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19
Making Nondeterminism Unambiguous
, 1997
"... We show that in the context of nonuniform complexity, nondeterministic logarithmic space bounded computation can be made unambiguous. An analogous result holds for the class of problems reducible to contextfree languages. In terms of complexity classes, this can be stated as: NL/poly = UL/poly Lo ..."
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Cited by 37 (10 self)
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We show that in the context of nonuniform complexity, nondeterministic logarithmic space bounded computation can be made unambiguous. An analogous result holds for the class of problems reducible to contextfree languages. In terms of complexity classes, this can be stated as: NL/poly = UL/poly LogCFL/poly = UAuxPDA(log n; n O(1) )/poly
Isolation, Matching, and Counting: Uniform and Nonuniform Upper Bounds
 Journal of Computer and System Sciences
, 1998
"... We show that the perfect matching problem is in the complexity class SPL (in the nonuniform setting). This provides a better upper bound on the complexity of the matching problem, as well as providing motivation for studying the complexity class SPL. Using similar techniques, we show that counting t ..."
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Cited by 22 (4 self)
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We show that the perfect matching problem is in the complexity class SPL (in the nonuniform setting). This provides a better upper bound on the complexity of the matching problem, as well as providing motivation for studying the complexity class SPL. Using similar techniques, we show that counting the number of accepting paths of a nondeterministic logspace machine can be done in NL/poly, if the number of paths is small. This clarifies the complexity of the class LogFew (defined and studied in [BDHM91]). Using derandomization techniques, we then improve this to show that this counting problem is in NL. Determining if our other theorems hold in the uniform setting remains an The material in this paper appeared in preliminary form in papers in the Proceedings of the IEEE Conference on Computational Complexity, 1998, and in the Proceedings of the Workshop on Randomized Algorithms, Brno, 1998. y Supported in part by NSF grants CCR9509603 and CCR9734918. z Supported in part by the ...
An Unambiguous Class Possessing a Complete Set
, 1996
"... In this work a complete problem for an unambiguous logspace class is presented. This is surprising since unambiguity is a `promise' or `semantic' concept. These usually lead to classes apparently without complete problems. 1 Introduction One of the most central questions of complexity theory is to ..."
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Cited by 15 (3 self)
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In this work a complete problem for an unambiguous logspace class is presented. This is surprising since unambiguity is a `promise' or `semantic' concept. These usually lead to classes apparently without complete problems. 1 Introduction One of the most central questions of complexity theory is to compare determinism with nondeterminism. Our inability to exhibit the precise relationship between these two features motivates the investigation of intermediate features such as symmetry or unambiguity. In this paper we will concentrate on the notion of unambiguity. Unfortunately, unambiguity of a device or of a language is in general an undecidable property. Unambiguous classes are not defined by a `syntactical' machine property but rather by a `semantical' restriction. A nasty consequence is the apparent lack of complete sets. In the case of time bounded computations there are relativizations of unambiguity which provably have no complete problem ([10]). For space bounded computations t...
Unambiguous Auxiliary Pushdown Automata And SemiUnbounded FanIn Circuits
, 1995
"... Notions of unambiguity for uniform circuits and AuxPDAs are studied and related to each other. In particular, a coincidence for counting and unambiguous versions of AuxPDAs and semiunbounded fanin circuits is shown. Moreover, an improved simulation of LOGUCFL (the class of languages logspace many ..."
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Cited by 15 (2 self)
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Notions of unambiguity for uniform circuits and AuxPDAs are studied and related to each other. In particular, a coincidence for counting and unambiguous versions of AuxPDAs and semiunbounded fanin circuits is shown. Moreover, an improved simulation of LOGUCFL (the class of languages logspace manyone reducible to unambiguous contextfree languages) by unambiguous circuits and AuxPDAs is developed. Next, an inductive counting technique on semiunbounded fanin circuits is presented and employed for several applications, especially an alternative proof for the closure under complementation of LOGCFL. A costfree simulation of polynomially ambiguity bounded AuxPDAs by unambiguous ones is given. A first nontrivial upper bound for a circuit class defined by Lange and its closure under complementation are indicated. Finally, a normal form for AuxPDAs is investigated. Inter alia it is shown that for unambiguous AuxPDAs operating in polynomial time and logarithmic space a pushdown height of...
Directed planar reachability is in unambiguous logspace
 In Proceedings of IEEE Conference on Computational Complexity CCC
, 2007
"... We show that the stconnectivity problem for directed planar graphs can be decided in unambiguous logarithmic space. 1. ..."
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Cited by 15 (4 self)
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We show that the stconnectivity problem for directed planar graphs can be decided in unambiguous logarithmic space. 1.
