The regular language (a+ b)âˆ—a (the words in alphabet {a, b} having a as the last letter) is at the moment a classical example of a language not recognizable by a one-way quantum finite automatonâ€¦ (More)

In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total boolean function is given by the function <i>f</i> onâ€¦ (More)

We present three new quantum algorithms in the quantum query model for graph-collision problem: â€“ an algorithm based on tree decomposition that uses O (âˆš nt 1/6 ) queries where t is the treewidth ofâ€¦ (More)

We show an equivalence between 1-query quantum algorithms and representations by degree2 polynomials. Namely, a partial Boolean function f is computable by a 1-query quantum algorithm with errorâ€¦ (More)

The paper gives a short introduction to mutually unbiased bases and the Welch bounds and demonstrates that the latter is a good technical tool to explore the former. In particular, a criterion for aâ€¦ (More)

In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total Boolean function is given by the function <i>f</i> onâ€¦ (More)