The aim of this chapter is to generalize concepts and techniques of formal language theory to two dimensions. Informally, a two-dimensional string is called a picture and is defined as a rectangular array of symbols taken from a finite alphabet. A two-dimensional language (or picture language) is a set of pictures.

Two-dimensional languages

Communication Complexity: Basics

The last 10 years have seen a sudden rise in interest in the use of Geographical Information Systems (GIS) in historical research. This has led to a field that has become known as `historical GIS'. This development started in the more quantitative ends of the discipline but has spread to encompass qualitative research as well. Interest in historical GIS is not restricted to researchers who would previously have regarded themselves as historical geographers, but has in fact led to an increased awareness of the importance of geography from across the discipline of history. This paper introduces historical GIS and critically evaluates how it is affecting the practice of historical geography.

http://journals.sagepub.com/doi/pdf/10.1177/0309132507081495

Historical GIS: structuring, mapping and analysing geographies of the past

About the same time, A.N. Shah gave a finite autom~ton with 5 pebbles which could search an arbitrary maze (the autonlaton may drop a pebble on a cell it is visiting, then upon returning to that cell later on can sense the pebble's presence, and if desired pick it up and move it to a new cell). Shah also conjectured that fewer than 5 pebbles would not suffice. The first of our two main results is that, contrary to Shah's conjecture, the search can be implemented with just two pebbles. The question is still open whether a finite automaton with just one pebble can search any maze.

On the power of the compass (or, why mazes are easier to search than graphs)

Algorithmics for Hard Problems

http://www.wseas.us/e-library/conferences/miami2004/papers/484-333.pdf

A note on two-dimensional finite automata

Several properties of two-dimensional alternating Turing machines are investigated. The first part of this paper investigates the relationship between the classes of sets accepted by space-bounded and finitely leaf-size bounded three-way two-dimensional alternating Turing machines and the classes of sets which are finite intersections of sets accepted by space-bounded three-way two-dimensional nondeterministic Turing machines. The second part of this paper investigates the accepting power and closure properties (under Boolean operations) of two-dimensional alternating Turing machines with only universal states.

Katsushi Inoue

Papers

A note on two-dimensional finite automata

Two-dimensional alternating turing machines with only universal states

Cyclic closure properties of automata on a two-dimensional tape

Three-way tape-bounded two-dimensional turing machines

Nonclosure Properties of Two-Dimensional On-Line Tessellation Acceptors and One Way Parallel Sequential Array Acceptors