# Query complexity for functions $f\colon\left\{0,1\right\}^n\to\left\{0,1\right\}^m$

I'm studying query complexity and I'm trying to understand Bernstein-Vazirani's problem (https://en.wikipedia.org/wiki/Bernstein%E2%80%93Vazirani_algorithm) and Simon's problem (https://en.wikipedia.org/wiki/Simon%27s_problem). However, I've only seen the query complexity model defined for functions $$f\colon\left\{0,1\right\}^n\to\left\{0,1\right\}$$ (for example, in the survey by Buhrman and de Wolf [1]) and I can't use it for those problems, since they are defined as functions $$f\colon\left\{0,1\right\}^n\to\left\{0,1\right\}^m$$ (more specifically, $$n=2^m$$ and $$m\geq 1$$ for these particular problems).

Do you know any references where they define the query complexity model for functions $$f\colon\left\{0,1\right\}^n\to\left\{0,1\right\}^m$$?

[1] Harry Buhrman and Ronald De Wolf. Complexity measures and decision tree complexity: a survey. Theoretical Computer Science, 288(1):21–43, 2002.

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• The Boolean-output case ($\{0,1\}$) easily generalizes to non-Boolean case. What prevents you from generalizing by yourself mentally? – Lwins May 22 at 19:53