Abstract
We survey the efficiency of the ‘fast’ parallel algorithms for the recognition and ranking of context-free languages on the Parallel Random Access Machine without write conflicts. The efficiency of the algorithm is the total number of operations (the product of time and number of processors). Such efficiency depends heavily on the class of context-free grammars and on the meaning of ‘fast’: log(n), log2n or sublinear time. The slower is the algorithm the better is its total efficiency. Several new results are presented in the paper. A new simpler version of the log(n) time parallel recognition of unambiguous cfl's is presented. The parallel complexity of ranking and max-word problems for several classes of cfl's is related to the complexity of certain (⊕,⊗)-transitive closure problems, where (⊕,⊗)=(+,*) for the ranking problem of unambiguous languages and (⊕,⊗)=(max,concat) for the max-word problem. This simplifies the ranking and max-word algorithms and reduces the number of processors.
The work of the first two authors was supported by the Deutsche Forschungsgemeinschaft, SFB 342, TP A4: “KLARA”. The work of the third author was supported by the grant KBN 2-1190-91-01 of the Polish Ministery of Education.
Preview
Unable to display preview. Download preview PDF.
Bibliography
A.Aho, J.Hopcroft, J.Ullman, The design and analysis of computer algorithms, Addison-Wesley 1974
C.Alvarez, B.Jenner, A very hard log space counting problem, 5th Structure in Compl. Conf. (1990) 154–168
L.Banachowski, A.Kreczmar, W.Rytter, Analysis of algorithms and data structures, Addison-Wesley 1991
A. Bertoni, M. Goldwurm, N. Sabatini. Computing the counting function of context-free languages. In Proc. of 4th STACS, LNCS 247, 1987, pages 169–179.
D. Bruschi, G. Pighizzini. The complexity of computing maximal word functions. In Proc. of FCT'91, 1991, pages 157–167.
G. Buntrock, B. Jenner, K.-J. Lange, P. Rossmanith. Unambiguity and fewness for logarithmic space. In Proc. of FCT'91, 1991, pages 168–179.
I. Bar-On, U.Vishkin, Optimal parallel generation of a computation tree form, ACM Trans. on Prog. Lan. and Systems 7:2 (1985) 348–357
M.Chytil, B.Monien, Caterpillars and context-free languages, STACS'90
M.Chytil, M. Crochemore, B.Monien, W.Rytter, On the parallel recognition of unambiguous context-free languages, Theoretical Computer Science 1991
J.Cohen, T.Hickey, J.Katcoff, Upper bounds for speedup in parallel parsing, JACM 29:2 (1982) 408–428
J.Cohen, S.Kolodner, Estimating the speedup in parallel parsing, IEEE Trans. Software Eng. SE-11 (1985) 114–124
P. Dymond, W. L. Ruzzo. Parallel RAM's with owned global memory and deterministic language recognition. 13th ICALP, pages 95–104.
K.Diks, W.Rytter, On optimal parallel computations for sequences of brackets, TCS 87 (1991) 251–262
S.Fortune, J.Wyllie, Parallelism in random access machines, in Proc. 10th ACM Symposium on Theory of Computation (1978) 114–118
A.Gibbons, W.Rytter, Efficient parallel algorithms, Cambridge Univ. Press 1988
A.Gibbons, W.Rytter, Optimal parallel algorithms for dynamic expression evaluation and context-free recognition, Information and Computation 81 (1989) 32–45
N.D. Jones, S. Skyum: Complexity of some problems concerning L systems, Math. Systems Theory 13, 29–43, 1979.
Huynh, The complexity of ranking. Math. Systems Theory 23, 1–19, 1990.
P.Klein, Parallel recognition of context free languages, B.A. thesis, Harvard University, Cambridge, MA, (1984)
R.Kosaraju, Speed of recognition of context free language by array automata, SIAM J.Comp. (1975) 333–340
Klein, J.Reif, Parallel time O(log n) acceptance of deterministic cfl's on an exclusive-write PRAM, SIAM J. Comp. 17 (1987) 463–485
K-J. Lange, Unambiguity of circuits. To appear in TCS.
