Related papers: The separation problem for regular languages by pi…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
Deciding the amalgamation property for a given class of finite structures is an important subroutine in classifying countable finitely homogeneous structures. We study the computational complexity of the amalgamation decision problem for…
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…
Given a bichromatic point set $P=\textbf{R} \cup \textbf{B}$ of red and blue points, a separator is an object of a certain type that separates $\textbf{R}$ and $\textbf{B}$. We study the geometric separability problem when the separator is…
Effectful programs interact in ways that go beyond simple input-output, making compositional reasoning challenging. Existing work has shown that when such programs are ``separate'', i.e., when programs do not interfere with each other, it…
Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node's neighbors, instead of the…
This paper is aimed to prove the strong duality theorem for continuous-time linear programming problems in which the coefficients are assumed to be piecewise continuous functions. The previous paper proved the strong duality theorem for the…
We present a simple new method for proving that languages are not regular. We prove the correctness of the method, illustrate the ease of using the method on well-known examples of nonregular languages, and prove two additional theorems on…
In natural speech, the speaker does not pause between words, yet a human listener somehow perceives this continuous stream of phonemes as a series of distinct words. The detection of boundaries between spoken words is an instance of a…
The class of problems complete for NP via first-order reductions is known to be characterized by existential second-order sentences of a fixed form. All such sentences are built around the so-called generalized IS-form of the sentence that…
Without prior knowledge, distinguishing different languages may be a hard task, especially when their borders are permeable. We develop an extension of spectral clustering -- a powerful unsupervised classification toolbox -- that is shown…
The Split and Rephrase (SPRP) task, which consists in splitting complex sentences into a sequence of shorter grammatical sentences, while preserving the original meaning, can facilitate the processing of complex texts for humans and…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
Separation logic is successful for software verification of heap-manipulating programs. Numbers are necessary to be added to separation logic for verification of practical software where numbers are important. However, properties of the…
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…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
Language models provide a key framework for studying linguistic theories based on prediction, but phonological analysis using large language models (LLMs) is difficult; there are few phonological benchmarks beyond English and the standard…
We give a universal kernel that renders all the regular languages linearly separable. We are not able to compute this kernel efficiently and conjecture that it is intractable, but we do have an efficient $\eps$-approximation.
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
The constrained synchronization problem (CSP) asks for a synchronizing word of a given input automaton contained in a regular set of constraints. It could be viewed as a special case of synchronization of a discrete event system under…