On injectivity of quantum finite automata
| Autor: | Paul C. Bell, Mika Hirvensalo |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
QA75
FOS: Computer and information sciences Rational number Pure mathematics General Computer Science Formal Languages and Automata Theory (cs.FL) Computer Networks and Communications Computer Science - Formal Languages and Automata Theory 0102 computer and information sciences 02 engineering and technology 01 natural sciences Measure (mathematics) Theoretical Computer Science 020204 information systems 0202 electrical engineering electronic engineering information engineering Quantum finite automata Algebraic number QA F.1.1 F.4.1 F.4.3 Mathematics T1 Applied Mathematics State vector Unitary matrix Injective function Undecidable problem Computational Theory and Mathematics 010201 computation theory & mathematics Computer Science::Formal Languages and Automata Theory |
| Zdroj: | Journal of Computer and System Sciences. 122:19-33 |
| ISSN: | 0022-0000 |
| DOI: | 10.1016/j.jcss.2021.05.002 |
| Popis: | We consider notions of freeness and ambiguity for the acceptance probability of Moore-Crutchfield Measure Once Quantum Finite Automata (MO-QFA). We study the injectivity problem of determining if the acceptance probability function of a MO-QFA is injective over all input words, i.e., giving a distinct probability for each input word. We show that the injectivity problem is undecidable for 8 state MO-QFA, even when all unitary matrices and the projection matrix are rational and the initial state vector is real algebraic. We also show undecidability of this problem when the initial vector is rational, although with a huge increase in the number of states. We utilize properties of quaternions, free rotation groups, representations of tuples of rationals as linear sums of radicals and a reduction of the mixed modification of Post's correspondence problem, as well as a new result on rational polynomial packing functions which may be of independent interest. Comment: Accepted journal version (with change of name from Acceptance Ambiguity for Quantum Automata) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect