Weak MSO+U with Path Quantifiers over Infinite Trees

This paper shows that over infinite trees, satisfiability is decidable for weak monadic second-order logic extended by the unbounding quantifier U and quantification over infinite paths. The proof is by reduction to emptiness for a certain automaton model, while emptiness for the automaton model is decided using profinite trees.Comment: version of an ICALP 2014 paper with appendice

Recognisable languages over monads

The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of composing structures into bigger structures. It so happens that category theory has an abstract concept for this, namely a monad. The goal of this paper is to propose monads as a unifying framework for discussing existing algebras and designing new algebras

Affine functions on CAT (κ)-spaces

Affine functions on CAT(kappa) space

Topological equivalence of discontinuous norms

0, h maps the Hilbert cube [-r,r](N) precisely onto the "elliptic cube" {x is an element of R-N : Sigma(i=1)(infinity)\x(i)\(p) less than or equal to r(p)}. This means that the supremum norm and, for instance, the Hilbert norm (p = 2) are topologically indistinguishable as functions on R-N. The result is obtained by means of the Bing Shrinking Criterion