0000000001106329
AUTHOR
ÖZlem Salehi
showing 4 related works from this author
Real-Time Vector Automata
2013
We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected k×k matrix. Only one entry of the vector can be tested for equality to 1 at any time. Classes of languages recognized by deterministic, nondeterministic, and "blind" versions of these machines are studied and compared with each other, and the associated classes for multicounter automata, automata with multiplication, and generalized finite automata.
Implementing Quantum Finite Automata Algorithms on Noisy Devices
2021
Quantum finite automata (QFAs) literature offers an alternative mathematical model for studying quantum systems with finite memory. As a superiority of quantum computing, QFAs have been shown exponentially more succinct on certain problems such as recognizing the language \(\mathtt {MOD}_\mathrm{p}= \{{a^{j}} \mid {j \equiv 0 \mod p}\} \) with bounded error, where p is a prime number. In this paper we present improved circuit based implementations for QFA algorithms recognizing the \(\mathtt {MOD}_\mathrm{p}\) problem using the Qiskit framework. We focus on the case \(p=11\) and provide a 3 qubit implementation for the \(\mathtt {MOD}_\mathrm{11}\) problem reducing the total number of requi…
New Results on Vector and Homing Vector Automata
2019
We present several new results and connections between various extensions of finite automata through the study of vector automata and homing vector automata. We show that homing vector automata outperform extended finite automata when both are defined over $ 2 \times 2 $ integer matrices. We study the string separation problem for vector automata and demonstrate that generalized finite automata with rational entries can separate any pair of strings using only two states. Investigating stateless homing vector automata, we prove that a language is recognized by stateless blind deterministic real-time version of finite automata with multiplication iff it is commutative and its Parikh image is …
Cost-efficient QFA Algorithm for Quantum Computers
2021
The study of quantum finite automata (QFAs) is one of the possible approaches in exploring quantum computers with finite memory. Despite being one of the most restricted models, Moore-Crutchfield quantum finite automaton (MCQFA) is proven to be exponentially more succinct than classical finite automata models in recognizing certain languages such as $\mathtt{MOD}_p = \{ a^{j} \mid j \equiv 0 \mod p\}$, where $p$ is a prime number. In this paper, we present a modified MCQFA algorithm for the language $\mathtt{MOD}_p$, the operators of which are selected based on the basis gates on the available real quantum computers. As a consequence, we obtain shorter quantum programs using fewer basis gat…