D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, Vol.54, pages 267--276, 1987. Home/Search Document Not in Database Summary Related Articles Check |
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Relating Hierarchy of Linear Temporal Properties to Model.. - Cerna, Pelanek (2003) (Correct)
....accepts a word w if all runs on w are accepting. Deterministic automata are such that #(q, a) 1for all q # Q, a # # (there is a unique run on each word) Alternating automata form a generalisation of nondeterministic and universal automata. For the definition of alternating # automata see e.g. [24]. By the abuse of notation, we use (q, r) # # with the meaning #a # # : r # #(q,a) For a run # we define the infinity set, Inf (#) to be the set of all states that appear infinitely often in # and the occurrence set, Occ(#) to be the set of states that appear at least once in #. Acceptance ....
D. E. Muller and P. E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267 -- 276, 1987.
Automata and Logic - Walukiewicz (2002) (Correct)
....for alternating automata is Exptime complete. The Exptime algorithm is to translate the automaton into a nondeterministic automaton and check the emptiness of the result. An important point here is that although the automaton grows exponentially in the translation, the acceptance conditions do not [39, 18]. Another important problem is the model checking problem: For a finite graph G and a calculus formula # decide if # holds in the given vertex of G . The problem is equivalent to the emptiness problem for Mostowski alternating tree automata over one letter alphabet [17] The later problem is in ....
D. Muller and P. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987.
... Afmc - Kupferman, Vardi (Correct)
....T trees( we denote by comp(T ) the set of labeled trees that are not in T ; thus comp(T ) trees( n T . Automata on infinite trees (tree automata, for short) run on leafless labeled trees. Alternating tree automata generalize nondeterministic tree automata and were first introduced in [MS87]. Symmetric alternating tree automata [JW95,Wil99] are capable of reading trees with variable branching degrees. When a symmetric automaton reads a node of the input tree it sends copies to all successors of that node or to some successor. Formally, for a given set X , let B (X) be the set of ....
.... calculus formulas are transformed into a disjunctive form. The removal of conjunctions described there is similar to the removal of universal branches in alternating tree automata (and indeed it involves the same determinization construction that is present in the automata theoretic approach [MS87]) It is then shown that disjunctive calculus formulas correspond to automata. Our focus here is on the translation of 2 formulas to symmetric monotonic nondeterministic Buchi tree automata. It is possible to recast our proof in an extension of the framework of automata [Wal03] but we ....
D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. TCS, 54:267--276, 1987.
The µ-Calculus Alternation-Depth Hierarchy is Strict on Binary.. - Arnold (1999) (Correct)
.... to characterize the weakly definable sets of trees [11] providing a direct proof of the Mostowski s result on the hierarchy of alternating automata [10] instead of relying on a result of Thomas [15] 1 Alternating parity automata An alternating parity automaton is an alternating automaton (see [12]) where the acceptance criterion is given by a parity condition. Namely, it is a tuple hA; Q; ffi; n; ri where ffl the alphabet A is a finite set of binary symbols, ffl Q is a finite set of states, ffl n is a natural number (n 0) called the type of A and r is a mapping from Q to f1; ....
....of trees over the alphabet fc i j i = 1; ng are exactly the tree languages defined by Niwi nski in [13] to show the strictness of the hierarchy of non deterministic automata. Let A be the automaton obtained from A by exchanging and . The complementation theorem of Muller and Schupp [12] now reads as follows, where TA is the set of all binary trees built on the alphabet A. A (q) L A (q) We denote by Sigma n (resp. Pi n ) the family of binary tree languages in the form L A (q) for some automaton A of type n. In particular, n 2 Sigma n and W n 2 Pi n . As a ....
D. E. Muller and P. E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987.
The ...-calculus on trees and Rabin's complementation theorem - Arnold (1994) (2 citations) (Correct)
.... complementation theorem [10] for any tree automaton A there is a tree automaton A such that L(A ) the set of infinite trees accepted by A , is the complement of L(A) The Rabin s proof of this theorem is usually considered as a hard one, and several other proofs have been offered [3, 5, 6, 2]. All these proofs obey the same pattern. They consider a class O of objects such that a set of trees L(O) is associated with any object O in this class, and they show that O has the two following properties: Equivalence property : for any set T of trees, there is an automaton A such that T = ....
