0000000000314040
AUTHOR
Jevgenijs Vihrovs
Quantum Algorithms for Some Strings Problems Based on Quantum String Comparator
We study algorithms for solving three problems on strings. These are sorting of n strings of length k, “the Most Frequent String Search Problem”, and “searching intersection of two sequences of strings”. We construct quantum algorithms that are faster than classical (randomized or deterministic) counterparts for each of these problems. The quantum algorithms are based on the quantum procedure for comparing two strings of length k in O(k) queries. The first problem is sorting n strings of length k. We show that classical complexity of the problem is Θ(nk) for constant size alphabet, but our quantum algorithm has O˜(nk) complexity. The second one is searching the most frequent string among n …
Zero-Error Affine, Unitary, and Probabilistic OBDDs
We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las Vegas unitary and probabilistic OBDDs can be quadratically narrower than deterministic OBDDs. We also obtain the same results by considering the automata versions of these models.