Lower-bound techniques in some parallel models of computation

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1989

OSTI ID:6223398

Yan, Peiyuan

The work described in this thesis is concerned with obtaining lower bounds on time and hardware for certain parallel models of computation. Several lower bound results are derived and their consequences in the context of complexity theory are discussed. Two parallel models of computation are studied in this thesis-constant depth unbounded fan-in circuits and parallel random access machines without simultaneous writes. Constant depth unbounded fan-in circuits have been studied extensively because of their mathematical simplicity and strong connection with other sequential and parallel models of computation. The question of separating ACC from NC{sup 1} is currently the frontier of the research. In attempt to gain insight of the structure of ACC, an algebraic technique for depth 2 circuits of Mod{sub p} and Mod{sub q} gates is developed. Using this algebraic technique, exponential lower bounds on the size for some special depth 2 and 3 circuits of mod{sub 2} and mod{sub q} gates are obtained. Parallel random access machines without simultaneous writes are among the most popular parallel models of computation. The restriction of without simultaneous writes puts limits on the way that processors of a parallel random access machine communicate with each other, which in turn limits the computational power of parallel random access machines. S. Cook et al. first studied this situation in 1982 and obtained a lower time bound of log{sub 4.79} n for parallel random access machines to compute a class of functions called critical functions. Following in this direction, the way processors of a parallel random access machine communicate with each other and its limit are further studied in this thesis. As the result of this study, a lower time bound of log{sub 4} n for computing critical functions is obtained.

• Research Organization: Pennsylvania State Univ., University Park, PA (USA)
• OSTI ID: 6223398
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGEBRA
ALGORITHMS
COMPUTER ARCHITECTURE
COMPUTER CALCULATIONS
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
MATHEMATICS
PARALLEL PROCESSING
PROGRAMMING