Parallel RAMs with owned global memory and deterministic context-free language recognition

We identify and study a natural and frequently occurring subclass of Concurrent Read, Exclusive Write Parallel Random Access Machines (CREW-PRAMs). Called Concurrent Read, <italic>Owner</italic> Write, or CROW-PRAMS, these are machines in which each global memory location is assigned a unique “owner” processor, which is the only processor allowed to write into it. Considering the difficulties that would be involved in physically realizinga full CREW-PRAM model and demonstrate its stability under several definitional changes. Second, we precisely characterize the power of the CROW-PRAM by showing that the class of languages recognizable by it in time <italic>O</italic>(log n) (and implicity with a polynomial number of processors) is exactly the class LOGDCFL of languages log space reducible to deterministic context-free languages. Third, using the same basic machinery, we show that the recognition problem for deterministic context-free languages can be solved quickly on a deterministic auxilliary pushdown automation having random access to its input tape, a log <italic>n</italic> space work tape, and pushdown store of small maximum height. For example, time <italic>O</italic>(<italic>n</italic><supscrpt>1 + ε</supscrpt>) is achievable with pushdown height <italic>O</italic>(log<supscrpt>2</supscrpt> <italic>n</italic>). These result extend and unify work of von Braunmöhl, Cook, Mehlhorn, and Verbeek, Klein and Reif; and Rytter.

[2]  Noam Nisan,et al.  CREW PRAMS and decision trees , 1989, STOC '89.

[3]  Stephen A. Cook,et al.  Deterministic CFL's are accepted simultaneously in polynomial time and log squared space , 1979, STOC.

[4]  Wojciech Rytter.  Parallel Time O(log n) Recognition of Unambiguous Context-free Languages , 1987, Inf. Comput..

[5]  Stephen A. Cook,et al.  Characterizations of Pushdown Machines in Terms of Time-Bounded Computers , 1971, J. ACM.

[6]  Stephen A. Cook,et al.  Hardware complexity and parallel computation , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[7]  Uzi Vishkin,et al.  Simulation of Parallel Random Access Machines by Circuits , 1984, SIAM J. Comput..

[8]  Faith Ellen,et al.  Toward Understanding Exclusive Read , 1990, SIAM J. Comput..

[9]  James K. Archibald,et al.  Cache coherence protocols: evaluation using a multiprocessor simulation model , 1986, TOCS.

[10]  Philip N. Klein,et al.  Parallel Time O(log n) Acceptance of Deterministic CFLs on an Exclusive-Write P-RAM , 1988, SIAM J. Comput..

[11]  Rolf Niedermeier,et al.  Data-Independences of Parallel Random Access Machines , 1993, FSTTCS.

[12]  Rolf Niedermeier,et al.  PRAM's Towards Realistic Parallelism: BRAM's , 1995, FCT.

[13]  Tero Harju.  A Simulation Result for the Auxiliary Pushdown Automata , 1979, J. Comput. Syst. Sci..

[14]  Leslie M. Goldschlager,et al.  A unified approach to models of synchronous parallel machines , 1978, STOC.

[15]  John H. Reif,et al.  Parallel time O(log N) acceptance of deterministic CFLs , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[16]  Steven Fortune,et al.  Parallelism in random access machines , 1978, STOC.

[17]  Wojciech Rytter.  On the recognition of context-free languages , 1984, Symposium on Computation Theory.

[18]  Peter Rossmanith,et al.  The Owner Concept for PRAMs , 1991, STACS.

[19]  Seymour Ginsburg,et al.  Stack automata and compiling , 1967, JACM.

[20]  Gary L. Miller,et al.  Isomorphism of k-Contractible Graphs. A Generalization of Bounded Valence and Bounded Genus , 1983, Inf. Control..

[21]  Leslie M. Goldschlager,et al.  A universal interconnection pattern for parallel computers , 1982, JACM.

[22]  Faith Ellen,et al.  Pointers versus arithmetic in PRAMs , 1993, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference.

[23]  Tak Wah Lam,et al.  The power of parallel pointer manipulation , 1989, SPAA '89.

[24]  Patrick W. Dymond.  Indirect addressing and the time relationships of some models of sequential computation , 1979 .

[25]  Ivan Hal Sudborough,et al.  On the Tape Complexity of Deterministic Context-Free Languages , 1978, JACM.

[26]  Wojciech Rytter,et al.  Corrigendum: Fast Recognition of Deterministic CFL's with a Smaller Number of Processors , 1994, Theor. Comput. Sci..

[27]  Michael A. Arbib,et al.  An Introduction to Formal Language Theory , 1988, Texts and Monographs in Computer Science.

[28]  Rolf Niedermeier,et al.  On Optimal Orow-Pram Algorithms for Computing Recursively Defined Functions , 1995, Parallel Process. Lett..

[29]  James Christopher Wyllie,et al.  The Complexity of Parallel Computations , 1979 .

[30]  Faith Ellen,et al.  Towards understanding exclusive read , 1989, SPAA '89.

[31]  Faith Ellen,et al.  The Complexity of Computation on the Parallel Random Access Machine , 1993 .

[32]  Richard J. Anderson,et al.  A comparison of shared and nonshared memory models of parallel computation , 1991 .

[33]  Larry J. Stockmeyer,et al.  A characterization of the power of vector machines , 1974, STOC '74.

[34]  Kurt Mehlhorn,et al.  The Recognition of Deterministic CFL's in Small Time and Space , 1983, Inf. Control..

[35]  Walter L. Ruzzo,et al.  Tree-size bounded alternation(Extended Abstract) , 1979, J. Comput. Syst. Sci..

[36]  Walter L. Ruzzo,et al.  Parallel RAMs with Owned Global Memory and Deterministic Context-Free Language Recognition (Extended Abstract) , 1986, ICALP.

[37]  Stephen A. Cook,et al.  Upper and Lower Time Bounds for Parallel Random Access Machines without Simultaneous Writes , 1986, SIAM J. Comput..

[38]  Martin Tompa,et al.  The complexity of short two-person games , 1990, Discret. Appl. Math..