J. Hartmanis, N. Immerman, and S. Mahaney. One-way log-tape reductions. In Proc. IEEE FOCS, pages 65--71, 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....quanti er free projections) and z 1 ; z 2 ; z k are free in and 0 . Proof. Sketch) Let be some problem accepted by the log space DOTM M with an NP oracle. Without loss of generality, we may assume that the oracle is HP (essentially because HP is complete for NP via 1 L reductions [19]) Also, by a result of Wagner [40] we may assume that on any input structure of size n, M makes O(log n) oracle queries. Consider a typical computation of M on some input structure of size n. There are some answers (0 or 1) to queries associated with this computation, and as there are O(log n) ....

J. Hartmanis, N. Immerman and S. Mahaney, One-way log-tape reductions, Proc. 19th Symp. Foundations of Computer Science, IEEE Press (1978) 65-71.

....counting classes to counting classes based on Turing machines. In section 3 we consider one way logspace counting classes. A one way Turing machine scans its input only once (from left to right, say) Studying this type of Turing machines has a long tradition in theoretical computer science [HU69] [HIM78]. It is obvious that one can define the counting classes #1L and span 1L via one way logspace Turing machines, similar to the well known classes #L and span L. In [AJ93] it is shown that 1UL = 1NL , #1L = span 1L , #1L opt 1L. From a result in communication complexity [MS82] it follows that 1UL ....

....there exists a logspace computable relation R and for all x it holds that f(x) jjfy : x; y) 2 Rgjj. A one way logspace TM (NTM, ATM) is a Turing machine with a logarithmic space bound, a one way read only input tape, and a one way write only output tape. We follow the definition (as, e.g. in [HIM78]) that c Delta dlog(n)e tape cells are marked on the work tapes before the beginning of a computation on an input of size n (c is a constant) We define F1L, 1NL, 1UL, #1L, 1NLMV, and span 1L similar to the classes FL, NL, UL, #L, NLMV, and span L except that we use one way logspace Turing ....

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J. Hartmanis, N. Immerman, and S. Mahaney. One-way log-tape reductions. In Proc. 19th IEEE Symp. Foundations of Computer Science, pages 65 -- 71. IEEE Computer Society Press, 1978.

....method of [ADKP89] can be carried out by a CFA S. However, the monoid of transformations of S contains GF(2) as a subgroup, so S is neither aperiodic nor a gh. Open Problem 1. Does every language accepted by a CFA in O(log n) passes belong to NC 1 (Such languages do belong to one way logspace [HIM78]. Open Problem 2. For k 1, is AC k = BM k (ap) In general, how do conditions on the structure of GSMs allowed to a BM correspond to circuit classes To conclude, the BM refines analyses which have been based on other vector models or Turing machine reversal complexity. The BM does not ....

J. Hartmanis, N. Immerman, and S. Mahaney. One-way log tape reductions. In Proc. 19th FOCS, pages 65--72, 1978.

....head. One way linear and superlinear space bounded Turing machines has the same power as corresponding two way machines (two way machines have two way read head on the input tape) But one way Turing machine sublinear space bounded machines are less powerful than two way machines (see for example [15]) In this paper we use the following one way machine model. On the input tape immediately after the last symbol of the input word there is written a special marker. The head on the input tape initial observes the first symbol of the input word; the worktape is empty. The set of states Q is ....

J. Hartmanis, N. Immerman, and S. Mahaney, One-way log-tape reductions, in Proc. of the 19th Annual IEEE Symposium on Foundations of Computer Science, (1978), 65-71.

....problem for growing grammars, i.e. the problem in which not only the tested word but also a growing grammar is a parameter. We solve this problem by proving (via generic reduction) its NP completeness. The reduction is of low complexity, namely one way log space. For such one way reductions see [HIM78, All88]. Having a very elegant and simple definition growing grammars appear at the first look to generate not an interesting class of languages. In particular, this class (we denote it by GCSL) seemed to be not closed under such basic operations as intersection with regular sets or inverse homomorphism. ....

