Jean-Christophe Janodet

Polynomial algorithms for subisomorphism of nD open combinatorial maps

Combinatorial maps describe the subdivision of objects in cells, and incidence and adjacency relations between cells, and they are widely used to model 2D and 3D images. However, there is no algorithm for comparing combinatorial maps, which is an important issue for image processing and analysis. In this paper, we address two basic comparison problems, i.e., map isomorphism, which involves deciding if two maps are equivalent, and submap isomorphism, which involves deciding if a copy of a pattern map may be found in a target map. We formally define these two problems for nD open combinatorial maps, we give polynomial time algorithms for solving them, and we illustrate their interest and feasibility for searching patterns in 2D and 3D images, as any child would aim to do when he searches Wally in Martin Handfords books.

Zulu: an interactive learning competition

Active language learning is an interesting task for which theoretical results are known and several applications exist. In order to better understand what the better strategies may be, a new competition called Zulu (http://labh-curien.univ-st-etienne.fr/zulu/) is launched: participants are invited to learn deterministic finite automata from membership queries. The goal is to obtain the best classification rate from a fixed number of queries.

A Polynomial Algorithm for Submap Isomorphism

In this paper, we address the problem of searching for a pattern in a plane graph, i.e. , a planar drawing of a planar graph. To do that, we propose to model plane graphs with 2-dimensional combinatorial maps, which provide nice data structures for modelling the topology of a subdivision of a plane into nodes, edges and faces. We define submap isomorphism, we give a polynomial algorithm for this problem, and we show how this problem may be used to search for a pattern in a plane graph. First experimental results show the validity of this approach to efficiently search for patterns in images.

Inference of W -languages from prefixes

Buchi automata are used to recognize languages of infinite strings. Such languages have been introduced to describe the behavior of real-time systems or infinite games. The question of inferring them from infinite examples has already been studied, but it may seem more reasonable to believe that the data from which we want to learn is a set of finite strings, namely the prefixes of accepted or rejected infinite strings. We describe the problems of identification in the limit and polynomial identification in the limit from given data associated to different interpretations of these prefixes: a positive prefix is universal (respectively existential) when all the infinite strings of which it is a prefix are in the language (respectively when at least one is); the same applies to the negative prefixes. We prove that the classes of regular ω-languages (those recognized by Buchi automata) and of deterministic ω-languages (those recognized by deterministic Buchi automata) are not identifiable in the limit, whatever interpretation for the prefixes is taken. We give a polynomial algorithm that identifies the class of safe languages from positive existential prefixes and negative universal prefixes. We show that this class is maximal for polynomial identification in the limit from given data, in the sense that no superclass can even be identified in the limit.

Learning Balls of Strings with Correction Queries

During the 80s, Angluin introduced an active learning paradigm, using an Oracle, capable of answering both membership and equivalence queries. However, practical evidence tends to show that if the former are often available, this is usually not the case of the latter. We propose new queries, called correction queries, which we study in the framework of Grammatical Inference. When a string is submitted to the Oracle, either she validates it if it belongs to the target language, or she proposes a correction, i.e., a string of the language close to the query with respect to the edit distance. We also introduce a non-standard class of languages: The topological balls of strings. We show that this class is not learnable in Angluins Mat model, but is with a linear number of correction queries. We conduct several experiments with an Oracle simulating a human Expert, and show that our algorithm is resistant to approximate answers.

LARS: A learning algorithm for rewriting systems

Whereas there is a number of methods and algorithms to learn regular languages, moving up the Chomsky hierarchy is proving to be a challenging task. Indeed, several theoretical barriers make the class of context-free languages hard to learn. To tackle these barriers, we choose to change the way we represent these languages. Among the formalisms that allow the definition of classes of languages, the one of string-rewriting systems (SRS) has outstanding properties. We introduce a new type of SRS’s, called Delimited SRS (DSRS), that are expressive enough to define, in a uniform way, a noteworthy and non trivial class of languages that contains all the regular languages,

Learning Languages from Bounded Resources: The Case of the DFA and the Balls of Strings

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Extracting plane graphs from images

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