Co-Higgs bundles are Higgs bundles in the sense of Simpson, but with Higgs fields that take values in the tangent bundle instead of the cotangent bundle. Given a vector bundle on P, we find necessary and sufficient conditions on its Grothendieck splitting for it to admit a stable Higgs field. We characterize the rank-2, odd-degree moduli space as a universal elliptic curve with a globally-defin...

This is a summary of the proof by G.E. Coxson [1] that P-matrix recognition is co-NP-complete. The result follows by a reduction from the MAX CUT problem using results of S. Poljak and J. Rohn [5].

We investigate the complexity of finding prime implicants and minimum equivalent DNFs for Boolean formulas, and of testing equivalence and isomorphism of monotone formulas. For DNF related problems, the complexity of the monotone case differs strongly from the arbitrary case. We show that it is DP-complete to check whether a monomial is a prime implicant for an arbitrary formula, but the equiva...

We give two nondeterministic reductions which yield new direct product theorems (DPTs) for Boolean circuits. In these theorems one assumes that a target function f is mildly hard against nondeterministic circuits, and concludes that the direct product f⊗t is extremely hard against (only polynomially smaller) probabilistic circuits. The main advantage of these results compared with previous DPTs...

In the formal study of security protocols and access control systems, fragments of intuitionistic logic play a vital role. These are required to be efficient, and are typically disjunction-free. In this paper, we study the complexity of adding disjunction to these subsystems. Our lower bound results show that very little needs to be added to disjunction to get co-NP-hardness, while our upper bo...

We investigate the complexity of finding prime implicants and minimal equivalent DNFs for Boolean formulas, and of testing equivalence and isomorphism of monotone formulas. For DNF related problems, the complexity of the monotone case strongly differs from the arbitrary case. We show that it is DP-complete to check whether a monomial is a prime implicant for an arbitrary formula, but checking p...