The size of shortest cut-free proofs of first-order formulas in intuitionistic sequent calculus is known to be non-elementary in the worst case in terms of the size of given sequent proofs with cuts of the same formulas. In contrast to that fact, we provide an elementary bound for the size of cut-free proofs for disjunction-free intuitionistic logic for the case where the cut-formulas of the or...

Field-Programmable Gate Arrays (FPGAs) are flexible and reusable circuits that can be easily reconfigured by the designer. One of the steps involved in the logic design with FPGA circuits is placement. In this step, the logic functions are assigned to specific cells of the circuit. In this paper we present a placement algorithm for FPGA circuits. In traditional min-cut based placement algorithm...

The objectives of this work were to determine the sample size (number plants) needed estimate mean cut and grazing sorghum (Sorghum bicolor (L.) Moench), Nutribem cultivar, traits investigate linear relations among traits. At 86 days after sowing, 110 plants selected at random. evaluated for each plant were: height, stem diameter, number nodes, leaves, leaf fresh matter, shoot dry matter. was d...

The paper corrects earlier upper bounds on the size of free-cut elimination. Free-cut elimination allows cut elimination to be carried out in the presence of non-logical axioms. The correction requires that the notion of a free-cut be modified so that a cut formula is anchored provided that all of its introductions are anchored, instead of only requiring that one of its introductions is anchore...

Free-cut elimination allows cut elimination to be carried out in the presence of non-logical axioms. Formulas in a proof are anchored provided they originate in a non-logical axiom or non-logical inference. This paper corrects and strengthens earlier upper bounds on the size of free-cut elimination. The correction requires that the notion of a free-cut be modified so that a cut formula is ancho...