Citations: Complexity Classes Defined via k-valued Functions

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U. Hertrampf. Complexity classes defined via k-valued functions. In Proceedings 9th Structure in Complexity Theory, pages 224--234. IEEE Computer Society Press, 1994.

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Finite Automata with Generalized Acceptance Criteria - Peichl, Vollmer (1999) (1 citation) (Correct)

....complexity measure. Let Phi be one of DTIME;NTIME;DSPACE;NSPACE; Sigma k TIME; TIME; Let t(n) n in case of a time restriction, and t(n) log n in case of a spacerestriction. Then Leaf Phi(t(n) Phi . In fact, using Hertrampf s locally definable acceptance types [8, 9], we obtain Leaf (F)TIME(t) F)TIME for any locally definable acceptance type F . This yields in particular: Corollary 4. 1) BLeaf ) ALINTIME. L) Leaf (L) LIN. NL) Leaf (NL) NLIN. POLYLOGSPACE) Leaf (POLYLOGSPACE) PSPACE. P) Leaf ....

U. Hertrampf. Complexity classes defined via k-valued functions. In Proceedings 9th Structure in Complexity Theory, pages 224--234. IEEE Computer Society Press, 1994.

Finite Automata with Generalized Acceptance Criteria - Peichl, Vollmer (2001) (1 citation) (Correct)

....space restriction. The proof given for Theorem 4. 3 remains valid in the case of these measures and bounds; hence we conclude that BLeaf FA F(t(n) F t(2 n ) Leaf FA F(t(n) F t(2 O(n) More generally, using Hertrampf s locally definable acceptance types [Her92, Her94] we conclude that BLeaf FA (F )TIME(t(n) F )TIME t(2 n ) Leaf FA (F )TIME(t(n) F )TIME t(2 O(n) for any locally definable acceptance type F . Hence we obtain in particular: Corollary 4.4 1. BLeaf FA (POLYLOGTIME) P. 2. BLeaf FA (NC 1 ) ....

U. Hertrampf. Complexity classes defined via k-valued functions. In Proceedings 9th Structure in Complexity Theory, pages 224--234. IEEE Computer Society Press, 1994.

Finite Automata with Generalized Acceptance Criteria - Peichl, Vollmer (2001) (1 citation) (Correct)

....The proof given for Theorem 4.3 remains valid in the case of these measures and bounds; hence we conclude that BLeaf FA # F(t(n) # = F # t(2 n ) # , Leaf FA # F(t(n) # = F # t(2 O(n) # . More generally, using Hertrampf s locally definable acceptance types [Her92, Her94] we conclude that BLeaf FA # (F )TIME(t(n) # = F )TIME # t(2 n ) # , Leaf FA # (F )TIME(t(n) # = F )TIME # t(2 O(n) # , for any locally definable acceptance type F . Hence we obtain in particular: Corollary 4.4 1. BLeaf FA (POLYLOGTIME) P. 2. BLeaf FA (NC ....

U. Hertrampf. Complexity classes defined via k-valued functions. In Proceedings 9th Structure in Complexity Theory, pages 224--234. IEEE Computer Society Press, 1994.

Unambiguous Computations and Locally Definable Acceptance.. - Niedermeier, Rossmanith (1996) (Correct)

....polynomial hierarchies can be defined. All these and many more classes were analyzed within the framework of locally definable acceptance types, which are part of a whole spectrum of acceptance mecha25 nisms defined via computation trees of nondeterministic polynomial time machines (see [18] for a survey) We can roughly distinguish three mechanisms: predicate classes, where the acceptance condition can depend on the complete tree [3] leaf languages, where the acceptance condition only depends on the leaf word [4,19] and locally definable acceptance types, where the acceptance ....

U. Hertrampf. Complexity classes defined via k-valued functions. In Proceedings of the 9th IEEE Symposium on Structure in Complexity, pages 224--234, 1994.

Finite Automata with Generalized Acceptance Criteria - Peichl, Vollmer (1999) (1 citation) (Correct)

....of DTIME;NTIME;DSPACE;NSPACE; Sigma k TIME; L TIME; Let t(n) n in case of a time restriction, and t(n) log n in case of a spacerestriction. Then Leaf FA Gamma Phi(t(n) Delta = Phi Gamma t(2 O(n) Delta . In fact, using Hertrampf s locally definable acceptance types [8, 9], we obtain Leaf FA Gamma (F)TIME(t) Delta = F)TIME Gamma t(2 O(n) Delta for any locally definable acceptance type F . This yields in particular: Corollary 4. 1) BLeaf FA (NC 1 ) ALINTIME. 2) BLeaf FA (L) Leaf FA (L) LIN. 3) BLeaf FA (NL) Leaf FA (NL) ....

U. Hertrampf. Complexity classes defined via k-valued functions. In Proceedings 9th Structure in Complexity Theory, pages 224--234. IEEE Computer Society Press, 1994.

Unambiguous Computations and Locally Definable Acceptance.. - Niedermeier, Rossmanith (Correct)

....unambiguous polynomial hierarchies can be defined. All these and many more classes were analyzed within the framework of locally definable acceptance types, which are part of a whole spectrum of acceptance mechanisms defined via computation trees of nondeterministic polynomial time machines (see [20] for a survey) We can roughly distinguish three mechanisms: predicate classes, where the acceptance condition can depend on the complete tree [5] leaf languages, where the acceptance condition only depends on the leaf word [7, 21] and locally definable acceptance types, where the acceptance ....

U. Hertrampf. Complexity classes defined via k-valued functions. In Proceedings of the 9th IEEE Symposium on Structure in Complexity, pages 224--234, 1994.

On Balanced vs. Unbalanced Computation Trees - Hertrampf, Vollmer, Wagner Self-citation (Hertrampf) (Correct)

....for a certain leaf symbol is nothing other than a Sigma p k machine asking a Path or PP oracle. It turns out that the result sketched above can be proved in a far more general context: It does not only hold for Sigma k computations, but for any (so called) locally definable acceptance scheme [10] that we might put on nondeterministic logarithmic time or polynomial time machines. That is, whenever we have nondeterministic machines where in the nodes of the computation tree a certain function f from k valued logic is applied, an analogue to the above holds, i.e. 1. f)P = BalancedLeaf P ....

U. Hertrampf, Complexity classes defined via k-valued functions; Proceedings of the 9th Structure in Complexity Theory Conference (1994), pp. 224--234.

On the Acceptance Power of Groups and Semigroups - Hertrampf (1996) Self-citation (Hertrampf) (Correct)

....to fit in the above model. ffl Locally definable acceptance types [He92a, He92b] were defined to generalize such an approach: not only the leaves, but every node of the computation tree influences the question of acceptance or rejection. However, in the case of an associative acceptance type [He94b], locally definable acceptance types are also one variant of the above described general phenomenon. ffl The most explicit model of this kind is the leaf language model, which was introduced in [BoCrSi91, BoCrSi92] by Bovet, Crescenzi, and Silvestri. Moreover, Bovet et al. gave a mechanism, how ....

U. Hertrampf, Complexity classes defined via k-valued functions; Proceedings of the 9th Structure in Complexity Theory Conference (1994), pp. 224--234.

On the Power of Number-Theoretic Operations with Respect .. - Hertrampf, Vollmer.. (1995) (19 citations) Self-citation (Hertrampf) (Correct)

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U. Hertrampf, Complexity classes defined via k-valued functions; 9th Structure in Complexity Theory Conference (1994), pp. 224--234.

Analysis of the Generic Cell Rate Algorithm Monitoring.. - Ritter (1994) (10 citations) (Correct)