What do you Understand by Multi-dimensional Turing Machine?

Before understanding about Multi-Dimensional Turing Machine, lets first understand about Turing Machine 

A Turing Machine with a two-way infinite tape is denoted by (Q,Σ, Γ, δ, q_acc , q₀ , q_rej) as in original model.

Q is a finite and nonempty set of states.

Σ is an alphabet called the input alphabet, which may not include the blank symbol.

Γ is an alphabet called the tape alphabet, which must satisfy Σ ∪ { } ⊆ Γ.

δ is a transition function having the form 

    δ : Q\{ q_acc , q_rej } × Γ → Q × Γ × {←, →}.

q₀ ∈ Q is the initial state.

q_acc, q_rej ∈ Q are the accept and reject states, which must satisfy q_acc ≠ q_rej.

      In a multi-dimensional Turing Machine, as the name suggests, this tape consists of a k-dimensional array of cells infinite in all 2k directions, for some fixed k. Depending on the state and the symbol scanned, the device changes its state, prints a new symbol and moves its tape head in one of the 2k directions, either positively or negatively, along with one of the k-axes. In this, sometimes you might get some strange topologies by putting strange connectedness properties on the tape. Like all even cells are connected to another cell. This will be sufficient to knows about multi-dimension Turing Machine.

Also, Study about: 

• Mealy Machine
• Moore Machine
• Rice Theorem
• Brief about Turing Machine
• Multi Dimension Turing Machine
• Multiple Turing Machine
• Parikh Theorem in TOC
• Parse Tree or Derivation Tree
• What do you Understand by Derivation
• MyHill Nerode Theorem
• Minimize Myhill Nerode Theorem
• Push Down Automata
• Know Where we use Automata
• What do you understand by Derivation of Grammar
• What is Context-free Grammar
• Example based on CFG
• Regular Expression in TOC

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