D. T. Huynh. Resource-bounded Kolmogorov complexity of hard languages. In Structure in Complexity Theory, pages 184--195, Berlin, 1986. Springer-Verlag.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... notion have recently been surveyed by Kolmogorov and Uspenskii [19] and Li and Vitanyi [21] In this paper we are primarily concerned with resource bounded Kolmogorov complexities, which have been investigated by Hartmanis [10] Sipser [39] Ko [17] Longpr e [22] Balc azar and Book [3] Huynh [13], Lutz [24] Allender and Watanabe [2] and many others. Martin Lof [29] showed that K(xjn) the conditional Kolmogorov complexity of infinite binary sequences x, exhibits a strong Shannon effect. Specifically, Martin Lof proved that if the series 1 X n=0 2 Gammaf (n) converges (e.g. if ....

....theory of pseudorandom sequences. Following work by Yao [45] Blum and Micali [5] Goldreich, Goldwasser, and Micali [8] Levin [20] Allender [1] and others on the generation of finite pseudorandom sequences from shorter random sequences, and following work by Schnorr [34,36] Wilber [43] Huynh [12,13], Ko [17] and others on pseudorandom properties of infinite sequences, Lutz [25,27] gave a measure theoretic definition of infinite pseudorandom sequences. This definition of pseudorandomness is analogous to the MartinL of [28] definition of randomness, but is based on resource bounded measure ....

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D.T. Huynh, Resource-bounded Kolmogorov complexity of hard languages, Structure in Complexity Theory, 1986, Lecture Notes in Computer Science, Vol. 223, pp. 184-- 195.

....a tight, exponential lower bound on the space bounded Kolmogorov complexities of languages that are weakly P=Poly T complete for ESPACE. Specifically, we prove that for every such language H , there exists ffl 0 such that KS 2 n ffl (Hn) 2 n ffl a.e. 1:3) This extends Huynh s proof [22] that (1.3) holds for every language H that is P T complete for ESPACE. In section 4, we also prove a Small Span Theorem for P=Poly T reductions in ESPACE. This result requires some explanation. A recurring tool and unifying theme of much work on the measure structure of complexity classes ....

....ESPACE. We also prove the Small Span Theorem for P=Poly T reducibility in ESPACE. This latter result implies that the set of all P=Poly T hard languages for ESPACE has pspace measure 0, and that every P=Poly T degree has measure 0 in ESPACE. The following theorem extends a result of Huynh [22]. Theorem 4.1. For every weakly P=Poly T hard language H for ESPACE, there exists ffl 0 such that KS 2 n ffl (Hn ) 2 n ffl a.e. Proof. Let H be weakly P=Poly T hard for ESPACE, and let X = fA f0; 1g j KS 2 2n (A=n ) 2 n Gamma p n a.e.g: Since (P=Poly) T (H) does ....

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D. T. Huynh, Resource-bounded Kolmogorov complexity of hard languages, Structure in Complexity Theory, 1986, pp. 184--195, Berlin. Springer-Verlag.

....[MS72] Stockmeyer and Chandra[SC89] and others. Such problems are correctly regarded as exceedingly complex. They are provably intractable in terms of computational time and space. They have exponential circuit size complexity [Kan82] weakly exponential space bounded Kolmogorov complexity [Huy86], and dense complexity cores [OS86, Huy87] Problems that are P m hard for ESPACE have all these properties and need not even be recursive. Notwithstanding these lower bounds on the complexity of P m hard problems for ESPACE, we will prove in x6 below that such problems are unusually simple ....

....co sparse complexity cores. In x6, we apply these results to our main topic, which is the complexity and distribution of P m hard problems for ESPACE. It is well known that such problems are not feasibly decidable and must obey certain lower bounds on their complexities. As noted above, Huynh[Huy86] has proven that every P m hard for ESPACE has weakly exponential (i.e. 2 n ffl for some ffl 0) space bounded Kolmogorov complexity; and Orponen and Schoning[OS86] have (essentially) proven that every P m hard language for ESPACE has a dense DSPACE(2 cn ) complexity core. ....

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D. T. Huynh. Resource-bounded Kolmogorov complexity of hard languages. In Proceedings of the First Annual Structure in Complexity Theory Conference, pages 184--195, 1986.

....complexity to measure the complexity of a language L is to consider the characteristic sequence of L: the sequence a 1 ; a 2 ; where a i is zero or one, according to whether or not x i 2 L, where x 1 ; x 2 ; is an enumeration of 6 3 . Investigations of this sort may be found in [Ko86, Huy85, Huy86, BDG87, MS90, Lut91]. For example, in [BDG87] it was shown that PSPACE poly is the class of all languages L such that each finite prefix of the characteristic sequence of L has small space bounded Kolmogorov complexity. It is often useful, however, to consider the complexity of the individual strings in a language ....

D. Huynh. Resource-bounded Kolmogorov complexity of hard languages. In Proc. Structure in Complexity Theory, Springer-Verlag, Lecture Notes in Computer Science 223:184--195, 1986. Eric Allender

....complexity to measure the complexity of a language L is to consider the characteristic sequence of L: the sequence a 1 ; a 2 ; where a i is zero or one, according to whether or not x i 2 L, where x 1 ; x 2 ; is an enumeration of Sigma . Investigations of this sort may be found in [Ko86, Huy85, Huy86, BDG87, MS90, Lut91]. For example, in [BDG87] it was shown that PSPACE poly is the class of all languages L such that each finite prefix of the characteristic sequence of L has small space bounded Kolmogorov complexity. It is often useful, however, to consider the complexity of the individual strings in a language ....

D. Huynh. Resource-bounded Kolmogorov complexity of hard languages. In Proc. Structure in Complexity Theory, Springer-Verlag, Lecture Notes in Computer Science 223:184--195, 1986. Eric Allender

No context found.

D. T. Huynh. Resource-bounded Kolmogorov complexity of hard languages. In Structure in Complexity Theory, pages 184--195, Berlin, 1986. Springer-Verlag.

No context found.

D.T. Huynh, Resource-bounded Kolmogorov complexity of hard languages, Structure in Complexity Theory, 1986, Lecture Notes in Computer Science, Vol. 223, pp. 184-- 195.

No context found.

D. T. Huynh. Resource bounded Kolmogorov complexity of hard languages. In Proc. 1st Conf. on Structure in Complexity Theory, Lecture Notes in Comput. Sci., 223, pages 184--195. Springer Verlag, 1986.

No context found.

D. T. Huynh. Resource bounded Kolmogorov complexity of hard languages. In Proc. 1st Conf. on Structure in Complexity Theory, Lecture Notes in Comput. Sci., 223, pages 184--195. Springer Verlag, 1986.

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