E.A. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In Proc. 29th IEEE Symp. on Foundations of Computer Science, pages 328--337, White Plains, October 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....function associated with I and ae, and the extension function associated with M and ae map, respectively, any concept C and the corresponding formula q(C) to the same subset of Delta = S. Hence the thesis follows. 2 It follows that we may transfer both decidability and complexity results ([73, 51, 106]) for the modal mu calculus to ALC. Thus, we can immediately state what is the complexity of reasoning with ALC concepts and ALC TBoxes. Theorem 56 Satisfiability of ALC concepts, satisfiability of ALC TBoxes, and logical implication in ALC TBoxes are EXPTIME complete problems. 112 The ....

....with ALC concepts and ALC TBoxes. Theorem 56 Satisfiability of ALC concepts, satisfiability of ALC TBoxes, and logical implication in ALC TBoxes are EXPTIME complete problems. 112 The description logic ALCN Proof Since the satisfiability problem for modal mu calculus is EXPTIME complete ([51]) by Theorem 55 the satisfiability of ALC concepts can be checked in deterministic exponential time (tight bound) Hence, by Theorem 54, the thesis follows. 8.6 The description logic ALCN In this section, study the description logic ALCN , obtained from ALC by including qualified number ....

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E. A. Emerson and C. S. Jutla. The complexity of tree automata and logics of programs. In Proceedings of the 20th Annual Symposium on the Foundations of Computer Science, pages 328--337, 1988.

.... Calculus is a tautology, i.e. it is valid in all models. It is known that it is possible to check validity not in all models but in all nite models only due to a so called nite model property of the Calculus formulae: a formula is satis able in a model i it is satis able in a nite model [11]. But this reduction does not make the problem trivial Moreover, the reduction itself is just a corollary of the decidability of the Calculus with an exponential upper bound. In principle, an exponential decidability result for this logic can be proved indirectly by means of an ....

....does not make the problem trivial Moreover, the reduction itself is just a corollary of the decidability of the Calculus with an exponential upper bound. In principle, an exponential decidability result for this logic can be proved indirectly by means of an automata theoretic technique [29, 11]. Basically, the automata theoretic approach comprises two stages: rst, a reduction of the decidability problem for a particular logic to the emptiness problem for a particular class of automata on in nite trees, and then application of a direct decision procedure for this emptiness problem. ....

Emerson E.A., Jutla C.S. The Complexity of Tree Automata and Logics of Programs. SIAM J. Comput., v.29, n1, 1999, p.132-158.

....t v t g. We say that a tree language T has the n branching property if for every tree t 2 T , there exists a tree t 0 v t of branching degree n such that [t 0 ; t] T . A typical emptiness test for parity tree automata starts with a statement similar to the following, see, for instance, [5]. Lemma 10 Every tree language recognized by a parity tree automaton with n states has the n branching property. We prove a similar statement for modal top down automata. Lemma 11 Every tree language recognized by a modal top down automaton with n states has the n branching property. Proof. To ....

....) branching property. For the proof of this, just consider the union of the two trees that are guaranteed to exist by the individual small branching properties. 7.1. 3 Emptiness Test Consider a typical emptiness test for a parity tree automaton A with n states, for instance, the one described in [5]. In the rst step, one exploits the n branching property. Using Safra s construction, one constructs a nondeterministic Rabin tree automaton A with 2 O(n log n) states and O(n) pairs which is equivalent to A on all n branching trees. This can be an automaton with transitions depending on ....

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E.A. Emerson and C.S. Jutla. The Complexity of Tree Automata and Logics of Programs (Exteded Abstract). In IEEE Symposium on Foundations of Computer Science (FOCS'88), pages 328-337, Los Alamitos, California, October 1988. IEEE Computer Society Press.

