A note on unambiguous function classes

Kosub, Sven

doi:10.1016/s0020-0190(99)00142-8

Cited by 5 publications

(18 citation statements)

References 12 publications

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“…• For our further separation examples, we return to the classes c#-coNP and c#-P NP , defined and characterized in Subsection 3.2 (see Table 2). These classes are related to other well-known function classes in [22]. However, some questions remained open.…”

Section: I=l+p(log K)mentioning

confidence: 96%

“…One can view this as a generalization of UP computations and it is known that c#-P = #• P if and only if UP = PP. For a more detailed discussion, see [22].…”

Section: Examples For Characterizations Of Classesmentioning

confidence: 99%

“…• A second open question in [22] is if c#-coNP = c#-P NP . Again, note that in the non-cluster world the answer is known: #• coNP = #• P NP as we already mentioned in Subsection 3.2.…”

Section: } -mentioning

confidence: 99%

“…In [22] it was shown that (relativizably) max-NP C c#-P NP . Hence, the corollary follows immediately from Theorem 6.2.…”

Section: } -mentioning

confidence: 99%

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Uniform Characterizations of Complexity Classes of Functions

Kosub

Schmitz

Vollmer

2000

Int. J. Found. Comput. Sci.

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We introduce a general framework for the definition of function classes. Our model, which is based on nondeterministic polynomial-time Turing transducers, allows uniform characterizations of FP, FP NP , FP NP [0(logn)], FP$ P , counting classes (#-P, #-NP, #-coNP, GapP, GapP NP ), optimization classes (max-P, min-P, max-NP, min-NP), promise classes (NPSV, #f ew -P, c#-P), multivalued classes (FewFP, NPMV), and many more. Each such class is defined in our model by a scheme how to evaluate computation trees of nondeterministic machines. We study a reducibility notion between such evaluation schemes, which leads to a necessary and sufficient criterion for relativizable inclusion between function classes. As it turns out, this criterion is easily applicable and we get as a consequence, e.g., that there is an oracle A, such that min-P^ % #-NP^ (note that no structural consequences are known to follow from the corresponding positive inclusion). Int. J. Found. Comput. Sci. 2000.11:525-551. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/23/15. For personal use only.

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Section: I=l+p(log K)mentioning

confidence: 96%

“…One can view this as a generalization of UP computations and it is known that c#-P = #• P if and only if UP = PP. For a more detailed discussion, see [22].…”

Section: Examples For Characterizations Of Classesmentioning

confidence: 99%

Section: } -mentioning

confidence: 99%

“…In [22] it was shown that (relativizably) max-NP C c#-P NP . Hence, the corollary follows immediately from Theorem 6.2.…”

Section: } -mentioning

confidence: 99%

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Uniform Characterizations of Complexity Classes of Functions

Kosub

Schmitz

Vollmer

2000

Int. J. Found. Comput. Sci.

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“…Finally, let us state the definitions of the function classes UPSV t and UPSV p [GS88,Kos99], which are the (respectively total and partial) unambiguous versions of the central, single-valued nondeterministic function classes NPSV t and NPSV p [BLS84, BLS85,Sel94]. When speaking of nondeterministic machines as computing (possibly partial) functions from Σ * to Σ * , we view each path as having no output if the path is a rejecting path, and if a path is an accepting path then it is viewed as outputting whatever string s ∈ Σ * is on the output tape (along that path) when that path halts.…”

Section: F (X) = #Acc M (X)mentioning

confidence: 99%

Cluster Computing and the Power of Edge Recognition

Hemaspaandra

Homan

Kosub

2006

Lecture Notes in Computer Science

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We study the robustness-the invariance under definition changes-of the cluster class CL#P [HHKW05]. This class contains each #P function that is computed by a balanced Turing machine whose accepting paths always form a cluster with respect to some length-respecting total order with efficient adjacency checks. The definition of CL#P is heavily influenced by the defining paper's focus on (global) orders. In contrast, we define a cluster class, CLU#P, to capture what seems to us a more natural model of cluster computing. We prove that the naturalness is costless: CL#P = CLU#P. Then we exploit the more natural, flexible features of CLU#P to prove new robustness results for CL#P and to expand what is known about the closure properties of CL#P.The complexity of recognizing edges-of an ordered collection of computation paths or of a cluster of accepting computation paths-is central to this study. Most particularly, our proofs exploit the power of unique discovery of edges-the ability of nondeterministic functions to, in certain settings, discover on exactly one (in some cases, on at most one) computation path a critical piece of information regarding edges of orderings or clusters.

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