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Context-free S grammars are introduced, for arbitrary (storage) type S, as a uniform framework for recursion-based grammars, automata, and transducers, viewed as programs. To each occurrence of a nonterminal of a context-free S grammar an…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
Syntactic Language Models (SLMs) can be trained efficiently to reach relatively high performance; however, they have trouble with inference efficiency due to the explicit generation of syntactic structures. In this paper, we propose a new…
Probabilistic context-free grammars (PCFGs), which are commonly used to generate trees randomly, have been well analyzed theoretically, leading to applications in various domains. Despite their utility, the distributions that the grammar…
A tree automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. Words can be regarded as specific…
This paper investigates a new property of formal languages called REG-measurability where REG is the class of regular languages. Intuitively, a language \(L\) is REG-measurable if there exists an infinite sequence of regular languages that…
Controlled generation refers to the problem of creating text that contains stylistic or semantic attributes of interest. Many approaches reduce this problem to training a predictor of the desired attribute. For example, researchers hoping…
Transformer-based language models have shown to be very powerful for natural language generation (NLG). However, text generation conditioned on some user inputs, such as topics or attributes, is non-trivial. Past approach relies on either…
Today's probabilistic language generators fall short when it comes to producing coherent and fluent text despite the fact that the underlying models perform well under standard metrics, e.g., perplexity. This discrepancy has puzzled the…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
The dominant language modeling paradigm handles text as a sequence of discrete tokens. While that approach can capture the latent structure of the text, it is inherently constrained to sequential dynamics for text generation. We propose a…
Natural Language Generation (NLG) for task-oriented dialogue systems focuses on communicating specific content accurately, fluently, and coherently. While these attributes are crucial for a successful dialogue, it is also desirable to…
We study varieties that contain unranked tree languages over all alphabets. Trees are labeled with symbols from two alphabets, an unranked operator alphabet and an alphabet used for leaves only. Syntactic algebras of unranked tree languages…
We study the notion of sparseness for regular languages over finite trees and infinite words. A language of trees is called sparse if the relative number of $n$-node trees in the language tends to zero, and a language of infinite words is…
We study the portraits of isometries of rooted trees - the labelling of the tree, at each vertex, by the permutation of its descendants - in terms of languages. We characterize regularly branched self-similar groups in terms of…
Controlled text generation (CTG) seeks to guide large language model (LLM) output to produce text that conforms to desired criteria. The current study presents a novel CTG algorithm that enforces adherence toward specific rhetorical…
Generic generation and manipulation of text is challenging and has limited success compared to recent deep generative modeling in visual domain. This paper aims at generating plausible natural language sentences, whose attributes are…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
State grammars are context-free grammars where the productions have states associated with them, and a production can only be applied to a nonterminal if the current state matches the state in the production. Once states are added to…
Current syntactic theory limits the range of grammatical variation so severely that the logical problem of grammar learning is trivial. Yet, children exhibit characteristic stages in syntactic development at least through their sixth year.…