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On theories of bounded arithmetic for NC¹

By Emil Jerábek


We develop an arithmetical theory VNC 1 ∗ and its variant VNC 1 ∗, corresponding to “slightly nonuniform ” NC 1. Our theories sit betweenVNC 1 and VL, and allow evaluation of log-depth bounded fan-in circuits under limited conditions. Propositional translations of ΣB 0 (LVNC 1)-formulas provable in VNC 1 ∗ admit L-uniform polynomial-size Frege proofs

Year: 2010
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