Alternating automata, the weak monadic theory of trees and its complexity

Muller, David E.; Saoudi, A.; Schupp, Paul E.

doi:10.1016/0304-3975(92)90076-r

Cited by 44 publications

(32 citation statements)

References 8 publications

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“…The notion of weakness employed in the wPRS formalism corresponds to that of weak automaton [MSS92] in automata theory. The behaviour of a weak state unit is acyclic, i.e.…”

Section: Extended Prsmentioning

confidence: 99%

“…This paper presents a hierarchy of PRS classes and their respective extensions of three types: fcPRS classes ( [Str02], inspired by concurrent constraint programming [SR90]), wPRS classes ( [KŘS03], PRS systems equipped with weak FSU inspired by weak automata [MSS92]), and state-extended PRS classes [JKM01]. The classes in the hierarchy (depicted in Figure 1) are related by their expressive power with respect to (strong) bisimulation equivalence.…”

Section: Introductionmentioning

confidence: 99%

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Extended Process Rewrite Systems: Expressiveness and Reachability

Křetínský

Řehák

Strejček

2004

CONCUR 2004 - Concurrency Theory

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Abstract. We unify a view on three extensions of Process Rewrite Systems (PRS) and compare their expressive power with that of PRS. We show that the class of Petri nets is less expressive up to bisimulation equivalence than the class of PA processes extended with a finite state control unit. Further we show our main result that the reachability problem for PRS extended with a so called weak finite state unit is decidable.

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“…The notion of weakness employed in the wPRS formalism corresponds to that of weak automaton [MSS92] in automata theory. The behaviour of a weak state unit is acyclic, i.e.…”

Section: Extended Prsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extended Process Rewrite Systems: Expressiveness and Reachability

Křetínský

Řehák

Strejček

2004

CONCUR 2004 - Concurrency Theory

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“…This result was first proved by Rabin [13] in terms of monadic second-order logic; the automata-theoretic statement was given by Muller, Saoudi, and Schupp [12] in terms of weak alternating automata. It is not difficult to adapt Rabin's proof to obtain aslightly stronger-separation property: any two disjoint Büchi recognizable sets of trees can be separated by a weakly recognizable set (see, e.g., [7]).…”

Section: Introductionmentioning

confidence: 84%

On the Separation Question for Tree Languages

Arnold¹,

Michalewski

Niwiński

2013

Theory Comput Syst

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We show that the separation property fails for the classes Σ n of the RabinMostowski index hierarchy of alternating automata on infinite trees. This extends our previous result (obtained with Szczepan Hummel) on the failure of the separation property for the class Σ 2 (i.e., for co-Büchi sets). The non-separation result is also adapted to the analogous classes induced by weak alternating automata.To prove our main result, we first consider the Rabin-Mostowski index hierarchy of deterministic automata on infinite words, for which we give a complete answer (generalizing previous results of Selivanov): the separation property holds for Π n and fails for Σ n -classes. The construction invented for words turns out to be useful for trees via a suitable game.It remains open if the separation property holds for all classes Π n of the index hierarchy for tree automata. To give a positive answer it would be enough to show the reduction property of the dual classes-a method well-known in descriptive set theory. We show that it cannot work here, because the reduction property fails for all classes in the index hierarchy.

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“…The following definition of weak automata generalizes the standard definition [13,17], where the automata's acceptance condition is a Büchi acceptance condition. Let A be the alternating S-automaton Q, Σ, (δ D ) D ⊆D , q I , A .…”

Section: Inherited Propertiesmentioning

confidence: 99%

Alternation Elimination for Automata over Nested Words

Dax

Klaedtke

2011

Foundations of Software Science and Computational Structures

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Abstract. This paper presents constructions for translating alternating automata into nondeterministic nested-word automata (NWAs). With these alternation-elimination constructions at hand, we straightforwardly obtain translations from various temporal logics over nested words from the literature like CaRet and μNWTL, and extensions thereof to NWAs, which correct, simplify, improve, and generalize the previously given translations. Our alternation-elimination constructions are instances of an alternation-elimination scheme for automata that operate over the tree unfolding of graphs. We obtain these instances by providing constructions for complementing restricted classes of automata with respect to the graphs given by nested words. The scheme generalizes our alternation-elimination scheme for word automata and the presented complementation constructions generalize existing complementation constructions for word automata.

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Alternating automata, the weak monadic theory of trees and its complexity

Cited by 44 publications

References 8 publications

Extended Process Rewrite Systems: Expressiveness and Reachability

Extended Process Rewrite Systems: Expressiveness and Reachability

On the Separation Question for Tree Languages

Alternation Elimination for Automata over Nested Words

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