Nondeterministic Quantum Query and Communication Complexities

Nondeterministic Quantum Query and Quantum Communication Complexities

We study nondeterministic quantum algorithms for Boolean functions f. Such algorithms have positive acceptance probability on input x iff f (x) = 1. In the setting of query complexity, we show that the nondeterministic quantum complexity of a Boolean function is equal to its " nondeterministic polynomial " degree. We also prove a quantum-vs.-classical gap of 1 vs. n for nondeterministic query c...

Nondeterministic Quantum Query and Communication Complexities

On Randomized and Quantum Query Complexities

We study randomized and quantum query (a.k.a. decision tree) complexity for all total Boolean functions, with emphasis to derandomization and dequantization (removing quantumness from algorithms). Firstly, we show that D(f) = O(Q1(f) ) for any total function f , where D(f) is the minimal number of queries made by a deterministic query algorithm and Q1(f) is the number of queries made by any qua...

Quantum Weakly Nondeterministic Communication Complexity

In this paper, we study a weak version of quantum nondeterministic communication complexity, corresponding to the most natural generalization of classical nondeterminism, in which a classical proof has to be checked with probability one by a quantum protocol. Another stronger definition of quantum nondeterminism has already been extensively studied, corresponding to the view of quantum nondeter...

Relationships Between Nondeterministic and Deterministic Tape Complexities

This paper first proves the Savitch Theorem: any nondeterminstic L(n)− tape bounded Turing Machine can be simulated by a deterministic [L(n)]− tape bounded Turing machine, provided L(n) ≥ log2n. Then as an attempt to answer the following question: “Given a nondeterministic tape bounded Turing machine which accepts set A, how much additional storage does a deterministic Turing machine require to...