Related papers: A Diamond Structure in the Transducer Hierarchy
This article extends Scholze's six functor formalism for diamonds to a very general class of stacky morphisms between v-stacks, using $\infty$-categorical techniques developed by Liu-Zheng.
We consider the synthesis of deterministic tree transducers from automaton definable specifications, given as binary relations, over finite trees. We consider the case of specifications that are deterministic top-down tree automatic,…
Diamondynes, a new class of diamond-like carbon allotropes composed of carbon with sp$^2$/sp$^3$-hybridized carbon networks, exhibit unique structural motifs that have not been previously reported in carbon materials. These architectures…
Letter-to-letter transducers are a standard formalism for modeling reactive systems. Often, two transducers that model similar systems differ locally from one another, by behaving similarly, up to permutations of the input and output…
We are interested in regular expressions and transducers that represent word relations in an alphabet-invariant way---for example, the set of all word pairs u,v where v is a prefix of u independently of what the alphabet is. Current…
Functional transductions realized by two-way transducers (equivalently, by streaming transducers and by MSO transductions) are the natural and standard notion of "regular" mappings from words to words. It was shown recently (LICS'13) that…
We analyse the pseudofinite monadic second order theory of words over a fixed finite alphabet. In particular we present an axiomatisation of this theory, working in a one-sorted first order framework. The analysis hinges on the fact that…
We investigate the complexity of embeddings between bi-embeddable structures. In analogy with categoricity spectra, we define the bi-embeddable categoricity spectrum of a structure $\mathcal A$ as the family of Turing degrees that compute…
We prove that functionality of compositions of top-down tree transducers is decidable by reducing the problem to the functionality of one top-down tree transducer with look-ahead.
A modular or distributive lattice is `diamond-colored' if its order diagram edges are colored in such a way that, within any diamond of edges, parallel edges have the same color. Such lattices arise naturally in combinatorial representation…
Idempotents dominate the structure theory of rings. The Peirce decomposition induced by an idempotent provides a natural environment for defining and classifying new types of rings. This point of view offers a way to unify and to expand the…
Characterizations of the star, minus and diamond orders of operators are given in various contexts and the relationship between these orders is made more transparent. Moreover, we introduce a new partial order of operators which provides a…
Classical Ramsey theory has successfully extended to relational structures, yielding a wealth of results that have profoundly influenced other areas of mathematics. Interestingly, the same development has not occurred in the case of dual…
We introduce the notion of a Lie-like algebra$^{\diamond}$ (superalgebra$^{\diamond}$) for $\diamond\in\{^{1-st}, ^{2-nd}, ^{3-rd} \}$.
We prove that for a given partial functional attributed tree transducer with monadic output, it is decidable whether or not an equivalent top-down transducer (with or without look-ahead) exists. We present a procedure that constructs an…
Concatenation hierarchies are classifications of regular languages. All such hierarchies are built through the same construction process: start from an initial class of languages and build new levels using two generic operations.…
We consider the family of energy-constrained diamond norms on the set of Hermitian-preserving linear maps (superoperators) between Banach spaces of trace class operators. We prove that any norm from this family generates the strong…
A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.
The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been treated as a fixed feature transformation, on top of which a…
The diamond norm is a norm defined over the space of quantum transformations. This norm has a natural operational interpretation: it measures how well one can distinguish between two transformations by applying them to a state of…