This paper continues the investigation of the connection between proof
systems and approximation. The emphasis is on proving ``tight''
non-approximability results via consideration of measures like the
``free bit complexity'' and the ``amortized free bit complexity'' of
proof systems.

The first part of the paper presents a collection of new ... more >>>

We prove an extremal combinatorial result regarding
the fraction of satisfiable clauses in boolean CNF
formulae enjoying a locally checkable property, thus
solving a problem that has been open for several years.

We then generalize the problem to arbitrary constraint
satisfaction problems. We ... more >>>

During the past three years there was an explosion of algorithms
solving MAX-SAT and MAX-2-SAT in worst-case time of the order
c^K, where c<2 is a constant, and K is the number of clauses
in the input formula. Such bounds w.r.t. the number of variables
instead of the number of ... more >>>

The maximum 2-satisfiability problem (MAX-2-SAT) is:
given a Boolean formula in $2$-CNF, find a truth
assignment that satisfies the maximum possible number
of its clauses. MAX-2-SAT is MAXSNP-complete.
Recently, this problem received much attention in the
contexts of approximation (polynomial-time) algorithms
... more >>>