I. H. Sudborough, \A note on tape-bounded complexity classes and linear context-free languages", Journal of the ACM, 22:4 (1975), 499{ 500.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... The main properties of linear context free grammars and the languages they generate have been uncovered already in the early days of formal language theory [1] One of their most attractive properties is low computational complexity: the general membership problem is known to be NLOGSPACE complete [5], while every particular language can be recognized in square time and linear space using a well known algorithm that inductively computes for each substring of the input string the set of nonterminals deriving that string. This algorithm is known to have a simple generalization for the case of ....

I. H. Sudborough, \A note on tape-bounded complexity classes and linear context-free languages", J. of the ACM, 22:4 (1975), 499-500. 12

....grammars are distinct. Linear context free languages have been studied since the early days or formal language theory [2 4,10] their fundamental properties have been discovered already in the sixties. The membership problem for linear context free grammars was shown to be NLOGSPACE complete [11] in 1975. The later theoretical research [5,6] in the area was mostly concerned with various special cases of linear context free grammars that are even easier from the point of view of computation complexity, but still retain some of the generative power of the original class. The subject of ....

I. H. Sudborough, \A note on tape-bounded complexity classes and linear context-free languages", Journal of the ACM, 22:4 (1975), 499-500.

.... grammars and the languages they generate have been uncovered already in the early days of formal language theory [1] One of the most attractive properties of these generative devices is their low computational complexity: the general membership problem is known to be NLOGSPACE complete [6], and for every linear context free language there exists a square time and linear space Turing machine that accepts it. The latter recognition algorithm uses dynamic programming method to compute the collection of sets fT ij g 16i6j6n (where n is the length of the input string) such that each T ....

I. H. Sudborough, \A note on tape-bounded complexity classes and linear context-free languages", Journal of the ACM, 22:4 (1975), 499-500. 20

.... grammars and the languages they generate have been uncovered already in the early days of formal language theory [1] One of the most attractive properties of these generative devices is their low computational complexity: the general membership problem is known to be NLOGSPACE complete [6], and for every linear context free language there exists a square time and linear space Turing machine that accepts it. The latter recognition algorithm uses dynamic programming method to compute the collection of sets fT ij g 16i6j6n (where n is the length of the input string) such that each T ....

I. H. Sudborough, \A note on tape-bounded complexity classes and linear context-free languages", Journal of the ACM, 22:4 (1975), 499-500.

....Together with the results of Section 6.1, this leads us to the following statement: Theorem 3 The membership problem for conjunctive grammars is P 6. 3 Membership problem for linear conjunctive grammars The membership problem for linear context free grammars is known to be NLOGSPACE complete [10]. We shall now demonstrate that a similar problem for linear conjunctive grammars turns out to be harder. Let us modify the construction of conjunctive grammar given in Section 6.2 to obtain the following result: Theorem 4 The membership problem for linear conjunctive grammars is P complete. ....

I. H. Sudborough, \A note on tape-bounded complexity classes and linear context-free languages", Journal of the Association for Computing Machinery, 22:4 (1975), 499-500.

.... applicable to our case [1] In fact, NL hardness of the xed membership problem for non centralized regular PCGS with two components already follows by its inclusion of the linear languages proved in [12] in combination with the well known NL hardness result for linear languages due to Sudborough [38]. We will discuss a variant of PCGS which we call PCGS with terminal transmission, PCGSTT for short, a model where only transmissions of terminal strings are allowed in order to exclude the in uence of the queried component grammar on the querying component grammar. Systems with this property ....

....known that the xed membership problem with xed index is NL complete in the case of programmed grammars of nite index, see [16, Fig. 1] This implies, in particular, that MAT (CF) is contained in NL due to [11, 35] Fortunately, the classical techniques developed by Sudborough are applicable [39, 38] to our language classes, so that we can show NL completeness for our variant rather straightforwardly. Namely, we have shown in Example 7 how to encode the graph accessibility problem of directed graphs into a PCGSTT with only three components. Hence, we can conclude: Corollary 23 For each n ....

I. H. Sudborough. A note on tape-bounded complexity classes and linear context-free languages. Journal of the Association for Computing Machinery, 22(4):499-500, 1975.

