Related papers: A General Approach to State Complexity of Operatio…
In this paper, we consider block languages, namely sets of words having the same length, and we propose a new representation for these languages. In particular, given an alphabet of size $k$ and a length $\ell$, a block language can be…
Most Formal Languages and Automata Theory courses explore the duality between computation models to recognize words in a language and computation models to generate words in a language. For students unaccustomed to formal statements, these…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
We consider generic pure $n$-qubit states and a general class of pure states of arbitrary dimensions and arbitrarily many subsystems. We characterize those states which can be reached from some other state via Local Operations assisted by…
This article examines what it means to use Large Language Models in everyday work. Drawing on a seven-month longitudinal qualitative study, we argue that LLMs do not straightforwardly automate or augment tasks. We propose the concept of…
The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of regular languages is the maximal syntactic complexity of languages in that subclass, taken as a function…
The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…
One-way quantum finite automata together with classical states (1QFAC) proposed in [Journal of Computer and System Sciences 81(2) (2015) 359--375] is a new one-way quantum finite automata (1QFA) model that integrates quantum finite automata…
We present a generalization of quantum Stein's Lemma to the situation in which the alternative hypothesis is formed by a family of states, which can moreover be non-i.i.d.. We consider sets of states which satisfy a few natural properties,…
A regular language $L$ is non-returning if in the minimal deterministic finite automaton accepting it there are no transitions into the initial state. Eom, Han and Jir\'askov\'a derived upper bounds on the state complexity of boolean…
Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set…
Given a finite alphabet $\Sigma$ and a right-infinite word $\bf w$ over $\Sigma$, we define the Lie complexity function $L_{\bf w}:\mathbb{N}\to \mathbb{N}$, whose value at $n$ is the number of conjugacy classes (under cyclic shift) of…
Analogous to regular string and tree languages, regular languages of directed acyclic graphs (DAGs) are defined in the literature. Although called regular, those DAG-languages are more powerful and, consequently, standard problems have a…
We study the sweep complexity of DFA in one-way jumping mode answering several questions posed earlier. This measure is the number of times in the worst case that such machines have to return to the beginning of their input after having…
We study possibilities for semantic and syntactic rigidity, i.e., the rigidity with respect to automorphism group and with respect to definable closure. Variations of rigidity and their degrees are studied in general case, for special…
Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of omega-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is…
Data analysis requires translating higher level questions and hypotheses into computable statistical models. We present a mixed-methods study aimed at identifying the steps, considerations, and challenges involved in operationalizing…
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…
Opacity is an information flow property that captures the notion of plausible deniability in dynamic systems, that is whether an intruder can deduce that "secret" behavior has occurred. In this paper we provide a general framework of…
Formality is one of the important characteristics of text documents. The automatic detection of the formality level of a text is potentially beneficial for various natural language processing tasks. Before, two large-scale datasets were…