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Classical and Quantum Automata

Classical and Quantum Automata. Abuzer Yakaryılmaz Advisor: Prof. Cem Say. Outline. Deterministic Finite Automa (DFA) 2-Way Deterministic Finite Automata (2-DFA) Probabilistic Finite Automata (PFA) 2-Way Probabilistic Finite Automata Quantum Physics Quantum Computation Quantum Automata

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Classical and Quantum Automata

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  1. Classical and Quantum Automata Abuzer Yakaryılmaz Advisor: Prof. Cem Say

  2. Outline • Deterministic Finite Automa (DFA) • 2-Way Deterministic Finite Automata (2-DFA) • Probabilistic Finite Automata (PFA) • 2-Way Probabilistic Finite Automata • Quantum Physics • Quantum Computation • Quantum Automata • 2-Way Quantum Finite Automata

  3. Deterministic Finite Automa (DFA) • Basic computation model • Read-only machines • Finite alphabet • Finite state (memory) • Transition function • Regular languages

  4. 2-Way Deterministic Finite Automata • Similar to DFA • But, 2-way move head (right,left,stationary) • More powerful than DFA? • Yes, fewer state, simple computation • No, just recognize regular languages

  5. Probabilistic Finite Automata • Transitions are probabilistic not deterministic • Bounded error – ε • Strings (tapes) are accepted or rejected with 1-ε probability • Any PFA with ε is equivalent to a DFA

  6. 2-Way Probabilistic Finite Automata • Transitions are probabilistic not deterministic • 2-way move head • Is equivalent to DFA? • 2PFA-POLYTIME = REGULAR • Freivalds machine [1981] recognizes some non-regular (and non-context-free languages)

  7. Quantum Physics • 20. century [Plank, Einstein, Bohr, Pauli, Heisenberg, Shrondinger,...] • New paradigm • Possibilities (complex numbers) • Multi-universe • Teleportation • Entanglement

  8. Quantum Computation • Feynman: Quantum events cannot be simulated in classical computers in feasible time • David Deutsch: Formalize the quantum computers (Quantum Turing Machine) • Hilbert Space, Unitary matrix • Superpositions of qubits, quantum gates • Shor’s factorization algorithm

  9. Quantum Automata • Quantum model of automata • Finite alphabet, finite states • Transitions are unitary matrix • Superpositon of states • Bounded error – ε • 1QFA recognize a proper subset of regular languages

  10. 2-Way Quantum Finite Automata • Recognize some non-regular and non-context free languages in polynomial time [Kondacs & Watrous, 1997] • MS Thesis (Fatih Mehmet Atak, 2006) • QFA simulator (java) • New methods • MS Thesis (Abuzer Yakaryılmaz, progress) • Formal analysis of FMA • (Maybe) PFA simulator • New methods • fewer state, fewer step, better bound error • Different approaches • New languages (practical or theoritical)

  11. COMMENTS & QUESTION

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