01216nas a2200157 4500008004100000245005100041210004400092300001400136490000800150520073400158100002400892700002200916700001700938700002500955856007800980 2014 eng d00aOn the complexity of quantified linear systems0 acomplexity of quantified linear systems a128–1340 v5183 aIn this paper, we explore the computational complexity of the conjunctive fragment of the first-order theory of linear arithmetic. Quantified propositional formulas of linear inequalities with (k−1) quantifier alternations are log-space complete in ΣkP or ΠkP depending on the initial quantifier. We show that when we restrict ourselves to quantified conjunctions of linear inequalities, i.e., quantified linear systems, the complexity classes collapse to polynomial time. In other words, the presence of universal quantifiers does not alter the complexity of the linear programming problem, which is known to be in P. Our result reinforces the importance of sentence formats from the perspective of computational complexity.1 aRuggieri, Salvatore1 aEirinakis, Pavlos1 aSubramani, K1 aWojciechowski, Piotr uhttps://kdd.isti.cnr.it/publications/complexity-quantified-linear-systems