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

Slides:

Advertisements

Similar presentations

Happy Birthday Michael !!. Probabilistic & Nondeterministic Finite Automata Avi Wigderson Institute for Advanced Study Very old (1996) joint work with.

Advertisements

University of Queensland

CS 345: Chapter 9 Algorithmic Universality and Its Robustness

Lecture 16 Deterministic Turing Machine (DTM) Finite Control tape head.

Lecture 6 Nondeterministic Finite Automata (NFA)

Recap CS605: The Mathematics and Theory of Computer Science.

Turing Machines (At last!). Designing Universal Computational Devices Was Not The Only Contribution from Alan Turing… Enter the year 1940: The world is.

Applied Computer Science II Chapter 1 : Regular Languages Prof. Dr. Luc De Raedt Institut für Informatik Albert-Ludwigs Universität Freiburg Germany.

Intro to DFAs Readings: Sipser 1.1 (pages 31-44) With basic background from Sipser 0.

Introduction to Computability Theory

Intro to DFAs Readings: Sipser 1.1 (pages 31-44) With basic background from Sipser 0.

March 11, 2015CS21 Lecture 271 CS21 Decidability and Tractability Lecture 27 March 11, 2015.

Courtesy Costas Busch - RPI1 Non Deterministic Automata.

Finite Automata Finite-state machine with no output. FA consists of States, Transitions between states FA is a 5-tuple Example! A string x is recognized.

Fall 2006Costas Busch - RPI1 Deterministic Finite Automata And Regular Languages.

1 Turing Machines. 2 The Language Hierarchy Regular Languages Context-Free Languages ? ?

Phase in Quantum Computing. Main concepts of computing illustrated with simple examples.

CS 310 – Fall 2006 Pacific University CS310 Turing Machines Section 3.1 November 6, 2006.

Turing Machines.

CS 310 – Fall 2006 Pacific University CS310 Finite Automata Sections: September 1, 2006.

Quantum Automata Formalism. These are general questions related to complexity of quantum algorithms, combinational and sequential.

CS 490: Automata and Language Theory Daniel Firpo Spring 2003.

Fall 2006Costas Busch - RPI1 Non-Deterministic Finite Automata.

CS5371 Theory of Computation Lecture 4: Automata Theory II (DFA = NFA, Regular Language)

Costas Busch - LSU1 Non-Deterministic Finite Automata.

Regular Expressions and Automata Chapter 2. Regular Expressions Standard notation for characterizing text sequences Used in all kinds of text processing.

Prof. Busch - LSU1 Turing Machines. Prof. Busch - LSU2 The Language Hierarchy Regular Languages Context-Free Languages ? ?

Grammars, Languages and Finite-state automata Languages are described by grammars We need an algorithm that takes as input grammar sentence And gives a.

Quantum Counters Smita Krishnaswamy Igor L. Markov John P. Hayes.

1 Non-Deterministic Finite Automata. 2 Alphabet = Nondeterministic Finite Automaton (NFA)

1 Turing Machines. 2 A Turing Machine Tape Read-Write head Control Unit.

REGULAR LANGUAGES.

4b 4b Lexical analysis Finite Automata. Finite Automata (FA) FA also called Finite State Machine (FSM) –Abstract model of a computing entity. –Decides.

Computation Model and Complexity Class. 2 An algorithmic process that uses the result of a random draw to make an approximated decision has the ability.

TRANSITION DIAGRAM BASED LEXICAL ANALYZER and FINITE AUTOMATA Class date : 12 August, 2013 Prepared by : Karimgailiu R Panmei Roll no. : 11CS10020 GROUP.

Finite Automata – Definition and Examples Lecture 6 Section 1.1 Mon, Sep 3, 2007.

Turing Machine Finite state automaton –Limitation: finite amount of memory –Prevents recognizing languages that are not regular {0 n 1 n |n = 0,1,2,…}

1 Linear Bounded Automata LBAs. 2 Linear Bounded Automata (LBAs) are the same as Turing Machines with one difference: The input string tape space is the.

1 Turing’s Thesis. 2 Turing’s thesis: Any computation carried out by mechanical means can be performed by a Turing Machine (1930)

Finite Automata Chapter 1. Automatic Door Example Top View.

Computability Review homework. Video. Variations. Definitions. Enumerators. Hilbert's Problem. Algorithms. Summary Homework: Give formal definition of.

1 CD5560 FABER Formal Languages, Automata and Models of Computation Lecture 12 Mälardalen University 2007.

NP has log-space verifiers with fixed-size public quantum registers ABUZER YAKARYILMAZ Faculty of Computing University of Latvia A. C. CEM SAY Department.

Prof. Busch - LSU1 Time Complexity. Prof. Busch - LSU2 Consider a deterministic Turing Machine which decides a language.

1 Turing Machines. 2 The Language Hierarchy Regular Languages Context-Free Languages ? ?

Costas Busch - LSU1 Deterministic Finite Automata And Regular Languages.

Attendance Syllabus Textbook (hardcopy or electronics) Groups s First-time meeting.

Fall 2004COMP 3351 Finite Automata. Fall 2004COMP 3352 Finite Automaton Input String Output String Finite Automaton.

Deterministic Finite-State Machine (or Deterministic Finite Automaton) A DFA is a 5-tuple, (S, Σ, T, s, A), consisting of: S: a finite set of states Σ:

Non Deterministic Automata

Busch Complexity Lectures: Turing Machines

Busch Complexity Lectures: Reductions

Linear Bounded Automata LBAs

Pumping Lemma Revisited

Uncountable Classical and Quantum Complexity Classes

Turing Machines (At last!).

Chapter 2 FINITE AUTOMATA.

CSE322 The Chomsky Hierarchy

Deterministic Finite Automata And Regular Languages Prof. Busch - LSU.

Non-Deterministic Finite Automata

Automata and Formal Languages (Final Review)

Non-Deterministic Finite Automata

CSE322 Definition and description of finite Automata

Non Deterministic Automata

Chapter 3 Turing Machines.

Chapter 1 Regular Language

Teori Bahasa dan Automata Lecture 4: Non-deterministic Finite Automata

The Chomsky Hierarchy Costas Busch - LSU.

Non Deterministic Automata

Presentation transcript:

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 2-Way Quantum Finite Automata

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

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

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

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)

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

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

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

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)

COMMENTS & QUESTION