U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In Proceedings 8th Structure in Complexity Theory, pages 200--207, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....operator A Delta . In fact we will introduce the more general notion of promise dot operators for which the BP operator is an example. In Section 3 we will study properties of dot operators. We will see for example that dot operators turn out to be a refinement of the leaf language concept (see [5, 31, 10, 12, 14, 19, 4], and the recent survey [32] because the class determined by a leaf language A equals A Delta P. Furthermore we show that dot operators are closed under composition, and that complementary dot operators keep the property of classes to have a many one complete set. In Section 4 we show that for ....

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, K. Wagner. On the power of polynomial time bit-reductions, Proc. 8th IEEE Structure in Complexity Theory Conference, 1993, pp. 200--207.

....problem is NP complete. Furthermore interesting connections to the well studied Constraint Satisfiability Problem are uncovered and exploited. 1 Introduction Using ideas and tools from algebraic automata theory, a number of algebraic characterizations of complexity classes have been uncovered ([1, 7] among many others) This has increased the importance of the study of problems whose computational complexity is parametrized by the properties of an underlying algebraic structure [6, 2, 11] In [6] Goldmann and Russell studied the computational complexity of solving single equations and ....

Hertrampf, Lautemann, Schwentick, Vollmer, and Wagner. On the power of polynomial time bit-reductions. In Conference on Structure in Complexity Theory, 1993.

....operator A Delta . In fact we will introduce the more general notion of promise dot operators for which the BP operator is an example. In Section 3 we will study properties of dot operators. We will see for example that dot operators turn out to be a refinement of the leaf language concept (see [5, 31, 10, 12, 14, 19, 4], and the recent survey [32] because the class determined by a leaf language A equals A Delta P. Furthermore we show that dot operators are closed under composition, and that complementary dot operators keep the property of classes to have a many one complete set. In Section 4 we show that for ....

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, K. Wagner. On the power of polynomial time bit-reductions, Proc. 8th IEEE Structure in Complexity Theory Conference, 1993, pp. 200--207.

....included in logspace. We then proceed to refine known leaf language characterizations of complexity classes, using the formal framework of leaf languages for branching programs (which we call NC 1 leaf languages) We argue that many characterizability results carry over from the polynomial time [19] and logspace [21] cases to that of NC 1 . We then draw consequences from the leaf language characterizations. Some of these consequences could be made to follow from characterizations via polynomial time leaf languages known prior to the present paper, although we discovered them in the course ....

....1 (Y ) is the class of languages recognized by uniform polynomial length programs 3 with leaf language Y . o o . o o o o Leaf . o , o Leaf o o o o o o . 15 . Leaf language classes have been studied in the context of polynomial time, logarithmic space, and logarithmic time computations [12, 19, 20, 21]. The numerous characterizations obtained in those papers make use of padding. Here we observe that in some sense the padding can be done by an automaton. This allows transferring in one blow many known characterizations to the Leaf NC 1 (1) setting. Consider the following automaton, in which ....

[Article contains additional citation context not shown here]

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K.W. Wagner. On the power of polynomial time bit-reductions. Proc. 8th Structure in Complexity Theory, pages 200-207, 1993.

.... 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 condition only depends on local, k valued functions in the tree [16,17] Clearly, the second and the third mechanisms are special cases of the first one. In all cases, however, in principle there are two possible agreements with ....

....studied both cases for predicate classes [3] Hertrampf studied the yes no case for locally definable acceptance types [16,17] whereas we studied the yes no forbidden case for them, thus obtaining strong relations to unambiguous computation. For leaf languages only the yes no case was studied [19], whereas the yes no forbidden case still remains open there. On the other hand, note that the concept of leaf languages was also applied to logarithmic space and NC 1 [20] As a whole, this paper provides an analysis of the power of locally definable acceptance types. It inspired and is ....

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In Proceedings of the 8th IEEE Symposium on Structure in Complexity, pages 200--207, 1993.