....in particular, that MAT (CF) is contained in NL due to [9, 25] Corollary 23 PC GSTT and PC GSTTfs are subsets of NL. Is the xed membership with xed number of components hard for NL in the case of PCGSTTfs The classical techniques developed by Sudborough does not seem to be applicable [30, 29]. The technique used by Abrahamson, Cai and Gordon to show NL hardness for so called coherent PCGS makes heavily use of non centralized features and is hence not applicable to our case either [1] 7 Concerning learnability We discuss PCGSTT whose grammar components are in some sense TDRL ....

I. H. Sudborough. A note on tape-bounded complexity classes and linear context-free languages. Journal of the Association for Computing Machinery, 22(4):499-500, 1975.

....is NC 1 complete, under weak reductions. 2. The xed membership for L(K; LIN) and L(KREG ; LIN) languages is NL complete. ut Proof. The rst statement follows from the result on the NC 1 completeness of the regular languages given by Barrington [8] and the second one by Sudborough s [33] proof on the NL completeness of the linear languages. ut For the remaining two language families L(K LIN ; REG) and L(K LIN ; LIN) we brie y mention that Fernau and Holzer [13, Theorem 12] have shown that both language families have a NL complete xed membership problem. Theorem 10. The xed ....

I. H. Sudborough. A note on tape-bounded complexity classes and linear contextfree languages. Journal of the Association for Computing Machinery, 22(4):499{ 500, October 1975. 14

.... any problem complete for NL, even in the nonuniform setting, although one might initially suspect that our results, combined with those of [Ryt87] would yield such algorithms, because of the following considerations: ffl NL is the class of languages reducible to linear context free languages [Sud75] ffl The class of languages accepted by deterministic AuxPDAs in logarithmic space and polynomial time coincides with the class of languages logspacereducible to deterministic context free languages. ffl LogCFL coincides with AuxPDA(log n; n O(1) That is, there is a close connection ....

I. H. Sudborough. A note on tape-bounded complexity classes and linear context-free languages. J. Association of Computing Machinery, 22:499--500, 1975.

....CFL, the family of context free languages, is NAuxPDA TIMESPACE (pol; log n) complete [17] 2. DCFL, the family of deterministic context free languages, is complete for the class DAuxPDA TIMESPACE(pol; log n) 17] 3. LIN , the family of linear context free languages, is NSPACE (log n) complete [16]. 4. REG, the family of regular languages, is NC 1 complete [2] Here we have to use very fine notions of reducibility in order to treat low level complexity classes like NC 1 or AC 0 . With respect to the usual logspace reductions the regular languages, for instance, would trivially be ....

....restrictions of linear grammars. The adequacy of this concept is reflected by its equivalence with DPDA 1 turn . This approach leads to family of deterministic linear languages with a DSPACE(log n) complete word problem, which fits in nicely into the framework of completeness results like [16, 17] (see Figure 1) In contrast to that both the deterministic linear languages according to Ibarra, Jiang, and Ravikumar [10] and those according to Nasu and Honda [15] are based on linear grammars restricted by an LL(1) condition. The word problem corresponding to this approach leads to apparently ....

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I. H. Sudborough. A note on tape-bounded complexity classes and linear contextfree languages. Journal of the Association for Computing Machinery, 22(4):499--500, October 1975.

....If we allow unbounded fan in we get the class AC k . For all k 0, AC k NC k 1 AC k 1 . The class NC is the union of the classes NC k over all k 1. Many natural problems have been shown to be in NC; in particular, it is known that nondeterministic logspace (NLOG) is in NC 2 [Sud75, Ruz80] Pippenger [Pip79] and Ruzzo [Ruz81] have given alternate characterizations of NC. Another related class that has been considered is the P uniform version of NC called PUNC. Allender [All89b] studied this class and provided alternate characterizations in terms of alternating Turing ....

I. Sudborough. A note on tape-bounded complexity classes and linear context-free languages. J. Assoc. Comput. Mach., 22(4):499--500, 1975.

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I. H. Sudborough, \A note on tape-bounded complexity classes and linear context-free languages", Journal of the ACM, 22:4 (1975), 499{ 500.

No context found.

I. H. Sudborough. A note on tape-bounded complexity classes and linear context-free languages. J. Association of Computing Machinery, 22:499--500, 1975.

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