.... this case the Equivalence property is 8A; 9G : L(A) L(G; I) 8G; 9A : L(A) L(G; II) and the Complementation property amounts to saying that for any game on any tree, one of the two players has a winning finite state strategy (see also the survey of Thomas [11] 1 For Muller and Schupp [6], O is the class of alternating automata, which contains the usual automata, so that the Equivalence property is: for any alternating automaton B there is an automaton A such that L(B) L(A) They do not prove this property but claim it can be easily obtained by Gurevich and Harrinton s method. ....
D. E. Muller, P. E. Schupp. Alternating automata on infinite trees. Theor. Comput. Sci., 54:267--276, 1987.
Pushdown Specifications - Kupferman, Piterman, Vardi (2002) (3 citations) (Correct)
....for every x 2 , we have (x) L( x) We then say that the size of the regular tree h ; i, denoted k k, is jQj, the number of states of D. Alternating two way tree automata Alternating automata on infinite trees generalize nondeterministic tree automata and were first introduced in [MS87] Here we describe alternating two way tree automata. For a finite set X , let B (X) be the set of positive Boolean formulas over X . For a set Y X and a formula 2 B (X) we say that Y satisfies iff assigning true to elements in Y and assigning false to elements in X nY makes ....
D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987.
Logics for Mazurkiewicz Traces - Leucker (2002) (4 citations) (Correct)
....final states of an automaton means that a path of a previously accepting run is it no longer since it visits only finitely many final states. We sum up: q 0 q 2 q 1 q 3 tt # Q 1 Q 3 Q 2 Figure 4.7: The transition graph of a weak alternating Buchi automaton and its partitions Theorem 4.2. 17 ( MS87] Q, #, q 0 , F ) be a weak alternating Buchi automaton over #. Then for = Q, #, q 0 , Q F ) we have where #(q, a) #(q, a) for all q #. A formal and simple proof of this result can be found in [LT00] Note that the sizes of the original and the complemented automaton are ....
D. E. Muller and P. E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987.
The Complexity of the Graded µ-Calculus - Kupferman, Sattler, Vardi (Correct)
....b. If is satisfiable, then is satisfied in a tree whose degree is at most l (b 1) 3 Graded Automata Automata over infinite trees (tree automata) run over labeled trees that have no leaves [Tho90] Alternating automata generalize nondeterministic tree automata and were first introduced in [MS87] Intuitively, while a nondeterministic automaton that visits a node x of the input tree send one copy of itself to each of the successors of x, an alternating automata can several copies of itself to the same node. 3.1 Graded Alternating Parity Tree Automata For a given set Y , let B (Y ) ....
D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987.
Automata for the µ-calculus and Related Results - Janin, Walukiewicz (1995) (Correct)
....disjunctions act like nondeterministic choices, conjunctions act rather like universal branching of alternating automata. Such an alternating behavior of conjunctions is the source of many difficulties. From automata theory we know that alternating automata are equivalent to nondeterministic ones [7]. This suggests that every formula should be equivalent to a formula which does not have universal branching behaviors represented by conjunctions. Of course we cannot discard conjunctions completely from positive formulas as shown by the formula (haip) a] p q) Note that the conjunction in ....
D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987.
Local Logics for Traces - Walukiewicz (Correct)
....a, S) b) # # # # # ( #, a, S # b ) if bDS ( #, a, S) if [bD(S # a ) # # ( #, a, S # b ) if (a, b) # D and [bDS] In the above, for a set S # # we write bDS to mean that (b, c) # D for some c # S. The definition of a run of such an automaton is standard (cf. [7]) In particular a run is a tree labelled with pairs consisting of a position in w and a state of A. A run of A is accepting if on every path P of it the number min ## q) q appears infinitely often on P is even. Most of the cases of the definition of transition function are standard. The ....
