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10
Lower Bounds for Oneway Probabilistic Communication Complexity
, 1992
"... this paper can be generalized to the optimal model? 8 Acknowledgment I wish to thank L. Hemachandra for his invitation to me to spend the spring semester at the University of Rochester and for his permanent attention to my research and helpfulness in all my problems and J. Seiferas for extensive c ..."
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Cited by 30 (2 self)
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this paper can be generalized to the optimal model? 8 Acknowledgment I wish to thank L. Hemachandra for his invitation to me to spend the spring semester at the University of Rochester and for his permanent attention to my research and helpfulness in all my problems and J. Seiferas for extensive comments on an earlier draft of this paper. The results of section 4.1 of the paper are the realization of J. Seiferas's advice to investigate the probabilistic complexity properties of almost all functions in comparison with Yao's [Y1] results. I wish also to thank P. Dietz for his comments, which helped to simplify the proof of lemma 4.1
The Structure of Complete Degrees
, 1990
"... This paper surveys investigations into how strong these commonalities are. More concretely, we are concerned with: What do NPcomplete sets look like? To what extent are the properties of particular NPcomplete sets, e.g., SAT, shared by all NPcomplete sets? If there are are structural differences ..."
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Cited by 29 (3 self)
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This paper surveys investigations into how strong these commonalities are. More concretely, we are concerned with: What do NPcomplete sets look like? To what extent are the properties of particular NPcomplete sets, e.g., SAT, shared by all NPcomplete sets? If there are are structural differences between NPcomplete sets, what are they and what explains the differences? We make these questions, and the analogous questions for other complexity classes, more precise below. We need first to formalize NPcompleteness. There are a number of competing definitions of NPcompleteness. (See [Har78a, p. 7] for a discussion.) The most common, and the one we use, is based on the notion of mreduction, also known as polynomialtime manyone reduction and Karp reduction. A set A is mreducible to B if and only if there is a (total) polynomialtime computable function f such that for all x, x 2 A () f(x) 2 B: (1) 1
On Growing ContextSensitive Languages
 Proc. 19th ICALP, Lecture Notes in Computer Science (W. Kuich,ed
, 1992
"... Growing contextsensitive grammars (GCSG) are investigated. The variable membership problem for GCSG is shown to be NPcomplete. This solves a problem posed in [DW86]. It is also shown that the languages generated by GCSG form an abstract family of languages and several implications are presented. ..."
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Cited by 12 (2 self)
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Growing contextsensitive grammars (GCSG) are investigated. The variable membership problem for GCSG is shown to be NPcomplete. This solves a problem posed in [DW86]. It is also shown that the languages generated by GCSG form an abstract family of languages and several implications are presented. Institut fur Informatik, Universitat Wurzburg, D8700 Wurzburg, Germany. y Instytut Informatyki, Uniwersytet Wroc/lawski, 51151 Wroc/law, Poland (permanent address). This research was supported by the Humboldt Foundation. 1 Introduction It is well known that the class of languages generated by contextsensitive grammars is equal to NSPACE(n) and that, even for fixed grammars, the membership problem can be PSPACEcomplete. On the other hand the contextfree grammars are known to have, for many applications, too weak derivative power. While many modifications extending contextfree grammars have been studied, only a few papers concern some restricted versions of contextsensitive gramm...
DSPACE(n) ? = NSPACE(n): A degree theoretic characterization
 in Proc. 10th Structure in Complexity Theory Conference
, 1995
"... It is shown that the following are equivalent. 1. DSPACE(n) = NSPACE(n). 2. There is a nontrivial ≤1−NL mdegree that coincides with a ≤1−L mdegree. 3. For every class C closed under loglin reductions, the ≤1−NL m coincides with the ≤1−L mcomplete degree of C. 1 ..."
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Cited by 3 (3 self)
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It is shown that the following are equivalent. 1. DSPACE(n) = NSPACE(n). 2. There is a nontrivial ≤1−NL mdegree that coincides with a ≤1−L mdegree. 3. For every class C closed under loglin reductions, the ≤1−NL m coincides with the ≤1−L mcomplete degree of C. 1
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.
Comparing Counting Classes for Logspace, Oneway Logspace, Logtime, and FirstOrder
 Proc. 20th Symposium on Mathematical Foundations of Computer Science, Springer Lecture Notes in Computer Science
, 1994
"... We generalize the definition of firstorder counting classes [SST92] to use !, SUCC, and + as linear orderings. It turns out that #\Pi2 [!] = #\Pi1[SUCC] = #\Pi1[+]. We introduce certain classes of logtime counting functions and show that the classes of firstorder definable counting functions are s ..."
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We generalize the definition of firstorder counting classes [SST92] to use !, SUCC, and + as linear orderings. It turns out that #\Pi2 [!] = #\Pi1[SUCC] = #\Pi1[+]. We introduce certain classes of logtime counting functions and show that the classes of firstorder definable counting functions are subclasses of the corresponding logtime counting classes. These logtime counting classes are itself subclasses of the corresponding oneway logspace counting classes. These logspace counting classes form a strict hierachy within #P: F1L` = #1L` = span1L` = #P: Using the logical characterization of #P we obtain a characterization of #P via universally branching logtime Turing machines. 1 Introduction An important open question in complexity theory is whether the two classes NL and NP are equal. Although in the case of computing partial multivalued functions nondeterministically the corresponding classes can be separated [Bur89], a solution for the class of decision problems is not in sight. ...
A Perspective on Lindström Quantifiers and Oracles
"... This paper presents a perspective on the relationship between Lindström quantiers in model theory and oracle computations in complexity theory. We do not study this relationship here in full generality (indeed, there is much more work to do in order to obtain a full appreciation), but instead w ..."
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This paper presents a perspective on the relationship between Lindström quantiers in model theory and oracle computations in complexity theory. We do not study this relationship here in full generality (indeed, there is much more work to do in order to obtain a full appreciation), but instead we examine what amounts to a thread of research in this topic running from the motivating results, concerning logical characterizations of nondeterministic polynomialtime, to the consideration of Lindström quantiers as oracles, and through to the study of some naturally arising questions (and subsequent answers). Our presentation follows the chronological progress of the thread and highlights some important techniques and results at the interface between nite model theory and computational complexity theory.
The Isomorphism Conjecture for NP
, 2009
"... In this article, we survey the arguments and known results for and against the Isomorphism Conjecture. 1 ..."
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In this article, we survey the arguments and known results for and against the Isomorphism Conjecture. 1
Polylog space compression, pushdown compression, and LempelZiv are incomparable
, 2009
"... The pressing need for efficient compression schemes for XML documents has recently been focused on stack computation [11, 17], and in particular calls for a formulation of informationlossless stack or pushdown compressors that allows a formal analysis of their performance and a more ambitious use o ..."
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The pressing need for efficient compression schemes for XML documents has recently been focused on stack computation [11, 17], and in particular calls for a formulation of informationlossless stack or pushdown compressors that allows a formal analysis of their performance and a more ambitious use of the stack in XML compression, where so far it is mainly connected to parsing mechanisms. In this paper we introduce the model of pushdown compressor, based on pushdown transducers that compute a single injective function while keeping the widest generality regarding stack computation. We also consider online compression algorithms that use at most polylogarithmic space (plogon). These algorithms correspond to compressors in the data stream model. We compare the performance of these two families of compressors with each other and with the general purpose LempelZiv algorithm. This comparison is made without any a priori assumption on the data’s source and considering the asymptotic compression ratio for infinite sequences. We prove that in all cases they are incomparable.