Parallel Algorithms for Relational Coarsest Partition Problems

Relational Coarsest Partition Problems (RCPPs) play a vital role in verifying concurrent systems. It is known that RCPPs are P-complete and hence it may not be possible to design polylog time parallel algorithms for these problems. In this paper, we present two efficient parallel algorithms for RCPP in which its associated label transition system is assumed to have m transitions and n states. The first algorithm runs in O(n/sup 1+/spl epsiv//) time using m/n/sup /spl epsiv// CREW PRAM processors, for any fixed /spl epsiv/<1. This algorithm is analogous to and optimal with respect to the sequential algorithm of P.C. Kanellakis and S.A. Smolka (1990). The second algorithm runs in O(n log n) time using m/n CREW PRAM processors. This algorithm is analogous to and nearly optimal with respect to the sequential algorithm of R. Paige and R.E. Tarjan (1987).

[1]  Jan A. Bergstra,et al.  Algebra of Communicating Processes with Abstraction , 1985, Theor. Comput. Sci..

[2]  Richard P. Brent,et al.  The Parallel Evaluation of General Arithmetic Expressions , 1974, JACM.

[3]  Edmund M. Clarke,et al.  Formal Methods: State of the Art and Future Directions Working Group Members , 1996 .

[4]  Scott A. Smolka,et al.  Towards efficient parallelization of equivalence checking algorithms , 1992, FORTE.

[5]  S. Sitharama Iyengar,et al.  Introduction to parallel algorithms , 1998, Wiley series on parallel and distributed computing.

[6]  Frank Thomson Leighton.  Introduction to parallel algorithms and architectures: arrays , 1992 .

[7]  Rance Cleaveland,et al.  Strategic directions in concurrency research , 1996, CSUR.

[8]  Sajal K. Das,et al.  Book Review: Introduction to Parallel Algorithms and Architectures : Arrays, Trees, Hypercubes by F. T. Leighton (Morgan Kauffman Pub, 1992) , 1992, SIGA.

[9]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[10]  Rance Cleaveland,et al.  The concurrency workbench: a semantics-based tool for the verification of concurrent systems , 1993, TOPL.

[11]  I. Lee,et al.  PARAGON: a paradigm for the specification, verification and testing of real-time systems , 1997, 1997 IEEE Aerospace Conference.

[12]  Sanjeev Saxena,et al.  On Parallel Prefix Computation , 1994, Parallel Process. Lett..

[13]  Scott A. Smolka,et al.  CCS expressions, finite state processes, and three problems of equivalence , 1983, PODC '83.

[14]  Jean-Claude Fernandez,et al.  An Implementation of an Efficient Algorithm for Bisimulation Equivalence , 1990, Sci. Comput. Program..

[15]  Richard Cole,et al.  Parallel merge sort , 1988, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[16]  José L. Balcázar,et al.  Parallel Complexity in the Design and Analysis on Conurrent Systems , 1991, PARLE.

[17]  Robert E. Tarjan,et al.  Three Partition Refinement Algorithms , 1987, SIAM J. Comput..

[18]  Rance Cleaveland,et al.  The Concurrency Factory - Practical Tools for Specification, Stimulation, Verification, and Implementation of Concurrent Systems , 1994, Specification of Parallel Algorithms.

[19]  Krzysztof Diks,et al.  Improved Deterministic Parallel Integer Sorting , 1991, Inf. Comput..

[20]  Joseph JáJá,et al.  An Introduction to Parallel Algorithms , 1992 .

[21]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.