Related papers: Deque languages, automata and planar graphs
Legal texts often contain computational legal clauses--provisions whose understanding requires complex logic. While frontier Large Reasoning Models (LRMs) can describe such clauses, building production-ready systems is limited by reasoning…
We consider a computational model which is known as set automata. The set automata are one-way finite automata with an additional storage---the set. There are two kinds of set automata---the deterministic and the nondeterministic ones. We…
The downward closure of a language $L$ of words is the set of all (not necessarily contiguous) subwords of members of $L$. It is well known that the downward closure of any language is regular. Although the downward closure seems to be a…
The $d$-Fibonacci digraphs $F(d,k)$, introduced here, have the number of vertices following generalized Fibonacci-like sequences. They can be defined both as digraphs on alphabets and as iterated line digraphs. Here we study some of their…
Computer-Aided Design (CAD) applications are used in manufacturing to model everything from coffee mugs to sports cars. These programs are complex and require years of training and experience to master. A component of all CAD models…
For a language $L$, we consider its cyclic closure, and more generally the language $C^k(L)$, which consists of all words obtained by partitioning words from $L$ into $k$ factors and permuting them. We prove that the classes of ET0L and…
When trained on tasks requiring an understanding of hierarchical structure, transformers have been found to represent this hierarchy in distinct ways: in the geometry of the residual stream, and in stack-like attention patterns maintaining…
Scheduling languages express to a compiler a sequence of optimizations to apply. Compilers that support a scheduling language interface allow exploration of compiler optimizations, i.e., exploratory compilers. While scheduling languages…
Recognition and classification of Figurative Language (FL) is an open problem of Sentiment Analysis in the broader field of Natural Language Processing (NLP) due to the contradictory meaning contained in phrases with metaphorical content.…
Ordering the collection of states of a given automaton starting from an order of the underlying alphabet is a natural move towards a computational treatment of the language accepted by the automaton. Along this path, Wheeler \emph{graphs}…
In computer science, divide and conquer (D&C) is an algorithm design paradigm based on multi-branched recursion. A D&C algorithm works by recursively and monotonically breaking down a problem into sub problems of the same (or a related)…
In general, the representation of combinatorial objects is decisive for the feasibility of several enumerative tasks. In this work, we show how a (unique) string representation for (complete) initially-connected deterministic automata…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…
We introduce Chunk-Distilled Language Modeling (CD-LM), an approach to text generation that addresses two challenges in current large language models (LLMs): the inefficiency of token-level generation, and the difficulty of adapting to new…
Large language models are increasingly used within larger systems ("LLM agents"). These make a sequence of LLM calls, each call providing the LLM with a combination of instructions, observations, and interaction history. The design of the…
Syntactic parsing is a key task in natural language processing. This task has been dominated by symbolic, grammar-based parsers. Neural networks, with their distributed representations, are challenging these methods. In this article we show…
Indexing strings via prefix (or suffix) sorting is, arguably, one of the most successful algorithmic techniques developed in the last decades. Can indexing be extended to languages? The main contribution of this paper is to initiate the…
It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type…
The Categorical Compositional Distributional (DisCoCat) framework models meaning in natural language using the mathematical framework of quantum theory, expressed as formal diagrams. DisCoCat diagrams can be associated with tensor networks…
The Distributional Compositional Categorical (DisCoCat) model is a mathematical framework that provides compositional semantics for meanings of natural language sentences. It consists of a computational procedure for constructing meanings…