The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
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STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Monadic second-order logic over rectangular pictures and recognizability by tiling systems
Information and Computation
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Handbook of formal languages, vol. 3
Languages, automata, and logic
Handbook of formal languages, vol. 3
The expression of graph properties and graph transformations in monadic second-order logic
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Automata, Languages, and Machines
Automata, Languages, and Machines
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Recognizability Equals Monadic Second-Order Definability for Sets of Graphs of Bounded Tree-Width
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
A topological approach to recognition
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
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DLT'11 Proceedings of the 15th international conference on Developments in language theory
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ICGT'06 Proceedings of the Third international conference on Graph Transformations
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Deterministic and nondeterministic finite-state recognizability over finite structures are introduced in an algebraic setting, avoiding detailed computational conventions as needed in the definition of finite-state acceptors. For deterministic recognizability, the classical approach is adopted, using a "uniform" homomorphism from the input domain (consisting of terms) into a finite algebra. For the nondeterministic case, we refer to relational input structures and to an acceptance via relational homomorphisms (which are applied "nonuniformly" since they depend on the input structures). We show how this approach encompasses known models of nondeterministic automata over finite words, trees, pictures, and graphs, and present some elementary metaresults connecting uniform recognizability, nonuniform recognizability, and monadic second-order logic.