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119
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 24 (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 ...
The directed planar reachability problem
 In Proc. 25th annual Conference on Foundations of Software Technology and Theoretical Computer Science (FST&TCS), number 1373 in Lecture Notes in Computer Science
, 2005
"... Abstract. We investigate the stconnectivity problem for directed planar graphs, which is hard for L and is contained in NL but is not known to be complete. We show that this problem is logspacereducible to its complement, and we show that the problem of searching graphs of genus 1 reduces to the ..."
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Cited by 23 (9 self)
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Abstract. We investigate the stconnectivity problem for directed planar graphs, which is hard for L and is contained in NL but is not known to be complete. We show that this problem is logspacereducible to its complement, and we show that the problem of searching graphs of genus 1 reduces to the planar case. We also consider a previouslystudied subclass of planar graphs known as grid graphs. We show that the directed planar stconnectivity problem reduces to the reachability problem for directed grid graphs. A special case of the gridgraph reachability problem where no edges are directed from right to left is known as the “acyclic grid graph reachability problem”. We show that this problem lies in the complexity class UL. 1
Nondeterministic Polynomial Time versus Nondeterministic Logarithmic Space
 In Proceedings, Twelfth Annual IEEE Conference on Computational Complexity
, 1996
"... We discuss the possibility of using the relatively old technique of diagonalization to separate complexity classes, in particular NL from NP. We show several results in this direction. ffl Any nonconstant level of the polynomialtime hierarchy strictly contains NL. ffl SAT is not simultaneously in ..."
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Cited by 23 (1 self)
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We discuss the possibility of using the relatively old technique of diagonalization to separate complexity classes, in particular NL from NP. We show several results in this direction. ffl Any nonconstant level of the polynomialtime hierarchy strictly contains NL. ffl SAT is not simultaneously in NL and deterministic n log j n time for any j. ffl On the negative side, we present a relativized world where P = NP but any nonconstant level of the polynomialtime hierarchy differs from P. 1 Introduction Separating complexity classes remains the most important and difficult of problems in theoretical computer science. Circuit complexity and other techniques on finite functions have seen some exciting early successes (see the survey of Boppana and Sipser [BS90]) but have yet to achieve their promise of separating complexity classes above logarithmic space. Other techniques based on logic and geometry also have given us separations only on very restricted models. We should turn back to...
FiniteModel Theory  A Personal Perspective
 Theoretical Computer Science
, 1993
"... Finitemodel theory is a study of the logical properties of finite mathematical structures. This paper is a very personalized view of finitemodel theory, where the author focuses on his own personal history, and results and problems of interest to him, especially those springing from work in his Ph ..."
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Cited by 20 (0 self)
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Finitemodel theory is a study of the logical properties of finite mathematical structures. This paper is a very personalized view of finitemodel theory, where the author focuses on his own personal history, and results and problems of interest to him, especially those springing from work in his Ph.D. thesis. Among the topics discussed are:
The Complexity of Reconfiguring Network Models
, 1992
"... This paper concerns some of the theoretical complexity aspects of the reconfigurable network model. The computational power of the model is investigated under several variants, depending on the type of switches (or switch operations) assumed by the network nodes. Computational power is evaluated by ..."
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Cited by 19 (5 self)
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This paper concerns some of the theoretical complexity aspects of the reconfigurable network model. The computational power of the model is investigated under several variants, depending on the type of switches (or switch operations) assumed by the network nodes. Computational power is evaluated by focusing on the set of problems computable in constant time in each variant. A hierarchy of such problem classes corresponding to different variants is shown to exist and is placed relative to traditional classes of complexity theory. Department of Mathematics and Computer Science, The Haifa University, Haifa, Israel. Email: yosi@mathcs2.haifa.ac.il y Department of Computer Science, Technische Universitat Munchen, 80290 Munchen, Germany. Email: lange@informatik.tumuenchen.de z Department of Applied Mathematics and Computer Science, The Weizmann Institute, Rehovot 76100, Israel. Email: peleg@wisdom.weizmann.ac.il. Supported in part by an Allon Fellowship, by a Bantrell Fellowship an...
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 19 (4 self)
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We show that the stconnectivity problem for directed planar graphs can be decided in unambiguous logarithmic space. 1.
When Worlds Collide: Derandomization, Lower Bounds, and Kolmogorov Complexity
 OF REDUCTIONS,IN“PROC.29THACM SYMPOSIUM ON THEORY OF COMPUTING
, 1997
"... This paper has the following goals:  To survey some of the recent developments in the field of derandomization.  To introduce a new notion of timebounded Kolmogorov complexity (KT), and show that it provides a useful tool for understanding advances in derandomization, and for putting vario ..."
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Cited by 17 (5 self)
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This paper has the following goals:  To survey some of the recent developments in the field of derandomization.  To introduce a new notion of timebounded Kolmogorov complexity (KT), and show that it provides a useful tool for understanding advances in derandomization, and for putting various results in context.  To illustrate the usefulness of KT, by answering a question that has been posed in the literature, and  To pose some promising directions for future research.
A Compendium of Problems Complete for Symmetric Logarithmic Space
 Computational Complexity
, 1996
"... . The paper's main contributions are a compendium of problems that are complete for symmetric logarithmic space (SL), a collection of material relating to SL, a list of open problems, and an extension to the number of problems known to be SLcomplete. Complete problems are one method of studyin ..."
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Cited by 13 (0 self)
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. The paper's main contributions are a compendium of problems that are complete for symmetric logarithmic space (SL), a collection of material relating to SL, a list of open problems, and an extension to the number of problems known to be SLcomplete. Complete problems are one method of studying SL, a class for which programming is nonintuitive. Our exposition helps make the class SL less mysterious and more accessible to other researchers. Key words. Completeness, SL, space complexity, symmetric logarithmic space. Subject classifications. 68Q17. 1. Introduction In this paper we describe problems that are logarithmic space manyone complete for symmetric logarithmic space (SL). Our hope in collecting these problems and extending this list is that more insight can be gained about the relationships between the complexity classes deterministic logarithmic space (DL), SL, and nondeterministic logarithmic space (NL). The symmetric Turing machine model introduced by Lewis & Papadimitriou ...
Grid Graph Reachability Problems
 IN ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY
, 2006
"... We study the complexity of restricted versions of stconnectivity, which is the standard complete problem for NL. Grid graphs are a useful tool in this regard, since • reachability on grid graphs is logspaceequivalent to reachability in general planar digraphs, and • reachability on certain classes o ..."
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Cited by 13 (9 self)
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We study the complexity of restricted versions of stconnectivity, which is the standard complete problem for NL. Grid graphs are a useful tool in this regard, since • reachability on grid graphs is logspaceequivalent to reachability in general planar digraphs, and • reachability on certain classes of grid graphs gives natural examples of problems that are hard for NC 1 under AC 0 reductions but are not known to be hard for L; they thus give insight into the structure of L. In addition to explicating the structure of L, another of our goals is to expand the class of digraphs for which connectivity can be solved in logspace, by building on the work of Jakoby et al. [11], who showed that reachability in seriesparallel digraphs is solvable in L. Our main results are: • Many of the natural restrictions on gridgraph reachability (GGR) are equivalent under AC 0
Descriptive Complexity: a Logician's Approach to Computation
 Notices of the American Mathematical Society
, 1995
"... this article is complete for NSPACE[log n].) ..."
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