Derivatives of approximate regular expressions

Automata, Logic and Semantics International audience Our aim is to construct a finite automaton recognizing the set of words that are at a bounded distance from some word of a given regular language. We define new regular operators, the similarity operators, based on a generalization of the notion of distance and we introduce the family of regular expressions extended to similarity operators, that we call AREs (Approximate Regular Expressions). We set formulae to compute the Brzozowski derivatives and the Antimirov derivatives of an ARE, which allows us to give a solution to the ARE membership problem and to provide the construction of two recognizers for the language denoted by an ARE. As far as we know, the family of approximative regular expressions is introduced for the first time in this paper. Classical approximate regular expression matching algorithms are approximate matching algorithms on regular expressions. Our approach is rather to process an exact matching on approximate regular expressions.

Querying Multimedia Data by Similarity in Relational DBMS

Multimedia objects – such as images, audio, and video – do not present the total ordering relationship, so the relational operators (‘<’, ‘=’, ‘=’, ‘>’) are not suitable to compare them. Therefore, similarity queries are the most useful, and often the only types of queries adequate to search multimedia objects stored in a database. Unfortunately, the ubiquitous query language SQL – the most widely employed language in Database Management Systems (DBMS) – does not provide effective support for similarity queries. This chapter presents an already validated strategy that adds similarity queries to SQL, supporting a powerful set of similarity operators. The chapter also describes techniques to store and retrieve multimedia objects in an efficient way and shows existing DBMS alternatives to execute similarity queries over multimedia data.

COMB GRAPHS AND SPECTRAL DECIMATION

We investigate the spectral properties of matrices associated with comb graphs. We show that the adjacency matrices and adjacency matrix Laplacians of the sequences of graphs show a spectral similarity relationship in the sense of work by L. Malozemov and A. Teplyaev (Self-similarity, operators and dynamics,Math. Phys. Anal. Geometry6(2003), 201–218), and hence these sequences of graphs show a spectral decimation property similar to that of the Laplacians of the Sierpiński gasket graph and other fractal graphs.