Results 11  20
of
46
On Bounded Set Theory
"... We consider some Bounded Set Theories (BST), which are analogues to Bounded Arithmetic. Corresponding provablyrecursive operations over sets are characterized in terms of explicit definability and PTIME or LOGSPACEcomputability. We also present some conservativity results and describe a relation ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
We consider some Bounded Set Theories (BST), which are analogues to Bounded Arithmetic. Corresponding provablyrecursive operations over sets are characterized in terms of explicit definability and PTIME or LOGSPACEcomputability. We also present some conservativity results and describe a relation between BST, possibly with AntiFoundation Axiom, and a Logic of Inductive Definitions (LID) and Finite Model Theory.
The Power Of Interaction
, 1991
"... : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : vii Chapter 1. INTRODUCTION : : : : : : : : : : : : : : : : : : : : : : : : : 1 2. PRELIMINARIES : : : : : : : : : : : : : : : : : : : : : : : : : 4 2.1 Basic Definitions : : : : : : : : : : : : : : : : : : : : : : : 4 2.1.1 Basics : : ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : vii Chapter 1. INTRODUCTION : : : : : : : : : : : : : : : : : : : : : : : : : 1 2. PRELIMINARIES : : : : : : : : : : : : : : : : : : : : : : : : : 4 2.1 Basic Definitions : : : : : : : : : : : : : : : : : : : : : : : 4 2.1.1 Basics : : : : : : : : : : : : : : : : : : : : : : : : 4 2.1.2 Boolean Formulas : : : : : : : : : : : : : : : : : 4 2.1.3 Arithmetic Formulas and Expressions : : : : : : 5 2.2 Computational Models : : : : : : : : : : : : : : : : : : : : 9 2.2.1 Deterministic Computation : : : : : : : : : : : : 9 2.2.2 Probabilistic Computation : : : : : : : : : : : : 11 2.2.3 NonDeterministic Computation : : : : : : : : : 12 2.2.4 Alternating Computations : : : : : : : : : : : : 13 2.2.5 Interactive Proof Systems : : : : : : : : : : : : : 13 2.2.6 Multiple Prover Interactive Proof Systems : : : 15 2.2.7 Computation relative to an Oracle : : : : : : : : 15 2.3 Complexity Classes : : : : : : : : : : : : : : : : : : : : ...
The Boolean Hierarchy over Level 1/2 of the StraubingThérien Hierarchy
, 1998
"... For some fixed alphabet A with jAj 2, a language L ` A is in the class L 1=2 of the StraubingTherien hierarchy if and only if it can be expressed as a finite union of languages A a 1 A a 2 A \Delta \Delta \Delta A anA , where a i 2 A and n 0. The class L 1 is defined as the boo ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
For some fixed alphabet A with jAj 2, a language L ` A is in the class L 1=2 of the StraubingTherien hierarchy if and only if it can be expressed as a finite union of languages A a 1 A a 2 A \Delta \Delta \Delta A anA , where a i 2 A and n 0. The class L 1 is defined as the boolean closure of L 1=2 . It is known that the classes L 1=2 and L 1 are decidable. We give a membership criterion for the single classes of the boolean hierarchy over L 1=2 . From this criterion we can conclude that this boolean hierarchy is proper and that its classes are decidable. In finite model theory the latter implies the decidability of the classes of the boolean hierarchy over the class \Sigma 1 of the FO[!]logic. Moreover we prove a "forbiddenpattern" characterization of L 1 of the type: L 2 L 1 if and only if a certain pattern does not appear in the transition graph of a deterministic finite automaton accepting L. We discuss complexity theoretical consequences of our results. C...
Completeness for Nondeterministic Complexity Classes
, 1991
"... We demonstrate differences between reducibilities and corresponding completeness notions for nondeterministic time and space classes. For time classes the studied completeness notions under polynomialtime bounded (even logarithmic space bounded) reducibilities turn out to be different for any class ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
We demonstrate differences between reducibilities and corresponding completeness notions for nondeterministic time and space classes. For time classes the studied completeness notions under polynomialtime bounded (even logarithmic space bounded) reducibilities turn out to be different for any class containing NE . For space classes the completeness notions under logspace reducibilities can be separated for any class properly containing LOGSPACE . Key observation in obtaining the separations is the honesty property of reductions, which was recently observed to hold for the time classes and can be shown to hold for space classes. 1 Introduction Efficient reducibilities and completeness are two of the central concepts of complexity theory. Since the first use of polynomial time bounded Turing reductions by Cook [4] and the introduction of polynomial time bounded manyone reductions by Karp[9], considerable effort has been put in the investigation of properties and the relative strengt...