....included in logspace. We then proceed to refine known leaf language characterizations of complexity classes, using the formal framework of leaf languages for branching programs (which we call NC 1 leaf languages) We argue that many characterizability results carry over from the polynomial time [19] and logspace [21] cases to that of NC 1 . We then draw consequences from the leaf language characterizations. Some of these consequences could be made to follow from characterizations via polynomial time leaf languages known prior to the present paper, although we discovered them in the course ....

....the fact that the leaf language class obtained is a refinement of the leaf language classes defined using log space or polynomial time machines. 5. 1 Padding techniques Leaf language classes have been studied in the context of polynomial time, logarithmic space, and logarithmic time computations [12, 19, 20, 21]. The numerous characterizations obtained in those papers make use of padding. Here we observe that in some sense the padding can be done by an automaton. This allows transferring in one blow many known characterizations to the Leaf NC 1 ( Delta) setting. Consider the following automaton, in ....

[Article contains additional citation context not shown here]

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K.W. Wagner. On the power of polynomial time bit-reductions. Proc. 8th Structure in Complexity Theory, pages 200-207, 1993.

No context found.

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In Proceedings 8th Structure in Complexity Theory, pages 200--207, 1993.

No context found.

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In Proceedings 8th Structure in Complexity Theory, pages 200--207, 1993.

....which are (1) taken from a (complexity) class defined via space or time restrictions for Turing machines, or (2) taken from a (formal language) class of the Chomsky hierarchy. The power of nondeterministic Turing machines whose acceptance is given by a leaf language is well studied, see, e.g. [4, 14, 10, 12]; recently the model has also been applied to Boolean circuits [6] However, in the context of the probably most basic type of computation device, the finite automaton, leaf languages have not been considered so far. The present paper closes this gap. As had to be expected, our results differ ....

.... over automata, a model which corresponds to the circuit class NC [2] our Leaf model can be obtained from this latter Leaf model by omitting the programs but taking only finite automata) Due to space restrictions, we cannot give precise definitions here, but refer the reader to [10, 12, 6]. 4 Acceptance Criteria Given by a Complexity Class We first turn to leaf languages defined by time or space bounded Turing machines. Theorem 2. Let t(n) log n. Then BLeaf = ATIME . Proof (sketch) Let A Sigma , A 2 ATIME via Turing machine M . Define the leaf ....

[Article contains additional citation context not shown here]

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In Proceedings 8th Structure in Complexity Theory, pages 200--207, 1993.

....that C=NC 1 L. We then proceed to refine known leaf language characterizations of complexity classes, using the formal framework of leaf languages for branching programs (which we call NC 1 leaf languages) We argue that many characterizability results carry over from the polynomial time [12] and logspace [14] cases to that of NC 1 . We then draw consequences from the leaf language characterizations 2 . These consequences include the unconditional separation of the circuit class ACC 0 from MOD PH (the oracle hierarchy defined using NP and all classes of the form MOD q P as ....

....x) 2 Y g : The class Leaf NC 1 (Y ) is the class of languages recognized by uniform polynomial length programs with leaf language Y . 5. 1 Padding techniques Leaf language classes have been studied in the context of polynomial time, logarithmic space, and logarithmic time computations [8, 12, 13, 14]. The numerous characterizations obtained in those papers make use of padding. Here we observe that in some sense the padding can be done by an automaton. This allows transferring in one blow many known characterizations to the Leaf NC 1 ( Delta) setting. Here is an automaton that is able to ....

[Article contains additional citation context not shown here]

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K.W. Wagner. On the power of polynomial time bit-reductions. Proc. 8th Structure in Complexity Theory, pages 200-207, 1993.

No context found.

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In Proceedings 8th Structure in Complexity Theory, pages 200--207, 1993.

.... alphabet) was developed by Papadimitriou and Sipser around 1979 while teaching a course on complexity at MIT [27] It was later rediscovered and published independently in [9, 36] and has since then been used actively in the study of complexity classes mostly in between NC 1 and PSPACE, see [16, 5, 15, 17, 6, 18, 7]. In a very similar way to the leaf language approach to de ne classes of sets, a function class in our framework is given by specifying how the computation of a nondeterministic polynomialtime Turing transducer is evaluated to compute the function value. We give this speci cation using so called ....

