Related papers: Nondeterministic state complexity of square root
In this paper we study the worst-case complexity of an inexact Augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded, we prove a complexity bound of $\mathcal{O}(|\log(\epsilon)|)$…
We study the state complexity of binary operations on regular languages over different alphabets. It is known that if $L'_m$ and $L_n$ are languages of state complexities $m$ and $n$, respectively, and restricted to the same alphabet, the…
We give an upper bound of $n((n-1)!-(n-3)!)$ for the possible largest size of a subsemigroup of the full transformational semigroup over $n$ elements consisting only of nonpermutational transformations. As an application we gain the same…
We show that there are quantum devices that accept all regular languages and that are exponentially more concise than deterministic finite automata (DFA). For this purpose, we introduce a new computing model of {\it one-way quantum finite…
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…
We examine deterministic and nondeterministic state complexities of regular operations on prefix-free languages. We strengthen several results by providing witness languages over smaller alphabets, usually as small as possible. We next…
We study the state complexity of regular operations in the class of ideal languages. A language L over an alphabet Sigma is a right (left) ideal if it satisfies L = L Sigma* (L = Sigma* L). It is a two-sided ideal if L = Sigma* L Sigma *,…
It is well known that computing a minimum DFA consistent with a given set of positive and negative examples is NP-hard. Previous work has identified conditions on the input sample under which the problem becomes tractable or remains hard.…
We use the language of semidefinite programming and duality to derive necessary and sufficient conditions for the optimal Lewenstein-Sanpera Decomposition (LSD) of 2-qubit states. We first provide a simple and natural derivation of the…
In this paper we examine the existence of multiple solutions of parametric fractional equations involving the square root of the Laplacian $A_{1/2}$ in a smooth bounded domain $\Omega\subset \mathbb{R}^n$ ($n\geq 2$) and with Dirichlet…
We study three notions of directability of fuzzy automata akin to the D1-, D2- and D3-directability of nondeterministic automata. Thus an input word $w$ of a fuzzy automaton is D1-directing if a fixed single state is reachable by $w$ from…
We solve stationarity equations of the geometric measure of entanglement for multi-qubit W-type states. In this way we compute analytically the maximal overlap of one-parameter $n$-qubit and two-parameter four-qubit W-type states and their…
In this research, we investigate a general shape optimization problem in which the state equation is expressed using a nonlocal and nonlinear operator. We prove the existence of a minimum point for a functional $F$ defined on the family of…
Descriptional complexity is the study of the conciseness of the various models representing formal languages. The state complexity of a regular language is the size, measured by the number of states of the smallest, either deterministic or…
We introduce a subclass of the commutative regular languages that is characterized by the property that the state set of the minimal deterministic automaton can be written as a certain Cartesian product. This class behaves much better with…
The single shortest path algorithm is undefined for weighted finite-state automata over non-idempotent semirings because such semirings do not guarantee the existence of a shortest path. However, in non-idempotent semirings admitting an…
In the field of computational logic, two classes of finite automata are considered fundamental: deterministic and nondeterministic automata (DFAs and NFAs). In a more fine-grained approach three natural intermediate classes were introduced,…
We study the sample complexity of approximate policy iteration (PI) for the Linear Quadratic Regulator (LQR), building on a recent line of work using LQR as a testbed to understand the limits of reinforcement learning (RL) algorithms on…
We consider the problem of testing whether an unknown $n$-qubit quantum state $|\psi\rangle$ is a stabilizer state, with only single-copy access. We give an algorithm solving this problem using $O(n)$ copies, and conversely prove that…
We introduce and study the repetitive variants of the deterministic and the nondeterministic finite automaton with translucent words (DFAwtw and NFAwtw). On seeing the right sentinel, a repetitive NFAwtw need not halt immediately, accepting…