We present upper bounds on the size of codes that are locally
testable by querying only two input symbols. For linear codes, we
show that any $2$-locally testable code with minimal distance
$\delta n$ over a finite field $F$ cannot have more than
$|F|^{3/\delta}$ codewords. This result holds even ... more >>>

We show that the class of integer-valued functions computable by
polynomial-space Turing machines is exactly the class of functions f
for which there is a nondeterministic polynomial-time Turing
machine with a certain order on its paths that on input x outputs a 3x3
matrix with entries from {-1,0,1} on each ... more >>>

The best-known representations of boolean functions f are those of disjunctions of terms (DNFs) and as conjuctions of clauses (CNFs). It is convenient to define the DNF size of f as the minimal number of terms in a DNF representing f and the CNF size as the minimal number of ... more >>>