....on all the paths. The complexity of decision problems for tree automata is more subtle than for word automata. Recall that the emptiness problem, is to decide if there is a tree accepted by a given automaton. For Buchi automata the problem is Ptime complete. For Rabin automata it is NP complete [18]. As Streett conditions are negations of Rabin conditions, the emptiness problem for these automata is coNP complete. The exact complexity of the emptiness problem for Mostowski automata is not known. The problem is in NP and co NP [17] Determining whether the problem is in Ptime is one of the ....

....of graphs is MSOL definable i# it is calculus definable. We briefly summarize the complexity of some decision problems for the calculus and alternating automata. The satisfiability problem for the calculus is to decide whether a given formula has a model. The problem is Exptime complete [51, 18]. For the lower bound one can reduce the problem of universality of tree automata. For the upper bound one can use the translation to alternating automata. The emptiness problem for alternating automata is Exptime complete. The Exptime algorithm is to translate the automaton into a ....

[Article contains additional citation context not shown here]

E. A. Emerson and C. S. Jutla. The complexity of tree automata and logics of programs. In 29th FOCS, 1988.

....emptiness problem of standard tree automata. We obtain an Exptime procedure for checking the non emptiness of TBTA as this problem is Ptime for BTA [BL69] a nondeterministic Exptime procedure for timed Rabin tree automata as this problem is known to be NP complete for Rabin tree automata [Rab72, EJ88] and an Expspace procedure for TMTA as this problem is Exptime for MTA [McN93] By Lemma 4.1, the non emptiness problem for TBTA is Exptime complete. Moreover, it is possible to prove that the complexity of checking the emptiness for TMTA is nondeterministic Exptime simply by observing the ....

E.A. Emerson and C.S. Jutla. The complexity of tree automata and logics of programs. In Proc. of the 29th IEEE-CS Symposium on Foundations of Computer Science, pages 328 { 337, 1988.

....and complementation. In the following remark, we recall some known results on the decision problems of B uchi and Rabin tree automata. Remark 2. The emptiness problem for BTA is decidable [13] and is LOGSPACE complete for PTIME [15] The non emptiness problem for RTA is NP complete [12, 5]. Given a TA A = hQ; Q 0 ; F i, we de ne the size of A, denoted by Size(A) as the sum of the sizes of Q, and F . Let T be a language, we de ne the size of T , denoted by Size TA (T ) as the minimum over the sizes of the TA s recognizing T , that is, Size TA (T ) Size(A) where A is a ....

....tree [14] we have the following lemma. Lemma 1. Any non empty language accepted by a Landweber tree automaton contains a regular tree. Since the constructed automaton R is linear in the size of the starting automaton L, and the non emptiness problem for Rabin tree automata is NPcomplete [5, 12], we get a nondeterministic polynomial time algorithm to solve the non emptiness problem for Landweber tree automata. In the following, we Algorithm 1. P Q repeat P P P ; for (q; a; q1 ; q2 ) 2 such that q 2 P do if (p; p 2 fq1 ; q2g, p 6= p , p 2 Q and p 2 P ) or q1 ....

E.A. Emerson and C.S. Jutla. The complexity of tree automata and logics of programs. In Proc. of the 29th IEEE-CS Symposium on Foundations of Computer Science, pages 328 - 337, 1988.

....Only three different degrees of solution are possible, corresponding to weak (E : F q) strong (A: F q) and strong cyclic (AE : F q) planning. Finally, we present a planning algorithm for the new goal language and we study its complexity. The algorithm is based on an automata theoretic approach [13, 18]: planning domains and goals are represented as suitable automata, and planning is reduced to the problem of checking whether a given automaton is nonempty. The proposed algorithm has a time complexity that is doubly exponential in the size of the goal formula. It is known that the planning ....

....theorem states that it is possible to build a tree automaton that accepts all the trees satisfying a CTL formula. The tree automaton has a number of states that is doubly exponential and a parity index that is exponential in the length of the formula. A proof of this theorem can be found in [13]. Theorem 2 Let be a CTL formula, and let D N be a finite set of arities. One can build a parity tree automaton A that accepts all and only the labelled D trees that satisfy . The automaton A has 2 states and parity index 2 , where j j is the length of formula . 3. A ....

E. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In Proc. of 29th IEEE Symp. on Foundations of Computer Science, pages 328--337, 1988.

.... calculus. The propositional calculus satisfies a finite model theorem, as first shown in [Kozen, 1988] Progressively better decidability results were obtained in [Kozen and Parikh, 1983; Vardi and Stockmeyer, 1985; Vardi, 1985b] culminating in a deterministic exponential time algorithm of [Emerson and Jutla, 1988] based on an automata theoretic lemma of [Safra, 1988] Since the calculus subsumes PDL, it is EXPTIME complete. In [Kozen, 1982; Kozen, 1983] an axiomatization of the propositional calculus was proposed and conjectured to be complete. The axiomatization consists of the axioms and rules ....

....Sherman, 1985] see [Harel et al. 2000] In recent years, the development of the automata theoretic approach to logics of programs has prompted renewed inquiry into the complexity of automata on infinite objects, with considerable success. See [Courcoubetis and Yannakakis, 1988; Emerson, 1985; Emerson and Jutla, 1988; Emerson and Sistla, 1984; Manna and Pnueli, 1987; Muller et al. 1988; Pecuchet, 1986; Safra, 1988; Sistla et al. 1987; Streett, 1982; Vardi, 1985a; Vardi, 1985b; Vardi, 1987; Vardi and Stockmeyer, 1985; Vardi and Wolper, 1986b; Vardi and Wolper, 1986a; Arnold, 1997a; Arnold, 1997b] and ....

[Article contains additional citation context not shown here]

E. A. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In Proc. 29th Symp. Foundations of Comput. Sci., pages 328--337. IEEE, October 1988.

....logic to automata. After the works of B uchi and Rabin [B uc62,Rab69] various classes of automata turned out to be well suited to solve decision procedures for logical problems, including some for temporal logics (see e.g. VW94,Var97,KVW00] for the calculus and its fragments (see e.g. EJ99,SE89,VW86,EJS01,Var98] and for description logics (see e.g. CDGL99,CGL02] to quote three families of logics. For instance, translating formulae in temporal logics to automata is a standard approach for implementing model checking, see e.g. the model checking tool SPIN [Hol97] More ....

A. Emerson and C. Jutla. The complexity of tree automata and logics of programs. SIAM Journal of Computing, 29:132-158, 1999.

.... since SIM contains a universal modal connective with a family of B modal connectives (see e.g. Spa93,CL94,Hem96] The ExpTime upper bound is established by an exponential reduction into the emptiness problem for B uchi automata on in nite trees that is known to be in PTime (see e.g. VW86,EJ88] As mentioned previously, this technique is nowadays standard for logics of programs, but it has never been applied to information logics. Indeed, relative information logics contain features that are not traditionally present in most logics of programs (e.g. the presence of nominals on the ....

....2 f1; Kg hr(s) T (s) r(s 1) r(s K)i 2 . A run r on T is accepting i for every path in T there is a state in F that occurs in nitely often. Deciding whether a B uchi tree automaton for ; K trees has an accepting run can be done in polynomial time [VW86] see also [Rab70,EJ88] For SIM, we only need to consider a restricted class of tree automata, namely those automata in which all the states are terminal, often referred to as safety automata. 7.1 The Construction Before giving the formal de nition of A , we give an intuitive description of it and the conditions ....

A. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In 29th Annual Symposium on Foundations of Computer Science, pages 328-337. IEEE Computer Society Press, 1988.

....PCTL # is equivalent to the one of monadic second order logic on infinite binary trees with second order quantifiers over infinite paths [18] Theorem 5.2 (Expressive completeness of CTL # and PCTL # ) CTL # and PCTL # are as expressive as MPL[ when interpreted over infinite binary trees. In [8], Emerson and Jutla prove that the problem of testing satisfiability for CTL # is 2EXPTIME complete. As pointed out by Hafer and Thomas [18] Theorem 5.2 can be generalized to CTL # k and PCTL # k with respect to MPL[ # i ) i=0 ] by incorporating successors into both temporal and monadic path ....

