In this paper we unify several existing regularity conditions for graphs, including strong regularity, k-isoregularity, and the t-vertex condition. We develop an algebraic composition/decomposition theory of conditions. Using our theoretical results show that a family non rank 3 graphs known to satisfy 7-vertex condition fulfills even stronger condition, (3,7)-regularity (the notion is defined ...

Regular model checking is an exploration technique for infinite state systems where spaces are represented as regular languages and transition relations expressed using rational over (or finite) strings. We extend the paradigm to permit use of more powerful relations: class relations, which a strict subset. language monadic second-order logic (MSO) on strings specify such adopt streaming string...