Algebraic methods for interactive proof systems
Journal of the ACM (JACM)
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
On isomorphisms and density of NP and other complete sets
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Computational Complexity
Note: The complexity of power-index comparison
Theoretical Computer Science
Competing provers yield improved Karp-Lipton collapse results
Information and Computation
Quantum and classical complexity classes: Separations, collapses, and closure properties
Information and Computation
Generation complexity versus distinction complexity
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
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In this thesis we examine some of the central problems in the theory of computational complexity, like the trade-offs between time and memory, the power of nondeterminism and parallelism, and the speed gained by adding new operations to random access machines. Our main result is the cahracterization of the power of multiplication in random access acceptors: we show, in Chapter 3, that for such models nondeterministic and deterministic computations are polynomially related and that there is a polynomial relationship between the amount of time required for acceptance by random access machines with multiplication, and the amount of tape required by Turing machines. Thus, the additional power gained by using multiplication is the same as that of memory over time (if any). We derive similar results for some other interesting instruction sets. We also have some results for probabilistic and nondeterministic computations: we define threshold machines and show how probabilistic Turing machines may simulate them, and exhibit a set of complete problems for threshold machines. For nondeterministic computations, we present a hierarchy of the elementary recursive languages obtained by polynomially bounded quantification over objects of higher and higher type, which represent nondeterministic time bounded computations with larger and larger bounds. Finally, we discuss some deterministic computations, and conclude with a look at some open problems.