Related papers: Generating function for Naturalized Series: The ca…
We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates. Linear ranking templates are parametrized, well-founded relations such that an assignment to the…
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
An important component of achieving language understanding is mastering the composition of sentence meaning, but an immediate challenge to solving this problem is the opacity of sentence vector representations produced by current neural…
Generative models reliant on sequential autoregression have been at the forefront of language generation for an extensive period, particularly following the introduction of widely acclaimed transformers. Despite its excellent performance,…
This paper describes tactical generation in Turkish, a free constituent order language, in which the order of the constituents may change according to the information structure of the sentences to be generated. In the absence of any…
Bracketed words are basic structures both in mathematics (such as Rota-Baxter algebras) and mathematical physics (such as rooted trees) where the locations of the substructures are important. In this paper we give the classification of the…
Neural language models are a critical component of state-of-the-art systems for machine translation, summarization, audio transcription, and other tasks. These language models are almost universally autoregressive in nature, generating…
We investigate combinatorial properties of a kind of insets we defined in an earlier paper, interpreting them now in terms of restricted ternary words. This allows us to give new combinatorial interpretations of a number of known integer…
This paper introduces a new approach to generating strongly constrained texts. We consider standardized sentence generation for the typical application of vision screening. To solve this problem, we formalize it as a discrete combinatorial…
Existing works have studied the impacts of the order of words within natural text. They usually analyze it by destroying the original order of words to create a scrambled sequence, and then comparing the models' performance between the…
Randomly generating structured objects is important in testing and optimizing functional programs, whereas generating random $'l$-terms is more specifically needed for testing and optimizing compilers. For that a tool called QuickCheck has…
In this paper, we study averaging operators from an algebraic and combinatorial point of view. We first construct free averaging algebras in terms of a class of bracketed words called averaging words. We next apply this construction to…
We find a generating function for interval-closed sets of the product of two chains poset by constructing a bijection to certain bicolored Motzkin paths. We also find a functional equation for the generating function of interval-closed sets…
In this note we investigate mixed partitions with extra condition on the sizes of the blocks. We give a general formula and the generating function. We consider in more details a special case, determining the generating functions, some…
We construct generating trees with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation,…
The dominant approach to sequence generation is to produce a sequence in some predefined order, e.g. left to right. In contrast, we propose a more general model that can generate the output sequence by inserting tokens in any arbitrary…
Generating natural language under complex constraints is a principled formulation towards controllable text generation. We present a framework to allow specification of combinatorial constraints for sentence generation. We propose TSMH, an…
Text generation rarely considers the control of lexical complexity, which limits its more comprehensive practical application. We introduce a novel task of lexical complexity controlled sentence generation, which aims at keywords to…
A generalized lexicographical order on infinite words is defined by choosing for each position a total order on the alphabet. This allows to define generalized Lyndon words. Every word in the free monoid can be factorized in a unique way as…
Recent neural sequence-to-sequence models with a copy mechanism have achieved remarkable progress in various text generation tasks. These models addressed out-of-vocabulary problems and facilitated the generation of rare words. However, the…