....time because the degree of the polynomial bounding its complexity is dependent on the grammar and can be arbitrary large. We give here a strong argument that this problem presumably is intractable, showing that it is NP complete under a weak type of reducibility, namely one way logspace (see [HIM78, All88] for more information about this type of reducibility) Let G denote a word coding a grammar G. Our problem consists in determining the complexity of the language LGCSL = fh G; wi : G is a growing context sensitive grammar and w 2 L(G)g: As a function coding grammars can be taken any ....

Juris Hartmanis, Neil Immerman, and Stephen R. Mahaney. One-way log-tape reductions. In 19th Annual Symposium on Foundations of Computer Science (FOCS), pages 65--71, 1978.

....grant CCR 9207797. Cook proved that the Boolean satisfiability problem (SAT) is NP complete via polynomialtime Turing reductions. Over the years SAT has been shown complete via weaker and weaker reductions, e.g. polynomial time many one [Kar] logspace many one [Jon] one way logspace many one [HIM], and first order projections (fops) Dah] These last reductions, defined in Section 3, are provably weaker than logspace reductions. It has been observed that natural complete problems for various complexity classes including NC 1 , L, NL, P, NP, and PSPACE remain complete via fops, cf. I87, ....

Juris Hartmanis, Neil Immerman, and Stephen Mahaney, "One-Way Log Tape Reductions," 19th IEEE FOCS Symp. (1978), 65-72.

....the time. In [Coo] Cook proved that the Boolean satisfiability problem (SAT) is NP complete via polynomial time Turing reductions. Over the years SAT has been shown complete via weaker and weaker reductions, e.g. polynomial time many one [Kar] logspace many one [Jon] one way logspace many one [HIM], and first order projections (fops) Dah] These last reductions, defined in Section 3, are provably weaker than logspace reductions. It has been observed that natural complete problems for various complexity classes remain complete via fops, cf. I87, IL, SV, Ste] On the other hand, Joseph and ....

Juris Hartmanis, Neil Immerman, and Stephen Mahaney, "One-Way Log Tape Reductions," 19th IEEE FOCS Symp. (1978), 65-72.

....Theorem 25 ( KMR89] If scrambling functions exist, then the complete 1 li degrees of each of NP, PSPACE, EXP, NEXP, and RE all fail to collapse. Thus, if any of the 1 li complete degrees of NP, PSPACE, EXP, NEXP, and RE collapse, then scrambling functions do not exist. 23 A 1 L reduction [HIM81] is roughly an m reduction that is computable by a logspace bounded Turing machine that has a one way input head. 1. The Structure of Complete Degrees 25 Disproving the existence of scrambling functions is likely to be hard because these functions exist relative to random oracles, see Theorem ....

J. Hartmanis, N. Immerman, and S. Mahaney. One-way logtape reductions. In Proceedings of the 19th Annual IEEE Symposium on Foundations of Computer Science, pages 65--72, 1981.

....In [Coo71] Cook proved that the boolean satisfiability problem (SAT) is NP complete via polynomial time Turing reductions. Over the years SAT has been shown complete via weaker and weaker reductions, e.g. polynomial time many one [Kar] logspace many one [Jon] one way logspace many one [HIM]. We find it astounding that SAT remains NP complete via reductions that are provably much weaker than L. Fact 3.10 ( Dah] SAT is complete for NP via quantifier free projections. 3 4 Operators and Normal Forms Many natural complete problems for other important complexity classes remain ....

....the coding of the problem. Our intuitive feeling when we started this work was that the coding does not matter very much as long as it is sensibly done. However, upon further reflection, we found that the coding really can matter in some cases. An example from the literature is Theorem 4. 2 from [HIM] which says that there are P complete and NP complete sets via logspace reductions that because of the coding are not complete via one way logspace reductions. Closer to home, we were unable to prove Theorem 5.2 the way we had originally encoded it: With the coding R(x; i; j) meaning that ....

Juris Hartmanis, Neil Immerman, and Stephen Mahaney (1978), One-Way Log Tape Reductions, 19th IEEE FOCS Symposium, 65-72.

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Juris Hartmanis, Neil Immerman, and Stephen Mahaney, "One-Way Log Tape Reductions," 19th IEEE FOCS Symposium, 1978, (65-72).

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J. Hartmanis, N. Immerman, and S. Mahaney. One-way log-tape reductions. In Proc. IEEE FOCS, pages 65--71, 1978.

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