Abstract
The computation of Boolean functions by parallel computers with shared memory (PRAMs and WRAMs) is considered. In particular complexity measures for parallel computers like critical and sensitive complexity are compared with other complexity measures for Boolean functions like branching program depth and length of prime implicants and clauses. The relations between these complexity measures and their asymptotic behavior are investigated for the classes of all Boolean functions, monotone functions and symmetric functions.
Supported in part by DFG grant We 1066/1-1
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Cook,S.; Dwork,C.; Reischuk,R.: Upper and lower time bounds for parallel random access machines without simultaneous writes, to appear: SIAM Journal on Computing
Erdös, P.; Rényi, A.: On the evolution of random graphs, Publ.Math.Inst. Hung.Acad.Sci. 5 A (1960) 17–61
Korshunov, A.D.: On the number of monotone Boolean functions (in Russian), Probl.Kibern. 38 (1981) 5–108
Rivest, R.L.; Vuillemin, J.: On recognizing graph properties from adjacency matrices, Theoretical Computer Science 3 (1976) 371–384
Simon, H.U.: A tight Ω (log log n) bound on the time for parallel RAM's to compute nondegenerate Boolean functions, FCT'83, Lecture Notes in Computer Science 158 (1983) 439–444
Turán,G.: The critical complexity of graph properties, Information Processing Letters (1984) 151–153
Vishkin, U.; Wigderson, A.: Trade-offs between depth and width in parallel computation, SIAM Journal on Computing 14 (1985) 303–314
Wegener, I.: Optimal decision trees and one-time-only branching programs for symmetric Boolean functions, Information and Control 62 (1984) 129–143
Wegener, I.: The critical complexity of all (monotone) Boolean functions and monotone graph properties, FCT'85, Lecture Notes in Computer Science 199 (1985) 494–502
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bublitz, S., Schürfeld, U., Voigt, B., Wegener, I. (1986). Properties of complexity measures for PRAMs and WARMs. In: Gruska, J., Rovan, B., Wiedermann, J. (eds) Mathematical Foundations of Computer Science 1986. MFCS 1986. Lecture Notes in Computer Science, vol 233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016246
Download citation
DOI: https://doi.org/10.1007/BFb0016246
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16783-9
Online ISBN: 978-3-540-39909-4
eBook Packages: Springer Book Archive