D. Muller and P. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987.
An Automata-Theoretic Approach to Reasoning about.. - Kupferman, Vardi (2000) (16 citations) (Correct)
....a labeled tree. We say that an ( Upsilon [ f g) Theta Sigma ) labeled Upsilon tree hT; V i is Upsilon exhaustive if for every node x 2 T , we have V (x) 2 fdir(x)g Theta Sigma . Alternating automata on infinite trees generalize nondeterministic tree automata and were first introduced in [MS87] Here we describe alternating two way tree automata. For a finite set X , let B (X) be the set of positive Boolean formulas over X (i.e. boolean formulas built from elements in X using and ) where we also allow the formulas true and false, and, as usual, has precedence over . For a set Y ....
D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987.
Extended Temporal Logic Revisited - Kupferman, Piterman, Vardi (2001) (4 citations) (Correct)
....state q; i.e, is A q = h Sigma; Q; q; ae; F i. Given a 2 way alternating Buchi automaton A = h Sigma; Q; q 0 ; ae; F i, the dual of A is the coB uchi automaton e A = h Sigma; Q; q 0 ; e ae; F i, where e ae(s; a) is the dual of ae(s; a) The automata A and e A accept complementary languages [MS87] i.e. L( e A) Sigma n L(A) Given an alternating hesitant automaton A = h Sigma; B; C; q 0 ; ae; F i, the dual of A is the alternating hesitant automaton e A = h Sigma; C; B; q 0 ; e ae; F i, where the set of Buchi states and the set of co Buchi states switch roles. Again, e A ....
D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987. 15
Clausal Resolution for CTL - Bolotov, Dixon, Fisher (Correct)
....definitions from the graph and automata theory. Due to the lack of the space we sketch outlines of these proofs, again referring to [3] for full details. First of all note, that within the proofs of the theorems 3 and 4, we utilise ideas from the alternating automata approach to temporal logic [13, 14, 2, 17] and essentially use the finite tree model property of CTL . The following observation is important for the proofs. The structure of a set of SNF C rules (see x3) can be related to that of a transition system. The initial rules provide the starting conditions while the step and ....
D. E. Muller and P. E. Schupp. Alternating automata on infinite trees. In Theoretical Computer Science, pp 267-276, vol.54, 1987.
The Complexity of Enriched -Calculi - Piero Bonatti Carsten (Correct)
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D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, Vol.54, pages 267--276, 1987.
Verification of Open Systems - Orna Kupferman Hebrew (Correct)
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D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987.
Automata-Theoretic Techniques for Temporal Reasoning - Vardi (2006) (Correct)
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D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987.
The Complexity of Enriched μ-Calculi - Bonatti, Lutz, Murano, Vardi (Correct)
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D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, Vol.54, pages 267--276, 1987.
Safraless Decision Procedures - Orna Kupferman Hebrew (Correct)
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D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987.
Safraless Decision Procedures - Orna Kupferman Hebrew (Correct)
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D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. In Automata on Infinite Words, volume 192, pages 100--107. Lecture Notes in Computer Science, Springer-Verlag, 1985.
The Bulletin of Symbolic Logic - Volume Number June (Correct)
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D. E. Muller and P. E. Schupp, Alternating automata on infinite trees, Theoretical Computer Science, vol. 54 (1987), pp. 267--276.
Model Checking for Database Theoreticians - Moshe Vardi Rice (Correct)
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D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987.
On the Decidability of Timed CCP - Valencia (Correct)
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D. E. Muller and P. E. Schupp. Alternating automata on infinite trees. Theor. Comput. Sci., 54(2-3):267--276, 1987.
Global Model-Checking of Infinite-State Systems - Piterman, Vardi (Correct)
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D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. TCS, 54, 1987.
On Translating Linear Temporal Logic into Alternating and.. - Tauriainen (2003) (3 citations) (Correct)
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D. E. Muller and P. E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987.
Methods for the Transformation of ω-Automata: Complexity.. - Löding (Correct)
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D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267--276, 1987. 4, 21, 23
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