Related papers: Slightly Non-Linear Higher-Order Tree Transducers
Terms in the lambda-calculus can be represented as planar trees decorated with symbols for abstraction and application, and having variables as leaves. In this paper, we concentrate on the branches of such trees, rather than on the trees…
A variant of Turing machines is introduced where the tape is replaced by a single tree which can be manipulated in a style akin to purely functional programming. This yields two benefits: first, the extra structure on the tape can be…
In 2005, Abramsky introduced various linear/affine combinatory algebras of partial involutions over a suitable formal language, to discuss reversible computation in a game-theoretic setting. These algebras arise as instances of the general…
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…
We introduce a framework for automatic differentiation with weighted finite-state transducers (WFSTs) allowing them to be used dynamically at training time. Through the separation of graphs from operations on graphs, this framework enables…
Algorithmic reasoning requires capabilities which are most naturally understood through recurrent models of computation, like the Turing machine. However, Transformer models, while lacking recurrence, are able to perform such reasoning…
Static resource analysis determines the resource consumption (e.g., time complexity) of a program without executing it. Among the numerous existing approaches for resource analysis, affine type systems have been one dominant approach.…
Incorporating hierarchical structures like constituency trees has been shown to be effective for various natural language processing (NLP) tasks. However, it is evident that state-of-the-art (SOTA) sequence-based models like the Transformer…
We consider weighted tree automata over strong bimonoids (for short: wta). A wta $\mathcal{A}$ has the finite-image property if its recognized weighted tree language $[\![\mathcal{A}]\!]$ has finite image; moreover, $\mathcal{A}$ has the…
Transformer-based models have demonstrated significant success in various source code representation tasks. Nonetheless, traditional positional embeddings employed by these models inadequately capture the hierarchical structure intrinsic to…
Affine automata provide a finite-state computational model that preserves the linear-algebraic structure of quantum computation while operating entirely over the reals. Recent work has shown that affine automata can far surpass classical…
We propose $\omega$MSO$\Join$BAPA, an expressive logic for describing countable structures, which subsumes and transcends both Counting Monadic Second-Order Logic (CMSO) and Boolean Algebra with Presburger Arithmetic (BAPA). We show that…
How can we effectively find the best structures in tree models? Tree models have been favored over complex black box models in domains where interpretability is crucial for making irreversible decisions. However, searching for a tree…
Non-deterministic Finite Automata (NFA) represent regular languages concisely, increasing their appeal for applications such as word recognition. This paper proposes a new approach to generate NFA from an interaction language such as UML…
Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs.…
The HOM problem, which asks whether the image of a regular tree language under a given tree homomorphism is again regular, is known to be decidable [Godoy & Gim\'enez: The HOM problem is decidable. JACM 60(4), 2013]. However, the problem…
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…
Abstract Meaning Representation parsing is a sentence-to-graph prediction task where target nodes are not explicitly aligned to sentence tokens. However, since graph nodes are semantically based on one or more sentence tokens, implicit…
In formal language theory, several different models characterize regular languages, such as finite automata, congruences of finite index, or monadic second-order logic (MSO). Moreover, several fragments of MSO have effective…
We discuss an autoencoder model in which the encoding and decoding functions are implemented by decision trees. We use the soft decision tree where internal nodes realize soft multivariate splits given by a gating function and the overall…