Related papers: Separating regular languages by piecewise testable…
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 \;…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
We study the problem of regular separability of languages of vector addition systems with states (VASS). It asks whether for two given VASS languages K and L, there exists a regular language R that includes K and is disjoint from L. While…
A natural language (or ordinary language) is a language that is spoken, written, or signed by humans for general-purpose communication, as distinguished from formal languages (such as computer-programming languages or the "languages" used…
A classical problem in grammatical inference is to identify a language from a set of examples. In this paper, we address the problem of identifying a union of languages from examples that belong to several different unknown languages.…
A basic question in the study of measure-once quantum finite automata is whether two distinct input words can be separated with certainty. The exact separation problem reduces to a trace-vanishing question in \(SU(2)\). The main difficulty…
We study the separability problem for automatic relations (i.e., relations on finite words definable by synchronous automata) in terms of recognizable relations (i.e., finite unions of products of regular languages). This problem takes as…
The paper considers algorithmic properties of classical and non-classical first-order logics and theories in bounded languages. The main idea is to prove the undecidability of various fragments of classical and non-classical first-order…
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…
We look at classes of languages associated to the fragment of first-order logic B{\Sigma}1 which disallows quantifier alternations. Each class is defined by choosing the set of predicates on positions that may be used. Two key such…
We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…
One of the key concepts in testing is that of adequate test sets. A test selection criterion decides which test sets are adequate. In this paper, a language schema for specifying a large class of test selection criteria is developed; the…
The problem of non-iterative one-shot and non-destructive correction of unavoidable mistakes arises in all Artificial Intelligence applications in the real world. Its solution requires robust separation of samples with errors from samples…
We continue our study of open and closed languages. We investigate how the properties of being open and closed are preserved under concatenation. We investigate analogues, in formal languages, of the separation axioms in topological spaces;…
There have been many attempts to solve the P versus NP problem. However, with a new proof method, P not equal NP can be proved. A time limit is set for an arbitrary Turing machine and an input word is rejected on a timeout. The time limit…
Splicing as a binary word/language operation is inspired by the DNA recombination under the action of restriction enzymes and ligases, and was first introduced by Tom Head in 1987. Shortly thereafter, it was proven that the languages…
Compounding is a highly productive word-formation process in some languages that is often problematic for natural language processing applications. In this paper, we investigate whether distributional semantics in the form of word…
We investigate in a method for proving separation results for abstract classes of languages. A well established method to characterize varieties of regular languages are identities. We use a recently established generalization of these…
We study modal separability for fixpoint formulae: given two mutually exclusive fixpoint formulae $\varphi,\varphi'$, decide whether there is a modal formula $\psi$ that separates them, that is, that satisfies…
We are lifting classical problems from single instances to regular sets of instances. The task of finding a positive instance of the combinatorial problem $P$ in a potentially infinite given regular set is equivalent to the so called…