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The Space Complexity of kTree Isomorphism
 In In Proceedings of ISAAC
, 2007
"... Abstract. We show that isomorphism testing of ktrees is in the class StUSPACE(log n) (strongly unambiguous logspace). This bound follows from a deterministic logspace algorithm that accesses a strongly unambiguous logspace oracle for canonizing ktrees. Further we give a logspace canonization algor ..."
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Abstract. We show that isomorphism testing of ktrees is in the class StUSPACE(log n) (strongly unambiguous logspace). This bound follows from a deterministic logspace algorithm that accesses a strongly unambiguous logspace oracle for canonizing ktrees. Further we give a logspace canonization algorithm for kpaths. 1
SPACE HIERARCHY RESULTS FOR RANDOMIZED MODELS
"... Abstract. 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 ..."
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Cited by 1 (1 self)
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Abstract. 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.
www.stacsconf.org SPACE HIERARCHY RESULTS FOR RANDOMIZED MODELS
, 2008
"... Abstract. 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 ..."
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Abstract. 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.
Unambiguous Functions in Logarithmic Space
"... Abstract. We investigate different variants of unambiguity in the context of computing multivalued functions. We propose a modification to the standard computation models of Turing Machines and configuration graphs, which allows for unambiguitypreserving composition. We define a notion of reductio ..."
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Abstract. We investigate different variants of unambiguity in the context of computing multivalued functions. We propose a modification to the standard computation models of Turing Machines and configuration graphs, which allows for unambiguitypreserving composition. We define a notion of reductions (based on function composition), which allows nondeterminism but controls its level of ambiguity. In light of this framework we establish reductions between different variants of path counting problems. We obtain improvements of results related to inductive counting.
Symmetry Coincides with Nondeterminism for TimeBounded Auxiliary Pushdown Automata
"... Abstract—We show that every language accepted by a nondeterministic auxiliary pushdown automaton in polynomial time (that is, every language in SAC 1 = Log(CFL)) can be accepted by a symmetric auxiliary pushdown automaton in polynomial time. ..."
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Abstract—We show that every language accepted by a nondeterministic auxiliary pushdown automaton in polynomial time (that is, every language in SAC 1 = Log(CFL)) can be accepted by a symmetric auxiliary pushdown automaton in polynomial time.
RUSPACE(log n) \subseteq DSPACE(log² n/log log n)
 THE 7TH ANNUAL INTERNATIONAL SYMPOSIUM ON ALGORITHMS AND COMPUTATION (ISAAC’96
, 1998
"... We present a deterministic algorithm running in space O , log n= log log n # solving the connectivity problem on strongly unambiguous graphs. In addition, we presentanO#log n# timebounded algorithm for this problem running on a parallel pointer machine. ..."
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We present a deterministic algorithm running in space O , log n= log log n # solving the connectivity problem on strongly unambiguous graphs. In addition, we presentanO#log n# timebounded algorithm for this problem running on a parallel pointer machine.
StUSPACE(log n) \subseteq DSPACE(log² n/ log log n)
"... We present a deterministic algorithm running in space O \Gamma log 2 n= log log n \Delta solving the connectivity problem on strongly unambiguous graphs. In addition, we present an O(logn) timebounded algorithm for this problem running on a parallel pointer machine. ..."
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We present a deterministic algorithm running in space O \Gamma log 2 n= log log n \Delta solving the connectivity problem on strongly unambiguous graphs. In addition, we present an O(logn) timebounded algorithm for this problem running on a parallel pointer machine.
Electronic Colloquium on Computational Complexity, Report No. 60 (2011)
, 2011
"... We show that two complexity classes introduced about two decades ago are equal. ReachUL is the class of problems decided by nondeterministic logspace machines which on every input have at most one computation path from the start configuration to any other configuration. ReachFewL, a natural general ..."
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We show that two complexity classes introduced about two decades ago are equal. ReachUL is the class of problems decided by nondeterministic logspace machines which on every input have at most one computation path from the start configuration to any other configuration. ReachFewL, a natural generalization of ReachUL, is the class of problems decided by nondeterministic logspace machines which on every input have at most polynomially many computation paths from the start configuration to any other configuration. We show that ReachFewL = ReachUL. 1