Related papers: A Diamond Structure in the Transducer Hierarchy
Structured sentences are important expressions in human writings and dialogues. Previous works on neural text generation fused semantic and structural information by encoding the entire sentence into a mixed hidden representation. However,…
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
A hierarchy of type universes is a rudimentary ingredient in the type theories of many proof assistants to prevent the logical inconsistency resulting from combining dependent functions and the type-in-type rule. In this work, we argue that…
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…
MSO transductions are binary relations between structures which are defined using monadic second-order logic. MSO transductions form a category, since they are closed under composition. We show that many notions from language theory, such…
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,…
The transformer neural network has significantly out-shined all other neural network architectures as the engine behind large language models. We provide a theoretical analysis of the expressivity of the transformer architecture through the…
These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…
It is shown that shape preservation is decidable for top-down tree transducers, bottom-up tree transducers, and for compositions of total deterministic macro tree transducers. Moreover, if a transducer is shape preserving, then it can be…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
We demonstrate formation of hierarchical structures in two-dimensional systems with multiple length scales in the inter-particle interaction. These include states such as clusters of clusters, concentric rings, clusters inside a ring, and…
Streaming Data String Transducers (SDSTs) were introduced to model a class of imperative and a class of functional programs, manipulating lists of data items. These can be used to write commonly used routines such as insert, delete and…
Human conversations can evolve in many different ways, creating challenges for automatic understanding and summarization. Goal-oriented conversations often have meaningful sub-dialogue structure, but it can be highly domain-dependent. This…
Automatic structures are infinite structures that are finitely represented by synchronized finite-state automata. This paper concerns specifically automatic structures over finite words and trees (ranked/unranked). We investigate the…
The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…
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…
A string diagram is a two-dimensional graphical representation that can be described as a one-dimensional term generated from a set of primitives using sequential and parallel compositions. Since different syntactic terms may represent the…
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…
Deterministic two-way transducers with pebbles (aka pebble transducers) capture the class of polyregular functions, which extend the string-to-string regular functions allowing polynomial growth instead of linear growth. One of the most…
We introduce a new definition of topological degree for a meaningful class of operators which need not be continuous. Subsequently, we derive a number of fixed point theorems for such operators. As an application, we deduce a new existence…