Iterated uniform finite-state transducers

A deterministic iterated uniform finite-state transducer (for short, iufst) operates the same length-preserving transduction on several left-to-right sweeps. The first sweep occurs on the input string, while any other sweep processes the output of the previous one. We focus on constant sweep bounded iufsts. We study their descriptional power vs. deterministic finite automata, and the state cost of implementing language operations. Then, we focus on non-constant sweep bounded iufsts, showing a nonregular language hierarchy depending on sweep complexity

Freezing 1-Tag Systems with States

We study 1-tag systems with states obeying the freezing property that only allows constant bounded number of rewrites of symbols. We look at examples of languages accepted by such systems, the accepting power of the model, as well as certain closure properties and decision problems. Finally we discuss a restriction of the system where the working alphabet must match the input alphabet.Comment: In Proceedings AFL 2023, arXiv:2309.0112

Latvian Quantum Finite State Automata for Unary Languages

We design Latvian quantum finite state automata (LQFAs for short) recognizing unary regular languages with isolated cut point 1/2. From an architectural point of view, we combine two LQFAs recognizing with isolated cut point, respectively, the finite part and the ultimately periodic part of any given unary regular language L. In both modules, we use a component addressed in the literature and here suitably adapted to the unary case, to discriminate strings on the basis of their length. The number of basis states and the isolation around the cut point of the resulting LQFA for L exponentially depends on the size of the minimal deterministic finite state automaton for L.Comment: In Proceedings NCMA 2023, arXiv:2309.0733

Basics and Applications in Quantum Optics

Quantum optics has received a lot of attention in recent decades due to the handiness and versatility of optical systems, which have been exploited both to study the foundations of quantum mechanics and for various applications. In this Special Issue, we collect some articles and a review focusing on some research activities that show the potential of quantum optics in the advancement of quantum technologies

Descriptional Complexity of Iterated Uniform Finite-State Transducers

We introduce the deterministic computational model of an iterated uniform finite-state transducer (IUFST). A IUFST performs the same length-preserving transduction on several left-to-right sweeps. The first sweep takes place on the input string, while any other sweep processes the output of the previous one. The IUFST accepts or rejects upon halting in an accepting or rejecting state along its sweeps. First, we focus on constant sweep bounded IUFSTs. We study their descriptional power vs. deterministic finite automata, and the state cost of implementing language operations. Then, we focus on non-constant sweep bounded IUFSTs, showing a nonregular language hierarchy depending on sweep complexity. The hardness of some classical decision problems on constant sweep bounded IUFSTs is also investigated

Computational and Descriptional Power of Nondeterministic Iterated Uniform Finite-State Transducers

An iterated uniform finite-state transducer (IUFST) runs the samelength-preserving transduction, starting with a sweep on the input string andthen iteratively sweeping on the output of the previous sweep. The IUFSTaccepts the input string by halting in an accepting state at the end of asweep. We consider both the deterministic (IUFST) and nondeterministic (NIUFST)version of this device. We show that constant sweep bounded IUFSTs and NIUFSTsaccept all and only regular languages. We study the state complexity ofremoving nondeterminism as well as sweeps on constant sweep bounded NIUFSTs,the descriptional power of constant sweep bounded IUFSTs and NIUFSTs withrespect to classical models of finite-state automata, and the computationalcomplexity of several decidability questions. Then, we focus on non-constantsweep bounded devices, proving the existence of a proper infinite nonregularlanguage hierarchy depending on the sweep complexity both in the deterministicand nondeterministic case. Though NIUFSTss are "one-way" devices we show thatthey characterize the class of context-sensitive languages, that is, thecomplexity class DSpace(lin). Finally, we show that the nondeterministicdevices are more powerful than their deterministic variant for a sublinearnumber of sweeps that is at least logarithmic

Iterated Uniform Finite-State Transducers: Descriptional Complexity of Nondeterminism and Two-Way Motion

An iterated uniform finite-state transducer executes the same length-preserving transduction in iterative sweeps. The first sweep occurs on the input string, while any subsequent sweep works on the output of the previous one. We consider devices with one-way motion and two-way motion, i.e., sweeps are either from left to right only, or alternate from left to right and from right to left. In addition, devices may work deterministically or nondeterministically. Here, we restrict to study devices performing a constant number of sweeps, which are known to characterize exactly the regular languages. We determine the descriptional costs of removing two-way motion, nondeterminism, and sweeps, and, in particular, the costs for the conversion to deterministic or nondeterministic finite automata. Finally, the special case of unary languages is investigated, and a language family is presented that is immune to the resources of nondeterminism and two-way motion, in the sense that both resources can neither reduce the number of states nor the number of sweeps