Related papers: Dynamic Membership for Regular Tree Languages
Much of the power of probabilistic methods in modelling language comes from their ability to compare several derivations for the same string in the language. An important starting point for the study of such cross-derivational properties is…
We study tree languages that can be defined in \Delta_2 . These are tree languages definable by a first-order formula whose quantifier prefix is forall exists, and simultaneously by a first-order formula whose quantifier prefix is . For the…
English verbs have multiple forms. For instance, talk may also appear as talks, talked or talking, depending on the context. The NLP task of lemmatization seeks to map these diverse forms back to a canonical one, known as the lemma. We…
We introduce a new dynamic vocabulary for language models. It can involve arbitrary text spans during generation. These text spans act as basic generation bricks, akin to tokens in the traditional static vocabularies. We show that, the…
Given a string $\sigma$ over alphabet $\Sigma$ and a grammar $G$ defined over the same alphabet, how many minimum number of repairs: insertions, deletions and substitutions are required to map $\sigma$ into a valid member of $G$ ? We…
The recent dramatic increase in online data availability has allowed researchers to explore human culture with unprecedented detail, such as the growth and diversification of language. In particular, it provides statistical tools to explore…
Given a probability distribution over a set of n words to be transmitted, the Huffman Coding problem is to find a minimal-cost prefix free code for transmitting those words. The basic Huffman coding problem can be solved in O(n log n) time…
We introduce session automata, an automata model to process data words, i.e., words over an infinite alphabet. Session automata support the notion of fresh data values, which are well suited for modeling protocols in which sessions using…
We prove that a uniformly random automaton with $n$ states on a 2-letter alphabet has a synchronizing word of length $O(n^{1/2}\log n)$ with high probability (w.h.p.). That is to say, w.h.p. there exists a word $\omega$ of such length, and…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
Large language models (LLMs), such as LLaMA, Alpaca, Vicuna, GPT-3.5 and GPT-4, have advanced the performance of AI systems on various natural language processing tasks to human-like levels. However, their generalisation and robustness when…
We describe a data structure that supports access, rank and select queries, as well as symbol insertions and deletions, on a string $S[1,n]$ over alphabet $[1..\sigma]$ in time $O(\lg n/\lg\lg n)$, which is optimal even on binary sequences…
An attractive mechanism to specify global constraints in rostering and other domains is via formal languages. For instance, the Regular and Grammar constraints specify constraints in terms of the languages accepted by an automaton and a…
When a problem instance is perturbed by a small modification, one would hope to find a good solution for the new instance by building on a known good solution for the previous one. Via a rigorous mathematical analysis, we show that…
We show how a few modifications to the red-black trees allow for $O(1)$ worst-case update time (once the position of the inserted or deleted element is known). The resulting structure is based on relaxing some of the properties of the…
We investigate the state complexity of the permutation operation, or the commutative closure, on Alphabetical Pattern Constraints (APC). This class corresponds to level $3/2$ of the Straubing-Th{\'e}rien Hierarchy and includes the finite,…
We describe a framework for maintaining forest algebra representations that are of logarithmic height for unranked trees. Such representations can be computed in O(n) time and updated in O(log(n)) time. The framework is of potential…
We introduce a flexible class of well-quasi-orderings (WQOs) on words that generalizes the ordering of (not necessarily contiguous) subwords. Each such WQO induces a class of piecewise testable languages (PTLs) as Boolean combinations of…
We consider the Modular Subset Sum problem: given a multiset $X$ of integers from $\mathbb{Z}_m$ and a target integer $t$, decide if there exists a subset of $X$ with a sum equal to $t \pmod{m}$. Recent independent works by Cardinal and…
Recent advancements in large language models (LLMs) have highlighted their potential across a variety of tasks, but their performance still heavily relies on the design of effective prompts. Existing methods for automatic prompt…