....(# i ) i=0 ] when interpreted over infinite k ary trees. Furthermore, a decision procedure for CTL # k can be obtained by means of the following non trivial adaptation of the decision procedure for CTL # originally developed by Emerson and Sistla [10] and later refined by Emerson and Jutla [8]. Let us assume k = 2 (the generalization to an arbitrary k is straightforward) As a preliminary step, we provide an embedding of PTL 2 into PTL. To this end, we define a translation # of formulas and models of PTL 2 , over an alphabet #, to formulas and models of PTL, over an extended alphabet ....

[Article contains additional citation context not shown here]

E.A. Emerson and C.S. Jutla. The complexity of tree automata and logics of programs. In Proceedings of the 29th Annual Symposium on Foundations of Computer Science, pages 328--337. IEEE, 1988.

.... (the emptiness problem is P complete for Buchi tree automata, and NP complete for Rabin tree automata) 114] In particular, the emptiness problem for a Rabin tree automaton with n states and m accepting pairs is solvable in time (n m) O(m) and hence it is linear in the number of states [34]. In the following, we compare the expressive power of the above defined finite state automata classes with that of the monadic theories introduced in Section 2.2. Recall that, as explained in Remark 2.1.1, labeled Kripke structures accepted by automata correspond to labeled relational structures ....

....] 35] Theorem 2.4.8 (Expressiveness of QCTL # k and EQCTL # k ) QCTL # k and EQCTL # k are expressively equivalent to MSOP [ pre , # i ) i=0 ] when interpreted over finite (resp. infinite) k ary trees. Emerson and Jutla proved that the satisfiability problem for CTL # is 2EXPTIMEcomplete [34]. Furthermore, a decision procedure for CTL # k can be obtained by means of the following non trivial adaptation of the decision procedure for CTL # originally developed by Emerson and Sistla [35] and later refined by Emerson and Jutla [34] We start by defining an auxiliary linear time logic, ....

[Article contains additional citation context not shown here]

E. A. Emerson and C. S. Jutla. The Complexity of tree Automata and Logics of Programs. In In Proceedings op the Annual IEEE-CS Symposium in Foundations of Computer Science, pages 328--337, 1988.

....automated inductive theorem proving [5] fast tree matching [28] automated model building in first order logic [37] etc. These applications deal with automata on finite trees. We won t deal with automata on infinite trees [42] which are also fundamental, e.g. in temporal and program logics [14]. Two way automata, a.k.a. pushdown processes, where transitions may not only construct but also destruct terms, are also classical. The relation with certain Horn sets was pioneered in [16] and refined in e.g. 7] Cartesian approximation is the key to define upper approximations of various ....

E. A. Emerson and C. S. Jutla. The complexity of tree automata and logics of programs (extended abstract). In 29th FOCS, pages 328--337, 1988.

....all the paths. The complexity of decision problems for tree automata is more subtle than for word automata. Recall that the emptiness problem, is to decide if there is a tree accepted by a given automaton. For B uchi automata the problem is Ptime complete. For Rabin automata it is NP complete [18]. As Streett conditions are negations of Rabin conditions, the emptiness problem for these automata is coNP complete. The exact complexity of the emptiness problem for Mostowski automata is not known. The problem is in NP and co NP [17] Determining whether the problem is in Ptime is one of the ....

....of graphs is MSOL de nable i it is calculus de nable. We brie y summarize the complexity of some decision problems for the calculus and alternating automata. The satis ability problem for the calculus is to decide whether a given formula has a model. The problem is Exptime complete [50, 18]. For the lower bound one can reduce the problem of universality of tree automata. For the upper bound one can use the translation to alternating automata. The emptiness problem for alternating automata is Exptime complete. The Exptime algorithm is to translate the automaton into a ....

