Generalising Automaticity to Modal Properties of Finite Structures

Authors:
Anuj Dawar;Stephan Kreutzer
Affiliations:
-;-
Venue:
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Year:
2002

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Generalising automaticity to modal properties of finite structures

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Abstract

We introduce a complexity measure of modal properties of finite structures which generalises the automaticity of languages. It is based on graph-automata like devices called labelling systems. We define a measure of the size of a structure that we call rank, and show that any modal property of structures can be approximated up to any fixed rank n by a labelling system. The function that takes n to the size of the smallest labelling system doing this is called the labelling index of the property. We demonstrate that this is a useful and fine-grained measure of complexity and show that it is especially well suited to characterise the expressive power of modal fixed-point logics. From this we derive several separation results of modal and non-modal fixed-point logics, some of which are already known whereas others are new.