Related papers: Transduction of Automatic Sequences and Applicatio…
This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…
In this paper, closed forms of the summation formulas for generalized Tribonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results. As special cases, we give summation formulas of…
We present a base class of automata that induce a numeration system and we give an algorithm to give the n-th word in the language of the automaton when the expansion of n in the induced numeration system is feeded to the automaton.…
The notion of transducer integer sequences is considered through a series of examples. By definition, transducer integer sequences are integer sequences produced, under a suitable interpretation, by finite automata encoding tree morphisms…
We give new algorithms based on the sum-of-squares method for tensor decomposition. Our results improve the best known running times from quasi-polynomial to polynomial for several problems, including decomposing random overcomplete…
We are interested in the problem of transition reduction of nondeterministic automata. We present some results on the reduction of the automata recognizing the language $L(E_n)$ denoted by the regular expression $E_n=(1+\varepsilon)...…
We introduce semantic form mid-tuning, an approach for transferring semantic knowledge from semantic meaning representations into transformer-based language encoders. In mid-tuning, we learn to align the text of general sentences -- not…
Sequence-to-sequence transduction is the core problem in language processing applications as diverse as semantic parsing, machine translation, and instruction following. The neural network models that provide the dominant solution to these…
Fibonacci sequence, generated by summing the preceding two terms, is a classical sequence renowned for its elegant properties. In this paper, leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of…
Automating the assessment of learner summaries provides a useful tool for assessing learner reading comprehension. We present a summarization task for evaluating non-native reading comprehension and propose three novel approaches to…
Summarization of long sequences into a concise statement is a core problem in natural language processing, requiring non-trivial understanding of the input. Based on the promising results of graph neural networks on highly structured data,…
We report on the automation of a technique to prove the correctness of program transformations in higher-order program calculi which may permit recursive let-bindings as they occur in functional programming languages. A program…
Sequence-to-sequence (SEQ2SEQ) models have been successfully applied to automatic math word problem solving. Despite its simplicity, a drawback still remains: a math word problem can be correctly solved by more than one equations. This…
As a generalization of the sum of digits function and other digital sequences, sequences defined as the sum of the output of a transducer are asymptotically analyzed. The input of the transducer is a random integer in $[0, N)$. Analogues in…
We give an extension of Sister Celine's method of proving hypergeometric sum identities that allows it to handle a larger variety of input summands. We then apply this to several problems. Some give new results, and some reprove already…
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…
Schur's transforms of a polynomial are used to count its roots in the unit disk. These are generalized them by introducing the sequence of symmetric sub-resultants of two polynomials. Although they do have a determinantal definition, we…
A uniformization of a binary relation is a function that is contained in the relation and has the same domain as the relation. The synthesis problem asks for effective uniformization for classes of relations and functions that can be…
Subset Sum is a classical optimization problem taught to undergraduates as an example of an NP-hard problem, which is amenable to dynamic programming, yielding polynomial running time if the input numbers are relatively small. Formally,…
The class of input-output systems representable as Chen-Fliess series arises often in control theory. One well known drawback of this representation, however, is that the iterated integrals which appear in these series are algebraically…