Applying abstract algebraic logic to classical automata theory : an exercise
Luís Descalço, Alexandre Madeira, Manuel A. Martins · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · 2010
In [4], Blok and Pigozzi have shown that a deterministic finite au- tomaton can be naturally viewed as a logical matrix. Following this idea, we use a generalisation of the matrix concept to deal with other kind of automata in the same algebraic perspective. We survey some classical concepts of automata theory using tools from algebraic logic. The novelty of this approach is the understand- ing of the classical automata theory within the standard abstract algebraic logic theory.