Related papers: Edit Distance for Pushdown Automata
We present an underapproximation for context-free languages by filtering out runs of the underlying pushdown automaton depending on how the stack height evolves over time. In particular, we assign to each run a number quantifying the…
Large Language Models (LLMs) have shown extraordinary capabilities in understanding and generating text that closely mirrors human communication. However, a primary limitation lies in the significant computational demands during training,…
We investigate the class of visibly pushdown languages in the sliding window model. A sliding window algorithm for a language $L$ receives a stream of symbols and has to decide at each time step whether the suffix of length $n$ belongs to…
An automaton is synchronizing if there is a word that maps all states onto the same state. \v{C}ern\'{y}'s conjecture on the length of the shortest such word is probably the most famous open problem in automata theory. We consider the…
Consider a binary word being transmitted through a communication channel that introduces deletable errors where each bit of the word is either retained, flipped, erased or deleted. The simplest code for correcting \emph{all} possible…
Suppose that we have two parties that possess each a binary string. Suppose that the length of the first string (document) is $n$ and that the two strings (documents) have edit distance (minimal number of deletes, inserts and substitutions…
Measuring the semantic similarity between two sentences is still an important task. The word mover's distance (WMD) computes the similarity via the optimal alignment between the sets of word embeddings. However, WMD does not utilize word…
In this paper we define a novel edit distance for merge trees, which we argue to be suitable for a good range of applications. Relying also on some technical results contained in other works, we investigate its stability properties, which…
We study Geometric Graph Edit Distance (GGED), a graph-editing model to compute the minimum edit distance of intersection graphs that uses moving objects as an edit operation. We first show an $O(n\log n)$-time algorithm that minimises the…
In this note we provide a (decidable) graph-structural characterisation of the infiniteness of $L(w_1, ..., w_k)$, where $L(w_1, ..., w_k) = \{w \in A^* | |w|_{w_1} = \cdots = |w|_{w_k}\}$ is the set of all words that contain the same…
Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages $L$ that assign to each word $w$ a real number $L(w)$. In the case of infinite words, the value of a run is…
Consider two remote nodes having binary sequences $X$ and $Y$, respectively. $Y$ is an edited version of ${X}$, where the editing involves random deletions, insertions, and substitutions, possibly in bursts. The goal is for the node with…
Pushdown automata may contain transitions that are never used in any accepting run of the automaton. We present an algorithm for detecting such useless transitions. A finite automaton that captures the possible stack content during runs of…
In this paper we consider an edit distance with swap and mismatch operations, called tilde-distance, and introduce the corresponding definition of tilde-isometric word. Isometric words are classically defined with respect to Hamming…
We study a connection between synchronizing automata and its set $M$ of minimal reset words, i.e., such that no proper factor is a reset word. We first show that any synchronizing automaton having the set of minimal reset words whose set of…
The linear-time simulation of 2-way deterministic pushdown automata (2DPDA) by the Cook and Jones constructions is revisited. Following the semantics-based approach by Jones, an interpreter is given which, when extended with random-access…
We study the problem of edit similarity joins, where given a set of strings and a threshold value $K$, we want to output all pairs of strings whose edit distances are at most $K$. Edit similarity join is a fundamental problem in data…
Editing human-written text has become a standard use case of large language models (LLMs), for example, to make one's arguments more appropriate for a discussion. Comparing human to LLM-generated edits, however, we observe a mismatch in…
A measure of similarity between text embeddings can be considered adequate only if it adheres to the human perception of similarity between texts. In this paper, we introduce the distance-to-distance ratio (DDR), a novel measure of…
We prove results on the decidability and complexity of computing the total variation distance (equivalently, the $L_1$-distance) of hidden Markov models (equivalently, labelled Markov chains). This distance measures the difference between…