The 2CNF Boolean formula satisfiability problem and the linear space hypothesis

We aim at investigating the solvability/insolvability of nondeterministic logarithmic-space (NL) decision, search, and optimization problems parameterized by natural size parameters using simultaneously polynomial time sub-linear space. are particularly focused on 2SAT3—a restricted variant 2CNF Boolean (propositional) formula satisfiability problem in which each variable a given appears most 3 times form literals—parameterized total number mvbl(ϕ) variables ϕ. propose new, practical working hypothesis, called linear space hypothesis (LSH), asserts that (2SAT3,mvbl) cannot be solved only “sub-linear” (i.e., mvbl(x)εpolylog(|x|) for constant ε∈[0,1)) all instances x. Immediate consequences LSH include L≠NL, LOGDCFL≠LOGCFL, SC≠NSC. For our investigation, we fully utilize key notion “short reductions”, under class PsubLIN polynomial-time sub-linear-space solvable is indeed closed.