Monadic second-order logic on tree-like structures

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 pr...

Sequentiality, Second Order Monadic Logic and Tree Automata

Given a term rewriting system R and a normalizable term t, a redex is needed if in any reduction sequence of t to a normal form, this redex will be contracted. Roughly, R is sequential if there is an optimal reduction strategy in which only needed redexes are contracted. More generally, G. Huet and J.-J. L evy deene in 9] the sequentiality of a predicate P on partially evaluated terms. We show ...

Tree-structured Graphs and Monadic Second-order Logic

Sequentiality, Monadic Second-Order Logic and Tree Automata

Given a term rewriting system R and a normalizable term t, a redex is needed if in any reduction sequence of t to a normal form, this redex will be contracted. Roughly, R is sequential if there is an optimal reduction strategy in which only needed redexes are contracted. More generally, G. Huet and J.-J. L evy de ne in [9] the sequentiality of a predicate P on partially evaluated terms. We show...

Asymptotic Monadic Second-Order Logic

In this paper we introduce so-called asymptotic logics, logics that are meant to reason about weights of elements in a model in a way inspired by topology. Our main subject of study is Asymptotic Monadic Second-Order Logic over infinite words. This is a logic talking about ωwords labelled by integers. It contains full monadic second-order logic and can express asymptotic properties of integers ...