads to a linear time algorithm for testing whether a given regular language is zero-one. In addition, we discuss the logical aspects of the zero-one law for regular languages.Comment: In Proceedings GandALF 2015, arXiv:1509.0685

Adding modular predicates to first-order fragments

We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which successfully covers the quantifier alternation hierarchy of first order logic and some of its fragments. We obtain that deciding this problem for each level of the alternation hierarchy of both first order logic and its two-variable fragment when equipped with all regular numerical predicates is not harder than deciding it for the corresponding level equipped with only the linear order and the successor. For two-variable fragments we also treat the case of the signature containing only the order and modular predicates.Relying on some recent results, this proves the decidability for each level of the alternation hierarchy of the two-variable first order fragmentwhile in the case of the first order logic the question remains open for levels greater than two.The main ingredients of the proofs are syntactic transformations of first order formulas as well as the algebraic framework of finite categories

Grammatical properties of pronouns and their representation : an exposition

This volume brings together a cross-section of recent research on the grammar and representation of pronouns, centering around the typology of pronominal paradigms, the generation of syntactic and semantic representations for constructions containing pronouns, and the neurological underpinnings for linguistic distinctions that are relevant for the production and interpretation of these constructions. In this introductory chapter we first give an exposition of our topic (section 2). Taking the interpretation of pronouns as a starting point, we discuss the basic parameters of pronominal representations, and draw a general picture of how morphological, semantic, discourse-pragmatic and syntactic aspects come together. In section 3, we sketch the different domains of research that are concerned with these phenomena, and the particular questions they are interested in, and show how the papers in the present volume fit into the picture. Section 4 gives summaries of the individual papers, and a short synopsis of their main points of convergence

The complexity of the list homomorphism problem for graphs

We completely classify the computational complexity of the list H-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph H the problem is either NP-complete, NL-complete, L-complete or is first-order definable; descriptive complexity equivalents are given as well via Datalog and its fragments. Our algebraic characterisations match important conjectures in the study of constraint satisfaction problems.Comment: 12 pages, STACS 201

Stative sentences in Japanese and the role of the nominative marker "ga" : a thesis submitted in partial fulfillment of the requirements for the degree of Master of Arts in Japanese at Massey University, Palmerston North, New Zealand

The Japanese nominative particle ga is normally associated with the marking of subjects. However, there are several constructions involving stative predicates, where it has been claimed, notably by those working within a generative framework, that a ga-marked NP can be an object and that such sentences are transitive. Such an analysis has particularly arisen in the case of sentences with more than one ga-marked NP, exhibiting so-called double ga marking. The following study makes two claims. Firstly, that one of the functions of ga in such sentences is to provide a discourse frame akin to the topic marking function of the postpositional particle wa. Secondly it argues that stative sentences associated with double ga-marking are in fact intransitive and that the ga-marked NP's that have been claimed to be objects are in fact subjects

B\"uchi VASS recognise w-languages that are Sigma^1_1 - complete

This short note exhibits an example of a Sigma^1_1-complete language that can be recognised by a one blind counter B\"uchi automaton (or equivalently a B\"uchi VASS with only one place)