The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
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Theoretical Computer Science
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Theoretical Computer Science
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Monadic second-order logic on tree-like structures
Theoretical Computer Science
Uniform and nonuniform recognizability
Theoretical Computer Science
Automata for the Modal mu-Calculus and related Results
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
Automata Theory on Trees and Partial Orders
TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
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CONCUR '93 Proceedings of the 4th International Conference on Concurrency Theory
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
The Monadic Quantifier Alternation Hierarchy over Graphs is Infinite
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
The recognizability of sets of graphs is a robust property
Theoretical Computer Science
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We investigate two models of finite-state automata that operate on rooted directed graphs by marking either vertices (V-automata) or edges (E-automata). Runs correspond to locally consistent markings and acceptance is defined by means of regular conditions on the paths emanating from the root. Comparing the expressive power of these two notions of graph acceptors, we show that E-automata are more expressive than V-automata. Moreover, we prove that E-automata are at least as expressive as the μ-calculus. Our main result implies that every MSO-definable tree language can be recognised by E-automata with uniform runs, that is, runs that do not distinguish between isomorphic subtrees.