Lower bounds on parallel, distributed, and automata computations
In this thesis the author presents a collection of lower bound results from several areas of computer science. Conventional wisdom states that lower bounds are much more difficult to prove than upper bounds. To get an upper bound one has to demonstrate just one scheme with the appropriate complexity. On the other hand, to prove lower bounds one has to deal with all possible schemes. The difficulty of lower bounds can be further demonstrated by the fact that wherever for some problem he has a very large gap between the lower and the upper bound, the conjecture for the truth usually is the known upper bound. His first two results are impossibility results for finite state automata. A hierarchy of complexity classes on tree languages (analogous to the polynomial hierarchy) accepted by alternating finite state machines is introduced. It turns out that the alternating class is equal to the well known tree language class accepted by the treeautomata. By separating the deterministic and the nondeterministic classes of his hierarchy he gives a negative answer to the folklore question whether the expressive power of the treeautomata is the same as that of the finite state automaton that can walk on the edges of the tree (bugautomaton). He proves that three-head one-way DFA cannot perform string-matching, that is, no three-head one-way DFA accepts the language L = (x{number sign}y {vert bar} x is a substring of y, where x,y {element of} (0,1){sup *}). He proves that in a one round fair coin flipping (or voting) scheme with n participants, there is at least one participant who has a chance to decide the outcome with probability at least 3/n {minus} o(1/n).
- Research Organization:
- Harvard Univ., Cambridge, MA (USA)
- OSTI ID:
- 5815133
- Resource Relation:
- Other Information: Thesis (Ph.D)
- Country of Publication:
- United States
- Language:
- English
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