2DFAs

2DFAs are a type of computational model used in theoretical computer science. They are a generalization of finite automata, which are typically used to recognize regular languages. A 2DFA operates on a two-dimensional tape, moving in any of the four cardinal directions (up, down, left, or right). This is in contrast to a standard finite automaton which has a read-write head that moves in only one dimension.

The states of a 2DFA include not only the internal states but also information about its current position and direction of movement on the two-dimensional tape. The transition function dictates how the automaton changes its state and moves based on the symbol it reads at its current position and its current direction. The set of languages recognized by 2DFAs is known as the class of two-dimensional context-free languages.

While standard finite automata recognize regular languages, 2DFAs are capable of recognizing a more complex class of languages. They have found applications in areas such as pattern recognition, image processing, and the analysis of two-dimensional structures. The study of 2DFAs contributes to a deeper understanding of computability and the power of different computational models. Research continues to explore their properties, limitations, and potential applications.