Varieties of Graphoids and Birkoff's Theorem for Graphs

The algebraic structure of graphoids is used in order to obtain the wellknown Birkhoff’s theorem in the framework of graphs. Namely we establish a natural bijection between the class of Σ-graphoids and the class of strong congruences overGR(Σ, X), which is the free graphoid over the doubly ranked alphabet Σ and the set of variables X.

[1]  Max Dauchet,et al.  Théorie des magmoïdes , 1978, RAIRO Theor. Informatics Appl..

[2]  Antonios Kalampakas,et al.  Recognizability of graph and pattern languages , 2006, Acta Informatica.

[3]  Wolfgang Wechler,et al.  Universal Algebra for Computer Scientists , 1992, EATCS Monographs on Theoretical Computer Science.

[4]  Enno Ohlebusch,et al.  Term Rewriting Systems , 2002 .

[5]  Joost Engelfriet,et al.  Context-free graph grammars and concatenation of graphs , 1997, Acta Informatica.

[6]  Carlo Ghezzi,et al.  Context-Free Graph Grammars , 1978, Inf. Control..

[7]  Desmond Fearnley-Sander,et al.  Universal Algebra , 1982 .

[8]  Chang Liu,et al.  Term rewriting and all that , 2000, SOEN.

[9]  Antonios Kalampakas,et al.  Graph automata , 2008, Theor. Comput. Sci..