We consider the complexity of the firefighter problem where ${b \geq 1}$ firefighters are available at each time step. This problem is proved NP-complete even on trees of degree at most three and budget one (Finbow et al. 2007) and on trees of bounded degree $b+3$ for any fixed budget ... more >>>

A 1976 theorem of Chaitin, strengthening a 1969 theorem of Meyer,says that infinitely many lengths n have a paucity of trivial strings (only a bounded number of strings of length n having trivially low plain Kolmogorov complexities). We use the probabilistic method to give a new proof of this fact. ... more >>>

We prove that 3-query linear locally correctable codes over the Reals of dimension $d$ require block length $n>d^{2+\lambda}$ for some fixed, positive $\lambda >0$. Geometrically, this means that if $n$ vectors in $R^d$ are such that each vector is spanned by a linear number of disjoint triples of others, then ... more >>>