Automata for Branching and Layered Temporal Structures: an Investigation into Regularities of Infinite Transition Systems

Gabriele Puppis (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

Since 2002, FoLLI, the Association for Logic, Language, and Information (www.folli.org), has awarded an annual prize for an outstanding dissertation in the fields of logic, language, and information. The prize is named after the well-known Dutch logician Evert Willem Beth, whose interdisciplinary interests are in many ways exemplary for the aims of FoLLI. It is sponsored by the E.W. Beth Foundation. Dissertations submitted for the prize are judged on technical depth and strength, originality, and impact made in at least two of the three fields of logic, language, and computation. Every year the competition is strong and the interdisciplinary character of the award stimulates lively discussions and debates. Recipients of the award are given the opportunity to prepare a book version of their thesis for publication in the FoLLI Publications on Logic, Language and Information. This volume is based on the PhD thesis of Gabriele Puppis, who was the winner of the E.W. Beth dissertation award for 2007. Puppis's thesis focuses on logic and computation and, more specifically, on automata-based decidability techniques for time granularity and on a new method for deciding monadic second-order theories of trees. In the first part of the thesis Puppis defines and systematically exploits various classes of sequential automata in order to solve a number of relevant problems in time granularity (e.g., equivalence, conversion, minimization, optimization, etc.). For each application, he investigates expressiveness and complexity and provides algorithms working on automatabased representations of time granularity. The core of the remaining part of Puppis's thesis is a generalization of the Elgot-Rabin automata-based decision method. He defines a powerful reduction over colored trees and obtains the generalization by overcoming a number of technical difficulties, and thus not only solves the original decision problems, but also gives a precise and inspiring comparison of the newly introduced technique with more classical ones, such as, for example, Shelah's composition method. In both parts of the thesis Dr. Puppis shows mastering and deep understanding of the topic, an elegant and concise presentation of the results, and an insightful overall view on the subject. The results presented by Puppis represent a significant step towards a better understanding of the changes in granularity levels that humans make so easily in cognition of time, space, and other phenomena, whereas their logical and computational structure poses difficult conceptual and computational challenges.

Domaines: Théorie et langage formel [cs.FL]; Logique en informatique [cs.LO]

Gabriele Puppis. Automata for Branching and Layered Temporal Structures: an Investigation into Regularities of Infinite Transition Systems. Springer, pp.1-206, 2010, LNAI, 978-3-642-11880-7. ⟨10.1007/978-3-642-11881-4⟩. ⟨hal-00717778⟩