[Article contains additional citation context not shown here]

E. A. Emerson and C. S. Jutla. The complexity of tree automata and logics of programs. In 29th FOCS, 1988.

....are based on tableaux techniques as in [Bal98, BGM98] see e.g. the proofs of Theorem 6 and Lemma 27) Related work. Formal language theory and automata theory are already used for logics such as modal calculus, Propositional Dynamic Logic PDL, Propositional Temporal Logic PTL, CTL (see e.g. [VW86, VW94, EJ99]) but from a di erent perspective than here. We can also mention the Extended Temporal Logic (ETL) that can express properties of a sequence de nable by a right linear grammar [Wol83, VW94] In our work, we are only dealing with automata on nite words. Furthermore, our work continues the line of ....

A. Emerson and C. Jutla. The complexity of tree automata and logics of programs. SIAM Journal of Computing, 29:132-158, 1999. Journal version of the FOCS'88 paper.

....(such as CTL or L ) can be reduced to S2S while preserving satisfiability. Thus Rabin s decidability result can be used to show decidability of these logics. However, as S1S, S2S is non elementary. A computationally more efficient approach is to reduce to the corresponding tree automata, c.f. [17, 58]. We conclude the tutorial with a look at S2S and tree automata and survey some of the expressiveness results currently known. The language of S2S is the monadic second order language of two successor functions. For the syntax, terms, ranged over by t, are generated by t : x j j t0 j t1 ....

E. A. Emerson and C. S. Jutla. The complexity of tree automata and logics of programs. In Proc. 29th Symp. Foundations of Computer Science, pages 328--337, 1988.

....Centre of the Danish National Research Foundation. can be encoded into the calculus. On binary trees the logic is as expressive as monadic second order logic of two successors [18, 6] On the other hand the logic is manageable. Satisfiability problem for the logic was shown to be EXPTIME complete [15, 23, 4] which means that it is of the same complexity as for many much less expressive logics. The best known upper bound for the model checking problem is exponential but it is polynomial if nesting of fixpoints is bounded [3, 1] One of lacking elements in this picture was finitary complete ....

E. Allen Emerson and Charanjit S. Jutla. The complexity of tree automata and logics of programs. In 29th IEEE Symp. on Foundations of Computer Science, 1988.

....by A f , i.e. L(M) L(A f ) This language inclusion problem may be decided in PSPACE . For the tree approach, Model Checking can be phrased as M 2 L(A f ) which is a membership problem. The complexity of determining membership depends on the acceptance conditions of the tree automaton [EJ 88] The model checking approach has by now been applied to a wide variety of logics such as branching time logics [CE 81, QS 82, EL 86] and linear time logic [LP 85] and to a variety of programming models such as finite state programs [CE 81, QS 82] and real time systems [ACD 90] 2.6 ....

Emerson, E.A., Jutla, C.S. The Complexity of Tree Automata and Logics of Programs (Extended Abstract), FOCS 1988.

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E.A. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In Proc. 29th IEEE Symp. on Foundations of Computer Science, pages 328--337, White Plains, October 1988.

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E.A. Emerson and C.S. Jutla. The complexity of tree automata and logics of programs. In FOCS'88, pages 328--337, 1988.

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E.A. Emerson and C.S. Jutla. The complexity of tree automata and logics of programs. In Proc. of the 29th IEEE-CS Symposium on Foundations of Computer Science, pages 328 -- 337, 1988.

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E.A. Emerson and C.S. Jutla. The complexity of tree automata and logics of programs. In Proceedings 29th Annual IEEE Symp. on Foundations of Computer Science, FOCS'88, pages 328 -- 337, 1988.

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E.A. Emerson and C.S. Jutla. The complexity of tree automata and logics of programs. In Proc. of the 29th IEEE-CS Symposium on Foundations of Computer Science, pages 328 - 337, 1988.

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E.A. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In FOCS'88, pages 328-337. IEEE Computer Society Press, 1988.

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E.A. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In FOCS'88, pages 328--337. IEEE Computer Society Press, 1988.

