Related papers: On Braid Words and Irreflexivity

In this note we give a simple unifying proof of the undecidability of several diagrammatic properties of term rewriting systems that include: local confluence, strong confluence, diamond property, subcommutative property, and the existence…

We study transfinite extensions of Japaridze's provability logic GLP and the well-founded relations that naturally occur within them. Every ordinal induces a partial order over the class of "words," which are iterated consistency statements…

This paper tackles the problem of the existence of solutions for recursive systems of Horn clauses with second-order variables interpreted as integer relations, and harnessed by quantifier-free difference bounds arithmetic. We start by…

The topological underpinnings are presented for a new algorithm which answers the question: `Is a given knot the unknot?' The algorithm uses the braid foliation technology of Bennequin and of Birman and Menasco. The approach is to consider…

We introduce the notion of additive filter and present a new proof of the existence of idempotent ultrafilters on N without any use of Zorn's Lemma, and where one only assumes the Ultrafilter Theorem for the continuum.

This is a review article on the Bennequin-Birman-Menasco machinery for studying embedded incompressible surfaces in 3-space via their `braid foliations'. Two cases are investigated: case (1) The surface has non-empty boundary; the boundary…

Succinctness is a natural measure for comparing the strength of different logics. Intuitively, a logic L_1 is more succinct than another logic L_2 if all properties that can be expressed in L_2 can be expressed in L_1 by formulas of…

We report complexity results about redundancy of formulae in 2CNF form. We first consider the problem of checking redundancy and show some algorithms that are slightly better than the trivial one. We then analyze problems related to finding…

We propose an exact iterative algorithm for minimization of a class of continuous cell-wise linear convex functions on a hyperplane arrangement. Our particular setup is motivated by evaluation of so-called rank estimators used in robust…

This paper explores the idea of using defunctionalization as a proof technique for higher-order programs. Defunctionalization builds on substituting functional values by a first-order representation. Thus, its interest is that one can use…

It is known that the behavior of the Mitchell order substantially changes at the level of rank-to-rank extenders, as it ceases to be well-founded. While the possible partial order structure of the Mitchell order below rank-to-rank extenders…

The elementary 2-terminal network consisting of a resistively ($R-$) shunted inductance ($L$) in series with a capacitatively ($C-$) shunted resistance ($R$) with $R = \sqrt{L/C}$, is known for its non-dispersive dissipative response,…

We construct a countable simple theory which, in Keisler's order, is strictly above the random graph (but "barely so") and also in some sense orthogonal to the building blocks of the recently discovered infinite descending chain. As a…

In [2], while studying a relevant class of polyominoes that tile the plane by translation, i.e., double square polyominoes, the authors found that their boundary words, encoded by the Freeman chain coding on a four letters alphabet, have…

The properties of the processes of deformation of a packing of rigid grains are analysed when the exact distribution of the normal forces at contacts is known. Importance of grain rotation and of counter-rotation of adjacent grains is…

All known structural extensions of the substructural logic $\mathsf{FL_e}$, Full Lambek calculus with exchange/commutativity, (corresponding to subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot, 1\}$-equations)…

This note demonstrates how both the concept of distance and the concept of holonomy can be constructed from a suitable network with directed edges (and no lengths). The number of different edge types depends on the signature of the metric…

Suppose that f is a projective birational morphism with at most one-dimensional fibres between d-dimensional varieties X and Y, satisfying ${\bf R}f_* \mathcal{O}_X = \mathcal{O}_Y$. Consider the locus L in Y over which f is not an…

Dependency distance minimization (DDm) is a well-established principle of word order. It has been predicted theoretically that DDm implies compression, namely the minimization of word lengths. This is a second order prediction because it…

Let $f$ be a homogeneous polynomial over a field. For many fields, including number fields and function fields, we prove that the strength of $f$ is bounded above by a constant multiple of the Birch rank of $f.$ The constant depends only on…