Galīgie kvantu automāti un matemātiskā loģika
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Latvijas Universitāte
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Abstract
Bakalaura darba mērķis ir noskaidrot, vai iespējams,
izmantojot matemātisko loģiku, saistīt sarežģītības klases
(lielāka uzmanība tiek pievērsta P un NP klasēm) ar kvantu automātu atpazīstamajām valodām. Darba gaitā apskatīti dažādi matemātiskās loģikas veidi (vispārīgie Lindstroma kvantori, mazākā nekustīgā punkta loģika u.c.), pazīstamākie kvantu automātu veidi (MO-QFA,
MM-QFA un 2QFA), kā arī sarežģītības klases. Darba rezultātā
pamatots, ka apskatītajiem automātiem šādu sakarību nav iespējams atrast.
The goal of Bachelor work is to establish whether it is possible to find connection between descriptive complexity classes (main focus goes to P and NP) and languages recognized by quantum automata, with help of mathematical logic. Many different kinds of mathematical logic (generalized Lindstrom quantifiers, least fixed point logic etc.) have been studied. Also known models of quantum automata (MO-QFA, MM-QFA, 2QFA) and descriptive complexity classes have been studied. In the corollary, it is clarfied that for studied auomata such connection does not exist.
The goal of Bachelor work is to establish whether it is possible to find connection between descriptive complexity classes (main focus goes to P and NP) and languages recognized by quantum automata, with help of mathematical logic. Many different kinds of mathematical logic (generalized Lindstrom quantifiers, least fixed point logic etc.) have been studied. Also known models of quantum automata (MO-QFA, MM-QFA, 2QFA) and descriptive complexity classes have been studied. In the corollary, it is clarfied that for studied auomata such connection does not exist.