Parallel Parsing on a One-Way Linear Array of Finite-State Machines

Efficient parallel algorithms for some parsing problems are presented. These problems include the parsing of linear context-free languages, languages accepted by nondeterministic one-counter automata, and transductions defined by a special class of two-tape nondeterministic finite-state transducers. The model of parallel computation is a one-way linear array of identical finite-state machines. The data movement in the array is one-way, from left to right. For inputs of length n, the array uses n nodes, but the design of the node (finite-state machine) is independent of n. Our algorithms can actually produce a parse, i.e., a sequence of rules (moves) that generates (accepts) an input, in linear time. When only a no/yes answer is required, the parsing problem becomes a recognition problem. The best serial (RAM) algorithms for the corresponding recognition problems take O(n2/log2n) time and space. Previous parallel algorithms for the recognition problems run in linear time on a one-way linear array of finite-state machines.

[1]  H. T. Kung,et al.  Fault-Tolerance and Two-Level Pipelining in VLSI Systolic Arrays , 1983 .

[2]  Daniel H. Younger,et al.  Recognition and Parsing of Context-Free Languages in Time n^3 , 1967, Inf. Control..

[3]  Oscar H. Ibarra,et al.  Some results concerning linear iterative (systolic) arrays , 1985, J. Parallel Distributed Comput..

[4]  Oscar H. Ibarra,et al.  Characterizations and Computational Complexity of Systolic Trellis Automata , 1984, Theor. Comput. Sci..

[5]  Oscar H. Ibarra,et al.  On Efficient Recognition of Transductions and Relations , 1985, Theor. Comput. Sci..

[6]  Sheila A. Greibach A Note on the Recognition of One Counter Languages , 1975, RAIRO Theor. Informatics Appl..

[7]  Michael A. Harrison,et al.  Parsing of General Context-Free Languages , 1976, Adv. Comput..

[8]  Arto Salomaa,et al.  Systolic trellis automatat , 1984 .

[9]  Daniel S. Hirschberg,et al.  A linear space algorithm for computing maximal common subsequences , 1975, Commun. ACM.

[10]  Seymour Ginsburg,et al.  The Equivalence of Stack Counter Acceptors and Quasi-Realtime Acceptors , 1974, J. Comput. Syst. Sci..

[11]  Jan van Leeuwen,et al.  Efficient Recognition of Rational Relations , 1982, Inf. Process. Lett..

[12]  Oscar H. Ibarra,et al.  Designing Systolic Algorithms Using Sequential Machines , 1986, IEEE Transactions on Computers.

[13]  Oscar H. Ibarra,et al.  VLSI algorithms for solving recurrence equations and applications , 1987, IEEE Trans. Acoust. Speech Signal Process..