Organiser: Professor Iain Stewart (Durham)
The study of the model-theoretic properties of finite structures emerged initially as a branch of classical model theory. However, in the late 1980s research concerning logics on finite structures diverged from work in classical model theory. The consideration of finite structures became intimately related with, for example, computational and descriptive complexity, model checking, database theory, verification, etc., so much so that the boundaries between these subjects are often hard to distinguish.
The methods employed in classical model theory (with its focus on infinite structures) and finite model theory also grew apart during this period. Probabilistic techniques, as well as machine simulations and reductions, play a prominent role in the study of finite structures, and stand in contrast to the geometric, algebraic, and analytic methods that pervade classical (infinite) model theory. Although both classical and finite model theory deal with restricted classes of structures, the conditions by which such classes are delimited also have been quite different. Finite model theory typically concentrates on classes for which particular computing formalisms, e.g., finite state automata or other restricted models of computation, can be used to normalize formulas, or for which decomposition methods from finite graph theory can be applied. In contrast, infinitary model theory usually places restrictions on combinatorial or geometric properties of the definable sets of a structure.
Yet, during the last five years or so there have been indications of a re-convergence of classical model theory and logical, finite aspects of computer science. This has resulted both from the interest of computer scientists in new computing and specification models that make use of infinitary structures, and from the development of powerful model-theoretic techniques that can provide insight into finite structures. Although many common themes have emerged and begun to gain attention, there is significant potential for wider interaction.
The goal of the workshop on finite and algorithmic model theory is to explore both emerging and potential connections between these two areas in greater depth. The workshop will consist of several 3-4-hour tutorials, as well as 2-hour and 1-hour research expositions. This format is designed to introduce researchers and graduate students in the two areas to those topics that are of fundamental interest and importance, to survey current research, and to discuss major unsolved problems and directions for future research.
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