Unambiguous polynomial hierarchies and exponential size
 In Proceedings of the 9th Structure in Complexity Theory Conference
, 1994
"... In the exponential case circuits of bounded depth characterize the polynomial hierachy. Using the notion of an unambiguous circuit we give a uniform framework to relate the various types of unambiguous polynomial hierarchies and to explain their differences. ..."
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Cited by 7 (2 self)
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In the exponential case circuits of bounded depth characterize the polynomial hierachy. Using the notion of an unambiguous circuit we give a uniform framework to relate the various types of unambiguous polynomial hierarchies and to explain their differences.
Reachability Problems: An Update
"... Abstract. There has been a great deal of progress in the fifteen years that have elapsed since Wigderson published his survey on the complexity of the graph connectivity problem [Wig92]. Most significantly, Reingold solved the longstanding question of the complexity of the st connectivity problem i ..."
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Cited by 3 (0 self)
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Abstract. There has been a great deal of progress in the fifteen years that have elapsed since Wigderson published his survey on the complexity of the graph connectivity problem [Wig92]. Most significantly, Reingold solved the longstanding question of the complexity of the st connectivity problem in undirected graphs, showing that this is complete for logspace (L) [Rei05]. This survey talk will focus on some of the remaining open questions dealing with graph reachability problems. Particular attention will be paid to these topics: – Reachability in planar directed graphs (and more generally, in graphs of low genus) [ADR05,BTV07]. – Reachability in different classes of grid graphs [ABC + 06]. – Reachability in mangroves [AL98]. The problem of finding a path from one vertex to another in a graph is the first problem that was identified as being complete for a natural subclass of P; it was shown to be complete for nondeterministic logspace (NL) by Jones [Jon75]. Restricted versions of this problem were subsequently shown to be complete for other natural complexity
Space Hierarchy Results for Randomized and Other Semantic Models
, 2007
"... We prove space hierarchy and separation results for randomized and other semantic models of computation with advice. Previous works on hierarchy and separation theorems for such models focused on time as the resource. We obtain tighter results with space as the resource. Our main theorems are the fo ..."
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Cited by 3 (1 self)
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We prove space hierarchy and separation results for randomized and other semantic models of computation with advice. Previous works on hierarchy and separation theorems for such models focused on time as the resource. We obtain tighter results with space as the resource. Our main theorems are the following. Let s(n) be any spaceconstructible function that is Ω(log n) and such that s(an) = O(s(n)) for all constants a, and let s ′ (n) be any function that is ω(s(n)). There exists a language computable by twosided error randomized machines using s ′ (n) space and one bit of advice that is not computable by twosided error randomized machines using s(n) space and min(s(n), n) bits of advice. There exists a language computable by zerosided error randomized machines in space s ′ (n) with one bit of advice that is not computable by onesided error randomized machines using s(n) space and min(s(n), n) bits of advice. The condition that s(an) = O(s(n)) is a technical condition satisfied by typical space bounds that are at most linear. We also obtain weaker results that apply to generic semantic models of computation. 1
Uniform Inclusions in Nondeterministic Logspace
 Randomized Algorithms
, 1998
"... We show that the complexity class LogFew is contained in NL " SPL. Previously, this was known only to hold in the nonuniform setting. Key Words: Nondeterministic Logspace Computation, Nonuniform Complexity, Derandomization, fflbiased Sample Space. 1 Introduction In [RA97], a probabilistic cons ..."
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Cited by 2 (2 self)
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We show that the complexity class LogFew is contained in NL " SPL. Previously, this was known only to hold in the nonuniform setting. Key Words: Nondeterministic Logspace Computation, Nonuniform Complexity, Derandomization, fflbiased Sample Space. 1 Introduction In [RA97], a probabilistic construction was used to show that the complexity classes NL/poly and UL/poly coincide. That is, in the context of nonuniform complexity, nonuniform logspace is no more powerful than unambiguous logspace. It was observed in [AR98] that the equality NL=UL holds also in the uniform setting, under a plausible hypothesis concerning pseudorandom number generators. However, it remains an important open question whether NL=UL can be established without resorting to unproved assumptions. The results and techniques of [RA97] were extended in [AR98] in a number of ways. One extension involves the class LogFew, defined in [BDHM92]. (Formal definitions appear below.) No inclusion relation was known between...
NLprintable sets and Nondeterministic Kolmogorov Complexity
, 2003
"... This paper introduces nondeterministic spacebounded Kolmogorov complexity, and we show that it has some nice properties not shared by some other resourcebounded notions of Kcomplexity. ..."
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Cited by 2 (0 self)
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This paper introduces nondeterministic spacebounded Kolmogorov complexity, and we show that it has some nice properties not shared by some other resourcebounded notions of Kcomplexity.