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The Class NP Nondeterministic polynomialtime
"... A language L (equivalently decision problem) is in the class P if there is a polynomial time algorithm A for deciding L; Given a string x, A correctly decides if x ∈ L and running time of A on x is polynomial in x, the length of x. Given a contextfree grammar and a string, can that string be g ..."
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A language L (equivalently decision problem) is in the class P if there is a polynomial time algorithm A for deciding L; Given a string x, A correctly decides if x ∈ L and running time of A on x is polynomial in x, the length of x. Given a contextfree grammar and a string, can that string
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 24 (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
Expressive Reasoning about Action in Nondeterministic Polynomial Time
 In IJCAI99
, 1999
"... The rapid development of efficient heuristics for deciding satisfiability for propositional logic motivates thorough investigations of the usability of NPcomplete problems in general. In this paper we introduce a logic of action and change which is expressive in the sense that it can represent ..."
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Cited by 1 (0 self)
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in turn includes a nontrivial polynomialtime fragment) previously introduced by Drakengren and Bjareland. 1 Introduction The rapid development of efficient heuristics for deciding satisfiability for propositional logic (GSAT and similar heuristics [ Selman et al., 1992 ] ) motivates thorough
NonDeterministic Exponential Time has TwoProver Interactive Protocols
"... We determine the exact power of twoprover interactive proof systems introduced by BenOr, Goldwasser, Kilian, and Wigderson (1988). In this system, two allpowerful noncommunicating provers convince a randomizing polynomial time verifier in polynomial time that the input z belongs to the language ..."
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Cited by 416 (37 self)
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We determine the exact power of twoprover interactive proof systems introduced by BenOr, Goldwasser, Kilian, and Wigderson (1988). In this system, two allpowerful noncommunicating provers convince a randomizing polynomial time verifier in polynomial time that the input z belongs
A NEW POLYNOMIALTIME ALGORITHM FOR LINEAR PROGRAMMING
 COMBINATORICA
, 1984
"... We present a new polynomialtime algorithm for linear programming. In the worst case, the algorithm requires O(tf'SL) arithmetic operations on O(L) bit numbers, where n is the number of variables and L is the number of bits in the input. The running,time of this algorithm is better than the ell ..."
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Cited by 860 (3 self)
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We present a new polynomialtime algorithm for linear programming. In the worst case, the algorithm requires O(tf'SL) arithmetic operations on O(L) bit numbers, where n is the number of variables and L is the number of bits in the input. The running,time of this algorithm is better than
Factoring polynomials with rational coefficients
 MATH. ANN
, 1982
"... In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomia ..."
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Cited by 961 (11 self)
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In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive
PolynomialTime Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
 SIAM J. on Computing
, 1997
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 1277 (4 self)
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A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration
The complexity of theoremproving procedures
 IN STOC
, 1971
"... It is shown that any recognition problem solved by a polynomial timebounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology. Here “reduced ” means, roughly speaking, that the first problem can be solved deterministi ..."
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Cited by 1050 (5 self)
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It is shown that any recognition problem solved by a polynomial timebounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology. Here “reduced ” means, roughly speaking, that the first problem can be solved
Model Checking of Probabilistic and Nondeterministic Systems
, 1995
"... . The temporal logics pCTL and pCTL* have been proposed as tools for the formal specification and verification of probabilistic systems: as they can express quantitative bounds on the probability of system evolutions, they can be used to specify system properties such as reliability and performance. ..."
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Cited by 291 (13 self)
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. In this paper, we present modelchecking algorithms for extensions of pCTL and pCTL* to systems in which the probabilistic behavior coexists with nondeterminism, and show that these algorithms have polynomialtime complexity in the size of the system. This provides a practical tool for reasoning
Results 1  10
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