ICE-TCS Lectures Series - Wlodzimierz Moczurad - Directed figure codes are decidable

The next ICE-TCS  talk for this semester will be delivered on Friday, 20 November, by Wlodzimierz Moczurad (Faculty of Computer Science, Nowy Sacz School of Business and Institute of Computer Science, Jagiellonian University, Poland). The talk, entitled Directed figure codes are decidable, will be held in room K5 at Reykjavík University (Kringlan 1) from 14:00 till 15:00. 

Further information about forthcoming ICE- TCS events may be found at the news page

Abstract

Two-dimensional structures of various kinds can be viewed as generalizations of words. Codicity verification and the defect effect, important properties related to word codes, are studied also in this context. Unfortunately, both are lost in the case of two common structures, polyominoes and figures. We consider directed figures defined as labelled polyominoes with designated start and end points, equipped with catenation operation that uses a merging function to resolve possible conflicts. We prove that in this setting verification whether a given finite set of directed figures is a code is decidable and we give a constructive algorithm. We also clarify the status of the defect effect for directed figures.

Keywords: directed figures, variable-length codes, codicity verification, Sardinas-Patterson algorithm, defect effect

This is joint work with Michal Kolarz (Jagiellonian University).