Tissue P systems generalize the membrane structure tree usual in original models of P systems to an arbitrary graph. Basic operations in these systems are communication rules, enriched in some variants with cell division or cell separation. Several variants of tissue P systems were recently studied, together with the concept of uniform families of these systems. Their computational power was sh...

Adleman, Demarrais, and Huang introduced the nondeterministic quantum polynomial-time complexity class NQP as an analogue of NP. It is known that, with restricted amplitudes, NQP is characterized in terms of the classical counting complexity class C=P. In this paper we prove that, with unrestricted amplitudes, NQP indeed coincides with the complement of C=P. As an immediate corollary, with unre...

A phylogeny is a tree capturing evolution and ancestral relationships of a set of taxa (e.g., species). Reconstructing phylogenies from molecular data plays an important role in many areas of contemporary biological research. A phylogeny is perfect if (in rough terms) it correctly captures all input data. Determining if a perfect phylogeny exists was shown to be intractable in 1992 by Mike Stee...

We prove the following results: (i) PV proves NP ⊆ P/poly iff PV proves coNP ⊆ NP/O(1). (ii) If PV proves NP ⊆ P/poly then PV proves that the Polynomial Hierarchy collapses to the Boolean Hierarchy. (iii) S2 proves NP ⊆ P/poly iff S 1 2 proves coNP ⊆ NP/O(log n). (iv) If S2 proves NP ⊆ P/poly then S 1 2 proves that the Polynomial Hierarchy collapses to P[log n]. (v) If S2 proves NP ⊆ P/poly the...

In this note we show that AMexp 6⊆ NP ∩ coNP/poly, where AMexp denotes the exponential version of the class AM. The main part of the proof is a collapse of EXP to AM under the assumption that EXP ⊆ NP ∩ coNP/poly

We study the shrinking and separation properties (two notions well-known in descriptive set theory) for NP and coNP and show that under reasonable complexity-theoretic assumptions, both properties do not hold for NP and the shrinking property does not hold for coNP. In particular we obtain the following results. 1. NP and coNP do not have the shrinking property, unless PH is finite. In general,...

Buhrman and Torenvliet created an oracle relative to which P NP = NEXP and thus P NP = P NEXP. Their proof uses a delicate nite injury argument that leads to a nonrecursive oracle. We simplify their proof removing the injury to create a recursive oracle making P NP = NEXP. In addition, in our construction we can make P = UP = NP \ coNP. This leads to the curious situation where LOW(NP) = P but ...