On the satisfiability of random regular signed SAT formulas

Regular signed SAT is a variant of the well-known satisfiability problem in which the variables can take values in a fixed set V ⊂ [0, 1], and the literals have the form “x ≤ a” or “x ≥ a” instead of “x” or “x̄”. We answer some open question regarding random regular signed k-SAT formulas: The probability that a random formula is satisfiable increases with |V |; there is a constant upper bound on the ratio m/n of clauses m over variables n, beyond which a random formula is asypmtotically almost never satisfied; for k = 2 and V = [0, 1], there is a phase transition at m/n = 2.