Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
Journal of the ACM (JACM)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Parallel Complexity Hierarchies Based on PRAMs and DLOGTIME-Uniform Circuits
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Hierarchies of DLOGTIME-uniform circuits
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
A Recursive Padding Technique on Nondeterministic Cellular Automata
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
A time hierarchy theorem for nondeterministic cellular automata
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
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We present translational lemmas for alternating Turing machines (ATMs) and parallel random access machines (PRAMs), and apply them to obtain tight hierarchy results on ATM- and PRAM-based complexity classes. It is shown that, for any small rational constant ε, there is a language which can be accepted by a c(9+ε)logrn-time d(4+ε)log n-space ATM with l worktapes but not by any clogrn-time dlog n-space ATM with the same l worktapes if the number of tape symbols is fixed. Here, c,d0 and r1 are arbitrary rational constants, and l≥2 is an arbitrary integer. It is also shown that, for any small rational constant ε, there is a language which can be accepted by a c(1+ε)logr1n-time PRAM with nr2 processors but not by any clogr1n-time PRAM with nr2(1+ε) processors, where c0, r11, and r2≥1 are arbitrary rational constants.