Timespace tradeoffs for undirected graph traversal
, 1990
"... We prove timespace tradeoffs for traversing undirected graphs. One of these is a quadratic lower bound on a deterministic model that closely matches the recent probabilistic upper bound of Broder, Karlin, Raghavan, and Upfal. The models used are variants of Cook and Rackoff’s “Jumping Automata for ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
We prove timespace tradeoffs for traversing undirected graphs. One of these is a quadratic lower bound on a deterministic model that closely matches the recent probabilistic upper bound of Broder, Karlin, Raghavan, and Upfal. The models used are variants of Cook and Rackoff’s “Jumping Automata for Graphs".
Resolution of Hartmanis' Conjecture for NLHard Sparse Sets
 Theoretical Computer Science
, 1995
"... en a graph G and a pair of vertices s; t, this reduction produces a polynomial number of graphs G 1 ; : : : ; G k of polynomial size, together with distinguished vertexpairs (s 1 ; t 1 ); : : : ; (s k ; t k ), that satisfy the following conditions. If there is no path from s to t in G, then no G i ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
en a graph G and a pair of vertices s; t, this reduction produces a polynomial number of graphs G 1 ; : : : ; G k of polynomial size, together with distinguished vertexpairs (s 1 ; t 1 ); : : : ; (s k ; t k ), that satisfy the following conditions. If there is no path from s to t in G, then no G i has a path from s i to t i ; if there is a path from s to t in G, then with high probability, at least one of the G i 's has a unique path from s i to t i . This reduction is due to Avi Wigderson [Wig94], and it exploits the "isolation lemma" of Mulmuley, Vazirani and Vazira
Tight lower bounds for stconnectivity on the NNJAG model
 SIAM J. on Computing
, 1999
"... Abstract. Directed stconnectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time– space lower bound on the probabilistic NNJAG model of Poon [Proc. 34th Annual Symposium on Foundations of Compu ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
Abstract. Directed stconnectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time– space lower bound on the probabilistic NNJAG model of Poon [Proc. 34th Annual Symposium on Foundations of Computer Science, Palo Alto, CA, 1993, pp. 218–227]. Let n be the number of nodes in the input graph and S and T be the space and time used by the NNJAG, respectively. We show that, for any δ>0, if an NNJAG uses space S ∈ O(n1−δ), then T ∈ 2Ω(log2 (n/S)) ; otherwise n log n) / log log n) S
A Note on Closure Properties of Logspace MOD Classes
 INFORMATION PROCESSING LETTERS
, 1999
"... ..."
On the Complexity of the stConnectivity Problem
, 1996
"... The directed stconnectivity problem is fundamental to computer science. There are many applications which require algorithms to solve the problem in small space and preferably in small time as well. Furthermore, its space and timespace complexities are related to several longstanding open probl ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
The directed stconnectivity problem is fundamental to computer science. There are many applications which require algorithms to solve the problem in small space and preferably in small time as well. Furthermore, its space and timespace complexities are related to several longstanding open problems in complexity theory. Depth and breadthfirst search are well known algorithms that solve the problem in optimal (i.e., O(n m)) time while using O(n log n) space where n and m are the number of nodes and edges in the graph respectively. It can also be solved in O(log 2 n) space and 2 O(log 2 n) time by Savitch's algorithm. For space S between \Theta(log 2 n) and \Theta(n log n), the best running time is T = 2 O(log 2 (n log n=S)) \Theta mn due to Barnes et al.. Establishing matching lower bounds on the Turing machine model ha...
Mathematical linguistics
, 2007
"... but in fact this is still an early draft, version 0.56, August 1 2001. Please do ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
but in fact this is still an early draft, version 0.56, August 1 2001. Please do