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We present a language model consisting of a collection of costed bidirectional finite state automata associated with the head words of phrases. The model is suitable for incremental application of lexical associations in a dynamic…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
This is a book on weighted tree automata. We present the basic definitions and some of the important results in a coherent form with full proofs. The concept of weighted tree automata is part of Automata Theory and it touches the area of…
We present an extension of the Angluin-style learning algorithm for tree automata that incorporates deductive inference. The learning algorithm is provided with a term rewriting system that specifies properties of the target tree language…
We consider the state complexity of basic operations on tree languages recognized by deterministic unranked tree automata. For the operations of union and intersection the upper and lower bounds of both weakly and strongly deterministic…
We propose a new arithmetic for non-empty rooted unordered trees simply called trees. After discussing tree representation and enumeration, we define the operations of tree addition, multiplication and stretch, prove their properties, and…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
"Quantitative languages are extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the…
Context free languages allow one to express data with hierarchical structure, at the cost of losing some of the useful properties of languages recognized by finite automata on words. However, it is possible to restore some of these…
The conversion of a given regular tree expression into a tree automaton has been widely studied. However, classical interpretations are based upon a Top-Down interpretation of tree automata. In this paper, we propose new constructions based…
Solving arithmetic word problems is a cornerstone task in assessing language understanding and reasoning capabilities in NLP systems. Recent works use automatic extraction and ranking of candidate solution equations providing the answer to…
We address the non-redundant random generation of $k$ words of length $n$ in a context-free language. Additionally, we want to avoid a predefined set of words. We study a rejection-based approach, whose worst-case time complexity is shown…
This is a tutorial on tabular parsing, on the basis of tabulation of nondeterministic push-down automata. Discussed are Earley's algorithm, the Cocke-Kasami-Younger algorithm, tabular LR parsing, the construction of parse trees, and further…
In this paper, we develop a framework to obtain graph abstractions for decision-making by an agent where the abstractions emerge as a function of the agent's limited computational resources. We discuss the connection of the proposed…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
Data augmentation methods for neural machine translation are particularly useful when limited amount of training data is available, which is often the case when dealing with low-resource languages. We introduce a novel augmentation method,…
We introduce the notion of quota trees in directed graphs. Given a nonnegative integer ``quota'' for each vertex of a directed multigraph $G$, a quota tree is an immersed rooted tree which hits each vertex of $G$ the prescribed number of…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
Treebanks traditionally treat punctuation marks as ordinary words, but linguists have suggested that a tree's "true" punctuation marks are not observed (Nunberg, 1990). These latent "underlying" marks serve to delimit or separate…
The game tree languages can be viewed as an automata-theoretic counterpart of parity games on graphs. They witness the strictness of the index hierarchy of alternating tree automata, as well as the fixed-point hierarchy over binary trees.…