Automata Theory on Trees and Partial Orders

@inproceedings{Thomas1997AutomataTO,
  title={Automata Theory on Trees and Partial Orders},
  author={Wolfgang Thomas},
  booktitle={TAPSOFT},
  year={1997}
}
  • W. Thomas
  • Published in TAPSOFT 14 April 1997
  • Computer Science
The paper reviews recent results which aim at generalizing finite automata theory from words and trees to labelled partial orders (presented as labelled directed acyclic graphs), with an emphasis on logical aspects. As an important type of labelled partial order we consider pictures (two-dimensional words). Graph acceptors and their specialization for pictures, “tiling systems”, are presented, and their equivalence to existential monadic second-order logic is reviewed. Other restricted versions… 
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References

SHOWING 1-10 OF 38 REFERENCES
Parallel and Two-Way Automata on Directed Ordered Acyclic Graphs
NONDETERMINISM VERSUS DETERMINISM OF FINITE AUTOMATA OVER DIRECTED ACYCLIC GRAPHS
TLDR
Three types of nite-state graph automata are compared over directed acyclic graphs (where vertices and edges are labelled) and it is shown that deterministic versions are strictly weaker.
A Kleene Theorem for a Class of Planar Acyclic Graphs
TLDR
A Kleene Theorem is proved linking these two characterizations of sets of graphs, finite automata on graphs and rational expressions that involve union, nondeterministic parallel composition, serial composition, and the iterations of these compositions.
The monadic quantifier alternation hierarchy over graphs is infinite
  • O. MatzW. Thomas
  • Computer Science, Mathematics
    Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science
  • 1997
We show that in monadic second-order logic over finite directed graphs, a strict hierarchy of expressiveness is obtained by increasing the (second-order) quantifier alternation depth of formulas.…
Tree Acceptors and Some of Their Applications
  • J. Doner
  • Mathematics, Computer Science
    J. Comput. Syst. Sci.
  • 1970
Monadic Second-Order Logic Over Rectangular Pictures and Recognizability by Tiling Systems
TLDR
It is shown that a set of pictures is recognized by a finite tiling system iff it is definable in existential monadic second-order logic, which generalizes finite-state recognizability over strings and also matches a natural logic.
Decidability of second-order theories and automata on infinite trees
Introduction. In this paper we solve the decision problem of a certain secondorder mathematical theory and apply it to obtain a large number of decidability results. The method of solution involves…
Decidability of second-order theories and automata on infinite trees.
Introduction. In this paper we solve the decision problem of a certain secondorder mathematical theory and apply it to obtain a large number of decidability results. The method of solution involves…
The Monadic Second-Order Logic of Graphs. I. Recognizable Sets of Finite Graphs
The Monadic Quantiier Alternation Hierarchy over Graphs Is Innnite
We show that the monadic second-order quantiier alternation hierarchy over nite directed graphs and over nite two-dimensional grids is innnite. For this purpose we investigate sets of grids where the…
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