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UNIVERSAL TURING
MACHINE
PRESENTED BY  GOPESH
TURING MACHINE
• MATHEMATICAL TOOL THAT IS EQUIVALENT TO A DIGITAL COMPUTER.
• IT HAS 7 TUPLES: (Q, T, B, ∑, Δ, Q0, F)
• Q * T  Q * T *( L * R )
• IT HAS AN INFINITE LENGTH TAPE.
DRAWBACK OF TURING
MACHINE
• WE HAVE TO CONSTRUCT A NEW TURING MACHINE FOR EVERY NEW
COMPUTATION THAT WE HAVE TO DO.
Universal Turing Machine
• This problem of Turing machine led to the formation of
universal Turing machine.
• UTM is a Turing machine that stimulates an arbitrary TM on
arbitrary input.
UNIVERSAL TURING MACHINE CONTD..
• IT CHANGES THE STATE BASED ON THE INPUT.
• IT HAS THREE BITS OF INFORMATION:
• DESCRIPTION OF TURING MACHINE.
• THE CONTENTS OF MACHINE TAPE.
• THE INTERNAL STATE OF MACHINE.
APPLICATIONS OF UNIVERSAL
TURING MACHINE
• RECURSIVE FUNCTION.
• DECIDE ANY RECURSIVE LANGUAGE.
• ACCEPT ANY RECURSIVELY ENUMERABLE LANGUAGE.
THANK YOU

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Universal Turing Machine.pptx

  • 2. TURING MACHINE • MATHEMATICAL TOOL THAT IS EQUIVALENT TO A DIGITAL COMPUTER. • IT HAS 7 TUPLES: (Q, T, B, ∑, Δ, Q0, F) • Q * T  Q * T *( L * R ) • IT HAS AN INFINITE LENGTH TAPE.
  • 3. DRAWBACK OF TURING MACHINE • WE HAVE TO CONSTRUCT A NEW TURING MACHINE FOR EVERY NEW COMPUTATION THAT WE HAVE TO DO. Universal Turing Machine • This problem of Turing machine led to the formation of universal Turing machine. • UTM is a Turing machine that stimulates an arbitrary TM on arbitrary input.
  • 4. UNIVERSAL TURING MACHINE CONTD.. • IT CHANGES THE STATE BASED ON THE INPUT. • IT HAS THREE BITS OF INFORMATION: • DESCRIPTION OF TURING MACHINE. • THE CONTENTS OF MACHINE TAPE. • THE INTERNAL STATE OF MACHINE.
  • 5. APPLICATIONS OF UNIVERSAL TURING MACHINE • RECURSIVE FUNCTION. • DECIDE ANY RECURSIVE LANGUAGE. • ACCEPT ANY RECURSIVELY ENUMERABLE LANGUAGE.