Read-only right moving Turing machines

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Read-only right moving Turing machines are a particular type of Turing machine.

Definition[edit]

The definition based on a single infinite tape defined to be a 7-tuple

M= \langle Q, \Gamma, b, \Sigma, \delta, q_0, F \rangle where

  • Q is a finite set of states
  • \Gamma is a finite set of the tape alphabet/symbols
  • b \in \Gamma is the blank symbol (the only symbol allowed to occur on the tape infinitely often at any step during the computation)
  • \Sigma, a subset of \Gamma not including b is the set of input symbols
  • \delta: Q \times \Gamma \rightarrow Q \times \Gamma \times \{R\} is a function called the transition function, R is a right movement (a right shift).
  • q_0 \in Q is the initial state
  • F \subseteq Q is the set of final or accepting states

In the case of these types of Turing Machines, the only movement is to the right. There must exist at least one element of the set F (a HALT state) for the machine to accept a regular language (Not in including the empty language).

An example Read Only right moving Turing machine

Q = { A, B, C, HALT }
Γ = { 0, 1 }
b = 0 = "blank"
Σ = \varnothing, empty set
δ = see state-table below
q0 = A = initial state
F = the one element set of final states {HALT}

State table for 3 state, 2 symbol read only machine:

Current state A: Current state B: Current state C:
Write symbol: Move tape: Next state: Write symbol: Move tape: Next state: Write symbol: Move tape: Next state:
tape symbol is 0: 1 R B 1 R A 1 R B
tape symbol is 1: 1 R C 1 R B 1 N HALT

See also[edit]

References[edit]

  • Davis, Martin; Ron Sigal; Elaine J. Weyuker (1994). Second Edition: Computability, Complexity, and Languages and Logic: Fundamentals of Theoretical Computer Science (2nd ed. ed.). San Diego: Academic Press, Harcourt, Brace & Company. ISBN 0-12-206382-1.