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In Proceedings 8th Structure in Complexity Theory, pages 200-207, 1993.

No context found.

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In Proceedings 8th Structure in Complexity Theory, pages 200--207, 1993.

No context found.

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In Proceedings 8th Structure in Complexity Theory, pages 200--207, 1993.

No context found.

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In 8th Ann. Conf. Structure in Complexity Theory, pages 200--207, 1993.

No context found.

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In Proceedings 8th Structure in Complexity Theory, pages 200--207, 1993.

....which are (1) taken from a (complexity) class defined via space or time restrictions for Turing machines, or (2) taken from a (formal language) class of the Chomsky hierarchy. The power of nondeterministic Turing machines whose acceptance is given by a leaf language is well studied, see, e.g. [4, 14, 10, 12]; recently the model has also been applied to Boolean circuits [6] However, in the context of the probably most basic type of computation device, the finite automaton, leaf languages have not been considered so far. The present paper closes this gap. As had to be expected, our results differ ....

.... over automata, a model which corresponds to the circuit class NC 1 [2] our Leaf FA model can be obtained from this latter Leaf NC 1 model by omitting the programs but taking only finite automata) Due to space restrictions, we cannot give precise definitions here, but refer the reader to [10, 12, 6]. 4 Acceptance Criteria Given by a Complexity Class We first turn to leaf languages defined by time or space bounded Turing machines. Theorem 2. Let t(n) log n. Then BLeaf FA Gamma ATIME(t(n) Delta = ATIME Gamma t(2 n ) Delta . Proof (sketch) Let A Sigma , A 2 ....

[Article contains additional citation context not shown here]

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In Proceedings 8th Structure in Complexity Theory, pages 200--207, 1993.

No context found.

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In Proceedings 8th Structure in Complexity Theory, pages 200--207, 1993.

No context found.

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In 8th Ann. Conf. Structure in Complexity Theory, pages 200--207, 1993.

....in a wide variety of cases. The organization of the paper is as follows: In Section 2 we give the formal definition of a complexity class with finite acceptance type, and we recall the connection between this kind of complexity and the concept of leaf languages from [BCS91, BCS92] see also [HLSVW93]) Section 3 introduces hypergraph sequences. We prove some easy facts on existence or nonexistence of special types of such sequences. Section 4 connects the existence question for hypergraph sequences with the inclusionship question for certain counting classes. Finally, in Section 5, the ....

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, K. W. Wagner, On the power of polynomial time bit-reductions, Proc. 8th Structure in Complexity Theory Conference (1993), pp. 200--207.

....(Veith, 1996) q As an immediate consequence of Theorem 3.1 we get a characterization of second order Lindstrom quantifiers by first order logics. Corollary 3.2 If B 2 N, then Q 1 B FO = Q sB . Thus we get the following special cases from well known leaf language characterizations of PSPACE (Hertrampf et al. 1993): Corollary 3.3 The succinct version of the accessibility problem for directed graphs of bounded width as well as the succinct version of the word problem of any nonsolvable monoid are PSPACE complete under FO reductions. In a similar spirit we can use other characterizations, e.g. those in ....

Hertrampf, U., Lautemann, C., Schwentick, T., Vollmer, H., and Wagner, K. W. (1993). On the power of polynomial time bit-reductions. In Proceedings 8th Structure in Complexity Theory, pages 200--207.

No context found.

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer and K. W. Wagner. On the power of polynomial time bit-reductions, Proc. 8th Structure in Complexity Theory, 1993, 200|207.

No context found.

Hertrampf, U., Lauteman, C., Schwentick, T., Vollmer, H., and Wagner, K. W. On the Power of Polynomial Time Bit-Reductions . In Proc. 8th Structure in Complexity Theory Conference (CoCo), pp. 200207. IEEE Computer Society Press, 1993.

No context found.

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. Wagner. On the power of polynomial time bit-reductions (extended abstract). In Proceedings of the 8th Structure in Complexity Theory Conference, pages 200--207. IEEE Computer Society Press, May 1993.

No context found.

U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In Proceedings 8th Structure in Complexity Theory, pages 200{ 207, 1993.

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