Monadic Second-Order Logic over Rectangular Pictures and Recognizability by Tiling Systems

Dora Giammarresi, Antonio Restivo, Sebastian Seibert, Wolfgang Thomas
1996 Information and Computation  
It is shown that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system iff it is definable in existential monadic second-order logic. As a consequence, finite tiling systems constitute a notion of recognizability over two-dimensional inputs which at the same time generalizes finite-state recognizability over strings and also matches a natural logic. The proof is based on the Ehrenfeucht Fra@ sse technique for first-order logic and an implementation of"threshold counting" within tiling systems. ]
doi:10.1006/inco.1996.0018 fatcat:wftquihpyjd5jojgjhqff3tlum