We introduce ``minimal'' two--sorted first--order theories VL, VSL, VNL and VP
that characterize the classes L, SL, NL and P in the same
way that Buss's $S^i_2$ hierarchy characterizes the polynomial time hierarchy.
Our theories arise from natural combinatorial problems, namely the st-Connectivity
Problem and the Circuit Value Problem.
It ... more >>>

Matroid intersection has a known polynomial time algorithm using an
oracle. We generalize this result to delta-matroids that do not have
equality as a restriction, and give a polynomial time algorithm for
delta-matroid intersection on delta-matroids without equality using an
oracle. We note that when equality is present, delta-matroid intersection
more >>>

We show that if an NP-complete problem has a non-adaptive
self-corrector with respect to a samplable distribution then
coNP is contained in NP/poly and the polynomial
hierarchy collapses to the third level. Feigenbaum and
Fortnow (SICOMP 22:994-1005, 1993) show the same conclusion
under the stronger assumption that an
more >>>