Editing Automata theory (section)

== Hierarchy in terms of powers ==
The following is an incomplete hierarchy in terms of powers of different types of virtual machines. The hierarchy reflects the nested categories of languages the machines are able to accept.<ref name="Aaniya B">{{cite book|last=Yan|first=Song Y.|title=An Introduction to Formal Languages and Machine Computation|year=1998|publisher=World Scientific Publishing Co. Pte. Ltd.|location=Singapore|pages=155–156|url=https://books.google.com/books?id=ySOwQgAACAAJ|isbn=978-981-02-3422-5}}</ref> 
{| class="wikitable" style="text-align:center"
|-
! Automaton
|-
| [[Deterministic Finite Automaton]] (DFA)  -- Lowest Power <br/>
(same power) &nbsp;&nbsp; <math>||</math>  &nbsp;&nbsp;(same power) <br/>
[[Nondeterministic Finite Automaton]] (NFA)<br/>
(above is weaker) &nbsp;&nbsp; <math>\cap</math> &nbsp;&nbsp; (below is stronger) <br/>
[[Deterministic pushdown automaton|Deterministic Push Down Automaton]]  (DPDA-I) <br/>
with 1 push-down store <br/>
<math>\cap</math> <br/>
[[Nondeterministic Push Down Automaton]] (NPDA-I) <br/>
with 1 push-down store <br/>
<math>\cap</math> <br/>
[[Linear bounded automaton|Linear Bounded Automaton]] (LBA) <br/>
<math>\cap</math> <br/>
[[Deterministic pushdown automaton|Deterministic Push Down Automaton]] (DPDA-II) <br/>
with 2 push-down stores <br/>
<math>||</math> <br/>
[[Nondeterministic Push Down Automaton]] (NPDA-II) <br/>
with 2 push-down stores <br/>
<math>||</math> <br/>
[[Deterministic Turing machine|Deterministic Turing Machine]] (DTM) <br/>
<math>||</math> <br/>
[[Nondeterministic Turing machine|Nondeterministic Turing Machine]] (NTM) <br/>
<math>||</math> <br/>
[[Probabilistic Turing machine|Probabilistic Turing Machine]] (PTM) <br/>
<math>||</math> <br/>
[[Multitape Turing machine|Multitape Turing Machine]] (MTM) <br/>
<math>||</math> <br/>
[[Turing machine equivalents#Other equivalent machines and methods|Multidimensional Turing Machine]]
|}