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Turing Machine Model

Turing Machine Model. Are there computations that no “reasonable” computing machine can perform? the machine should not store the answer to all possible problems it should process information (execute instructions) at a finite speed

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Turing Machine Model

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  1. Turing Machine Model • Are there computations that no “reasonable” computing machine can perform? • the machine should not store the answer to all possible problems • it should process information (execute instructions) at a finite speed • it is capable of performing a particular computation only if it can generate the answer in a finite number of steps • Alan M. Turing (1912-1954) in 1936 defined an abstract model for use in describing the decision problem Processor Read/Write Head Data Tape ... ...

  2. Diagramming a Turing Machine X Halt Halt % % S0 S1 b X R R R Y Y L b b @ S3 S2 X b R R L % Y “The Turing Machine”, Isaac Malitz, Byte, November 1987, pp 345-357. Halt

  3. Finite State Automatons • A Finite-State Automaton (FSA) consists of: • a set I, the input alphabet; • a set S, the states; • an initial state; • a subset of S called accepting states; • a state transition function N: S x I S • N(s,m) is the state to which the FSA goes if m is the input when the FSA is in state s.

  4. Petri Nets • A Petri Net is a bipartite directed graph and consists of: • a set P of places (a state in which the system could be observed); • a set T of transitions (the rules “fire” causing state changes); • an input function I:TP*; a mapping from transitions to “bags” of places • an output function O:TP*; a mapping from transitions to “bags” of places; • a marking M:P {0,1,2,…} which assigns tokens to places: • M’(p) = M(p) + 1 if p is a member of O(t) and p is not a member of I(t), • M’(p) = M(p) - 1 if p is a member of I(t) and p is not a member of O(t), • M’(p) = M(p) otherwise. • a transition is enabled if M(p) > 0 for all p members of I(t)

  5. A Marked Petri Net Example P7 P5 T2 T3 P9 P11 T7 T6 T1 I1 P4 P1 P2 P3 O1 T10 T5 T4 T8 P10 T9 P12 P6 P8

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