Monadic second-order logic on tree-like structures

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Monadic second-order logic on tree-like structures
An operation M which constructs from a given structure M a tree-like structure whose domain consists of the finite sequences of elements of M is considered. A notion of automata running on such tree-like structures is defined. It is shown that automata of this kind characterise expressive power of monadic second-order logic (MSOL) over tree-like structures. Using this characterisation it is proved that MSOL theory of a tree-like structure is effectively reducible to that of the original structure. As another application of the characterisation it is shown that MSOL on trees of arbitrary degree is equivalent to first-order logic extended with unary least fixpoint operator.
Igor Walukiewicz
Added 23 Dec 2010
Updated 23 Dec 2010
Type Journal
Year 2002
Where TCS
Authors Igor Walukiewicz
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