Linear 3SAT. The 3SAT problem is defined in Section 8.1. Briefly, the input is a Boolean formula—expressed as a set of clauses—over some set of variables and the goal is to determine whether there is an assignment (of true/false values) to these variables that makes the entire formula evaluate to true.
Consider a 3SAT instance with the following special locality property. Suppose there are n variables in the Boolean formula, and that they are numbered 1,2,..., n in such a way that each clause involves variables whose numbers are within ±10 of each other. Give a linear-time algorithm for solving such an instance of 3SAT.
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