$1$ PAC$-$learning $-$ Finite Hypothesis Classes $[7+7=14$ points$]$

We want to PAC$-$learn a variant of decision lists formed by a set of if$-$then$-$rules as follows:

$"($if $l_1$ then $l_2)$ else $($ if $l_3$ then $l_4)$ else $($ if $l_5$ then $l_6)...$ else $($ if $l_k$ then $l_{k+1})"$

Assume literals of each variable appear in the formula at most once.

For example, the following is a hypothesis that is consistent with the following table:

$($a$)$ Describe a polynomial$-$time algorithm that either returns a consistent hypothesis or guarantees no such hypothesis

exists. Explain the run$-$time of the algorithm.

$($b$)$ Count the number of possible hypotheses and use your result to find an upper bound for the sample complexity for

PAC$-$learning the formula with parameters $lon$ and $.$