Current Trends and New Perspectives for First-Order Model Checking (Invited Talk)
نویسنده
چکیده
The model-checking problem for a logic L is the problem of decidig for a given formula φ ∈ L and structure A whether the formula is true in the structure, i.e. whether A |= φ. Model-checking for logics such as First-Order Logic (FO) or Monadic Second-Order Logic (MSO) has been studied intensively in the literature, especially in the context of algorithmic meta-theorems within the framework of parameterized complexity. However, in the past the focus of this line of research was model-checking on classes of sparse graphs, e.g. planar graphs, graph classes excluding a minor or classes which are nowhere dense. By now, the complexity of first-order model-checking on sparse classes of graphs is completely understood. Hence, current research now focusses mainly on classes of dense graphs. In this talk we will briefly review the known results on sparse classes of graphs and explain the complete classification of classes of sparse graphs on which first-order model-checking is tractable. In the second part we will then focus on recent and ongoing research analysing the complexity of first-order model-checking on classes of dense graphs. 1998 ACM Subject Classification F.4.1 Computational Logic
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