2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/31313As is well known, Buss' theory of bounded arithmetic $S^{1}_{2}$ proves $Σ_{0}^{b}(Σ_{1}^{b})-LIND$; however, we show that Allen's $D_{2}^{1}$ does not prove $Σ_{0}^{b}(Σ_{1}^{b})-LLIND$ unless $P = NC$. We also give some interesting alternative axiomatisations of $S^{1}_{2}$.Logic in Computer ScienceComputational ComplexityF.4.1text