| J. Balcazar, J. Daz, and J. Gabarro, Structural Complexity I, EATCS Monographs on Theoretical Computer Science, Springer-Verlag, 1988. |
....and poly(log n) is a fixed polynomial in log n. DTIME(n ) refers to the class of problems that can be solved by a deterministic Turing machine in quasi polynomial time. More information about these and related topics is available in any standard textbook in structural complexity theory, such as [5, 14]. We omit any precise definition of the size of an instance of the SAT problem and the size of an instance (G; of the label cover problem, since those will not be necessary. 29 Using this Theorem and ideas of Arora et.al. 2] we can prove the following theorem. Theorem 23 Assume that we ....
J. L. Balcazar, J. D iaz and J. Gabarro, Structural Complexity I, EATCS Monographs on Theoretical Computer Science, Springer-Verlag, 1988.
....in this section. We let NEXP denote the complexity class fNT IME(2 )jp is a polynomial g and DEXP denote fDT IME(2 )jp is a polynomial g. m complete for NEXP . 4 Proof: Let K be the m complete set for NE defined above. It is easy to see (cf. Balc azar, D iaz, and Gabarr o [1]) that K is m complete for NEXP as well. The set B will be constructed so that its only elements are of the form he; x; l; ii, i = 0 or i = 1. B will be complete via the 2 Gammad reduction: he; x; li 2 K [he; x; l; 0i 2 B] he; x; l; 1i 2 B] To ensure that B is not m complete we ....
Balc'azar J.L., J. D'iaz & J. Gabarr'o. Structural Complexity I . W. Brauer, G. Rozenberg & A. Salomaa (eds.) EATCS Monographs on Theoretical Computer Science 11 (1988) Springer Verlag.
....with the properties as described in Theorem 22 for this . refers to the class of problems that can be solved by a deterministic Turing machine in quasi polynomial time. More information about these and related topics is available in any standard textbook in structural complexity theory, such as [5,15]. We omit any precise definition of the size of an instance of the SAT problem and the size of an instance (G; of the label cover problem, since those will not be necessary. 36 First, following the same approach as in [2] we delete all (e = v; w) b; d) in such that for some edge ....
J. L. Balcazar, J. D iaz and J. Gabarro, Structural Complexity I, EATCS Monographs on Theoretical Computer Science (Springer, Berlin, New York, 1988). 40
....polynomial size kp(n) the p(n) first letters of each of the k advices of M, and then simulates M. Hence the computational pover of analog automata is bounded by P poly. Let L be a language in P poly. By definition, L is recognized by a Turing machine M vith an advice function f: N 0, 1 (see [5]) We can construct a vord 7 of infinite length as the concatenation, vith delim iters, of f(1) f(2) tc . In order to recognize L, an analog automaton M, on input iv C 0, 1 , first makes advice 7 appear. Then M seeks in the value of f( iv[ This operation can be done in polynomial time, ....
J. L. BalcAzar, J. DiAz, and J. Gabarr6. Structural Complexity I. EATCS Monographs on Theoretical Computer Science. Springer-Verlag, 1988.
....BPP, boundederror probabilistic polynomial time. Both these classes, though perhaps not feasible in the sense of deterministic polynomial time, are feasible in practice, as a Turing machine with a coin can accept languages from these classes with very low error probability. Definition 1 ([16, 2]) 1. BPP is the class of languages recognized by polynomial time probabilistic Turing machines whose error probability is bounded above by some positive constant # 1 2. 2. R is the class of languages accepted by polynomial time probabilistic Turing machines that have zero error probability for ....
J. Balcazar, J. Daz, and J. Gabarro. Structural Complexity I. EATCS Monographs in Theoretical Computer Science. Springer-Verlag, 1988.
....P = NP . Furthermore, we can show that C is not contained in AveP (thus it is not trivial) unless all DistNP are solvable in polynomial time on average by randomized zero error computation. 2 Preliminaries We use standard notations and definitions from computability theory, see, e.g. [BDG88]. We briefly recall the definitions of the average case complexity classes used in the following. For definitions and discussion, see [Gur91] A distributional problem consists of a set L and a distribution on strings defined by the distribution function , i.e. a (real) valued function such that ....
J. Balcazar, J. Daz, and J. Gabarro, Structural Complexity I, EATCS Monographs on Theoretical Computer Science, Springer-Verlag, 1988.
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J. Balcazar, J. Daz, and J. Gabarro, Structural Complexity I, EATCS Monographs on Theoretical Computer Science, Springer-Verlag, 1988.
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J.L.Balc'azar, J.Diaz, J.Gabarr'o, Structural Complexity I,II ( EATCS Monographs of Theoretical Computer Science, vol. 11 and vol. 22, Springer-Verlag, Berlin, 1988.
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J. L. Balcazar, J. Daz, and J. Gabarro. Structural complexity, vols I and II. EATCS Monographs on Theoretical Computer Science. Springer, Berlin, 1988.
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J. L. Balcazar, J. Daz, and J. Gabarro. Structural Complexity, vols I and II. EATCS Monographs on Theoretical Computer Science. Springer, Berlin, 1988.
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J. L. Balcazar, J. Daz, and J. Gabarro. Structural Complexity, volumes I and II. EATCS Monographs on Theoretical Computer Science. Springer, Berlin, 1988.
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J.L. Balc'azar, J. D'iaz and J. Gabarr'o: Structural Complexity I, EATCS Monographs on Theoretical Computer Science 11 (1988).
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J. L. Balcazar, J. Daz, J. Gabarro, Structural Complexity, volumes I and II, EATCS Monographs on Theoretical Computer Science, Springer-Verlag, Berlin, 1988.
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J. Balc'azar, J. D'iaz and J. Gabarr'o: Structural Complexity I, EATCS Monographs on Theoretical Computer Science, Springer-Verlag, Berlin, 1988.
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J. Balc'azar, J. D'iaz and J. Gabarr'o: Structural Complexity I, EATCS Monographs on Theoretical Computer Science, Springer-Verlag, Berlin, 1988.
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J. Balc'azar, J. D'iaz, and J. Gabarr'o. Structural Complexity I. EATCS Monographs on Theoretical Computer Science. SpringerVerlag, 1988.
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