K-J. Lange, P. Rossmanith. Characterizing unambiguous augmented pushdown automata by circuits. MFCS '90, pages 399–406.
L.Larmore, W.Rytter, Efficient sublinear parallel time algorithms for dynamic programming and context-free recognition, STACS'92
K-J. Lange, P. Rossmanith, W.Rytter, On the parallel complexity of ranking and max-word problems for simple languages, manuscript, Techn. University of Munich, 1991
R.Mattheyses, C.Fiduccia, Parsing Dyck languages on parallel machines, 20th Allerton Conf. on Communication, Control and Computing, 1982
B.Monien, W.Rytter, H.Schäpers, Fast recognition of cfl's with smaller number of processors. To appear in TCS
G.Miller, J.Reif, Parallel tree contraction and its application, 26th FOCS, 478–489
E.W.Meyr, R.Werchner, Optimal routing of parentheses on the hypercube, manuscript, J.W.Goethe-University, Frankfurt, 1992
W.Plandowski, W.Rytter, T.Szymacha, Exact analysis of three tree contraction algorithms, in FCT'91
G.Pietsch, E. Schoemer, Optimal parallel recognition of bracket languages on hypercubes, STACS'91, 434–443
J.Reif, O(log n) time parallel acceptance of deterministic context free languages, FOCS (1985)
W.Rytter, R.Giancarlo, Optimal parallel parsing of bracket languages, TCS 53 (1987) 295–306
W.Rytter, A.Saoudi, Parallel recognition of two-dimensional languages, International Conf. on Pattern Recognition, Delft, 1992
W.Rytter, A.Saoudi, On the complexity of parallel recognition of 2D-images, IPL 38 (1991) 225–229
W.Rytter, On the complexity of parallel parsing of general context free languages, TCS 47 (19870 315–322
W.Rytter, The complexity of two-way pushdown automata and recursive programs, in Combinatorial algorithms on words (ed. A.Apostolico, Z.Galil), Springer-Verlag 1985
W.Rytter, Parallel time O(log n) recognition of unambiguous cfl's. Information and Computation 73, (1987), 75–86
W.Rytter, Efficient parallel computations of the cost of paths on a grid graph, Inf.Proc.Letters (1988)
W. Rytter:, On parallel evaluation of expressions and straight line programs, Computers and Artificial Intelligence 9 (1990) 427–431
W.Rytter, On the recognition of context-free languages, in Fifth Symposium on Computation Theory, Lecture Notes in Computer Science 208 (1985) 318–325
W.Rytter, Fast parallel computations for some dynamic programming problems, TCS 1989
W.Rytter, A note on parallel transformations of regular expressions to nondeterministic finite automata, IPL (1988)
W.Ruzzo, Tree-size bounded alternation, JCSS 21 (1980) 218–235
D.Skillicorn, D.Barnard, Parallel parsing on the connection machine, IPL 31 (1989)111–117
Y.Srikant, P.Shankar, Parallel parsing of programming languages, Inf. Sciences 43 (1987) 55–83
I.H. Sudborough: The time and tape complexity of developmental languages, In Proc. 4th ICALP, Springer LNCS 52, 509–521, 1977.
V.Vinay, Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits, 6th Structure in Compl. Conf. (1991) 270–284
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lange, KJ., Rossmanith, P., Rytter, W. (1992). Parallel recognition and ranking of context-free languages. In: Havel, I.M., Koubek, V. (eds) Mathematical Foundations of Computer Science 1992. MFCS 1992. Lecture Notes in Computer Science, vol 629. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-55808-X_3
Download citation
DOI: https://doi.org/10.1007/3-540-55808-X_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55808-8
Online ISBN: 978-3-540-47291-9
eBook Packages: Springer Book Archive