Related papers: The tree machine
This paper presents an algebraic theory of instruction sequences with instructions for Turing tapes as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction between such…
The present paper introduces and studies an alternative concept of two-way finite automata called input-erasing two-way finite automata. Like the original model, these new automata can also move the reading head freely left or right on the…
We introduce a new type of generalized Turing machines (GTMs), which are intended as a tool for the mathematician who studies computability in Analysis. In a single tape cell a GTM can store a symbol, a real number, a continuous real…
The trie data structure is a good choice for finite maps whose keys are data structures (trees) rather than atomic values. But what if we want the keys to be patterns, each of which matches many lookup keys? Efficient matching of this kind…
The task of translating between programming languages differs from the challenge of translating natural languages in that programming languages are designed with a far more rigid set of structural and grammatical rules. Previous work has…
Multiway Turing machines (also known as nondeterministic Turing machines or NDTMs) with explicit, simple rules are studied. Even very simple rules are found to generate complex behavior, characterized by complex multiway graphs, that can be…
Tree-structured multi-task architectures have been employed to jointly tackle multiple vision tasks in the context of multi-task learning (MTL). The major challenge is to determine where to branch out for each task given a backbone model to…
In this paper, we introduce a set of tools for providing user-friendly explanations in an explanation-based constraint programming system. The idea is to represent the constraints of a problem as an hierarchy (a tree). Users are then…
The derivation trees of a tree adjoining grammar provide a first insight into the sentence semantics, and are thus prime targets for generation systems. We define a formalism, feature-based regular tree grammars, and a translation from…
Can we do arithmetic in a completely different way, with a radically different data structure? Could this approach provide practical benefits, like operations on giant numbers while having an average performance similar to traditional…
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…
Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…
We propose a transformer architecture and training strategy for tree generation. The architecture processes data at multiple resolutions and has an hourglass shape, with middle layers processing fewer tokens than outer layers. Similar to…
Graphs are a generalized concept that encompasses more complex data structures than trees, such as difference lists, doubly-linked lists, skip lists, and leaf-linked trees. Normally, these structures are handled with destructive assignments…
Tree-structured neural networks encode a particular tree geometry for a sentence in the network design. However, these models have at best only slightly outperformed simpler sequence-based models. We hypothesize that neural sequence models…
Information, stored or transmitted in digital form, is often structured. Individual data records are usually represented as hierarchies of their elements. Together, records form larger structures. Information processing applications have to…
One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
This paper discusses "computational" systems capable of "computing" functions not computable by predefined Turing machines if the systems are not isolated from their environment. Roughly speaking, these systems can change their finite…
Designers of statistical machine translation (SMT) systems have begun to employ tree-structured translation models. Systems involving tree-structured translation models tend to be complex. This article aims to reduce the conceptual…