Related papers: On Separation by Locally Testable and Locally Thre…
We consider simulation games played between Spoiler and Duplicator on two B\"uchi automata in which the choices made by Spoiler can be buffered by Duplicator in several buffers before she executes them on her structure. We show that the…
Automatic segmentation of text into minimal content-bearing units is an unsolved problem even for languages like English. Spaces between words offer an easy first approximation, but this approximation is not good enough for machine…
Scaling existing applications and solutions to multiple human languages has traditionally proven to be difficult, mainly due to the language-dependent nature of preprocessing and feature engineering techniques employed in traditional…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Regular constraints restrict valid substitutions of…
Language Identification is the task of identifying a document's language. For applications like automatic spell checker selection, language identification must use very short strings such as text message fragments. In this work, we…
We study the space complexity of the following problem: For a fixed regular language $L$, we receive a stream of symbols and want to test membership of a sliding window of size $n$ in $L$. For deterministic streaming algorithms we prove a…
System prompts provide a lightweight yet powerful mechanism for conditioning large language models (LLMs) at inference time. While prior work has focused on English-only settings, real-world deployments benefit from having a single prompt…
Pointer arithmetic is widely used in low-level programs, e.g. memory allocators. The specification of such programs usually requires using pointer arithmetic inside inductive definitions to define the common data structures, e.g. heap lists…
A classical result (often credited to Y. Medvedev) states that every language recognized by a finite automaton is the homomorphic image of a local language, over a much larger so-called local alphabet, namely the alphabet of the edges of…
In the constrained synchronization problem we ask if a given automaton admits a synchronizing word coming from a fixed regular constraint language. We show that intersecting a given constraint language with an ideal language decreases the…
Let $\Sigma = X\cup X^{-1} = \{ x_1 ,x_2 ,..., x_m ,x_1^{-1} ,x_2^{-1} ,..., x_m^{-1} \}$ and let $G$ be a group with set of generators $\Sigma$. Let $\mathfrak{L} (G) =\left\{ \left. \omega \in \Sigma^* \; \right\vert \;\omega \equiv e \;…
We study a model where two opposing provers debate over the membership status of a given string in a language, trying to convince a weak verifier whose coins are visible to all. We show that the incorporation of just two qubits to an…
For supervised classification problems involving design, control, other practical purposes, users are not only interested in finding a highly accurate classifier, but they also demand that the obtained classifier be easily interpretable.…
Two planar sets are circularly separable if there exists a circle enclosing one of the sets and whose open interior disk does not intersect the other set. This paper studies two problems related to circular separability. A linear-time…
The class of local languages is a well-known subclass of the regular languages that admits many equivalent characterizations. In this short note we establish the PSPACE-completeness of the problem of determining, given as input a…
Implementing automated unit tests is an important but time-consuming activity in software development. To assist developers in this task, many techniques for automating unit test generation have been developed. However, despite this effort,…
The design and implementation of unit tests is a complex task many programmers neglect. This research evaluates the potential of Large Language Models (LLMs) in automatically generating test cases, comparing them with manual tests. An…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
Reasoning encompasses two typical types: deductive reasoning and inductive reasoning. Despite extensive research into the reasoning capabilities of Large Language Models (LLMs), most studies have failed to rigorously differentiate between…
We show that a well-known family of deterministic finite automata can be used to distinguish distinct binary strings of the same length from every start state. Further, we establish almost matching lower and upper bounds on the number of…