We consider bounded occurrence (degree) instances of a minimum
constraint satisfaction problem MIN-LIN2 and a MIN-BISECTION problem for
graphs. MIN-LIN2 is an optimization problem for a given system of linear
equations mod 2 to construct a solution that satisfies the minimum number
of them. E3-OCC-MIN-E3-LIN2 ... more >>>

We consider the following optimization problem:
given a system of m linear equations in n variables over a certain field,
a feasible solution is any assignment of values to the variables, and the
minimized objective function is the number of equations that are not
satisfied. For ... more >>>

We introduce a second-order system V_1-Horn of bounded arithmetic
formalizing polynomial-time reasoning, based on Graedel's
second-order Horn characterization of P. Our system has
comprehension over P predicates (defined by Graedel's second-order
Horn formulas), and only finitely many function symbols. Other
systems of polynomial-time reasoning either ... more >>>