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Emerson, E., & Jutla, C. (1988). The complexity of tree automata and logics of programs. In Proc. of 29th IEEE Symp. on Foundations of Computer Science, pp. 328--337.

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E.A. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In Proc. 29th IEEE Symp. on Foundations of Computer Science, pages 328--337, White Plains, October 1988.

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E. A. Emerson and C. Jutla, The complexity of tree automata and logics of programs, Proceedings of the 29th IEEE symposium on foundations of computer science, White Plains, October 1988, pp. 368--377.

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E.A. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In Proc. 29th IEEE Symp. on Foundations of Computer Science, pages 328--337, White Plains, October 1988.

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E.A. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In Proceedings of the 29th IEEE Symposium White Plains, October 1988.

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E. Emerson and C. Jutla. The complexity of tree automata and logics of programs. SIAM Journal on Computation, 29(1):132--158, 1999.

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E. Allen Emerson and Charanjit S. Jutla. The complexity of tree automata and logics of programs. In Proc. 29th IEEE Symposium on Foundations of Computer Science, pages 328--

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E.A. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In Proc. 29th IEEE Symp. on Foundations of Computer Science, pages 328-337, White Plains, October 1988.

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E. A. Emerson and C. S. Jutla. The complexity of tree automata and logics of programs. SIAM Journal on Computing, 29(1):132--158, February 2000.

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E. A. Emerson and C. S. Jutla. The complexity of tree automata and logics of programs. In FOCS, pages 328--337, 1988.

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E.A. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In Foundations of Computer Science (FOCS), pages 328--337. IEEE Computer Society Press, 1988.

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Emerson, E., and Jutla, C. (1988). The complexity of tree automata and logics of programs. Procs. 29th IEEE Symp. on Foundations of Comput. Science, 328-337.

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E. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In Proc. Foundations of Computer Science, pages 328--337. IEEE Press, 1988.

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E. Allen Emerson and Charanjit S. Jutla. The complexity of tree automata and logics of programs (extended abstract). In FoCS

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E. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In Proceedings of the Twenty-ninth Annual Symposium on Foundations of Computer Science, pp. 328--337. IEEE, 1988.

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E. A. Emerson and C. S. Jutla. The complexity of tree automata and logics of programs. In Foundations of Computer Science, pages 328-337, 1988.

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A. Emerson and C. Jutla, The complexity of tree automata and logics of programs, in Proc. 29th IEEE Symp. on Foundations of Computer Science, 1988, pp. 328-337.

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E. A. Emerson and C. S. Jutla. The complexity of tree automata and logics of programs. In Foundations of Computer Science, pages 328337, 1988.

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E.A. Emerson and C.S. Jutla. The complexity of tree automata and logics of programs. In Proc. of the 29th IEEE-CS Symposium on Foundations of Computer Science, pages 328 - 337, 1988.

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E.A. Emerson and C.S. Jutla. The Complexity of Tree Automata and Logics of Programs (Exteded Abstract). In IEEE Symposium on Foundations of Computer Science (FoCS'88), pages 328-337, Los Alamitos, California, October 1988. IEEE Computer Society Press.

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E. A. Emerson and C. S. Jutla. The complexity of tree automata and logics of programs. SIAM Journal on Computing, 29(1):132--158, February 2000.

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E. A. Emerson and C. S. Jutla. The complexity of tree automata and logics of programs. SIAM Journal on Computing, 29(1):132-158, February 2000.

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E.A. Emerson and C.S. Jutla. The complexity of tree automata and logics of programs. In Proceedings of the 29th Annual Symposium on Foundations of Computer Science, pages 328--337. IEEE, 1988.

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E.A. Emerson and C.S. Jutla. The complexity of tree automata and logics of programs. In Proceedings of the 29th IEEE-CS Symposium on Foundations of Computer Science, pages 328 - 337, 1988.

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E.A. Emerson and C.S. Jutla. The complexity of tree automata and logics of programs. In 29th IEEE Symp. on Foundations of Computer Science, 1988.

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