Uniform and nonuniform recognizability

Wolfgang Thomas
2003 Theoretical Computer Science  
Deterministic and nondeterministic ÿnite-state recognizability over ÿnite structures are introduced in an algebraic setting, avoiding detailed computational conventions as needed in the deÿnition of ÿnite-state acceptors. For deterministic recognizability, the classical approach is adopted, using a "uniform" homomorphism from the input domain (consisting of terms) into a ÿnite algebra. For the nondeterministic case, we refer to relational input structures and to an acceptance via relational
more » ... morphisms (which are applied "nonuniformly" since they depend on the input structures). We show how this approach encompasses known models of nondeterministic automata over ÿnite words, trees, pictures, and graphs, and present some elementary metaresults connecting uniform recognizability, nonuniform recognizability, and monadic second-order logic.
doi:10.1016/s0304-3975(01)00229-8 fatcat:4btfarn3pfdchiijplmiesg4wa