Given an initial distribution of sand in an Abelian sandpile, what final state does it relax to after all possible avalanches have taken place? In d = 3*, we show that this problem is P-complete, so that explicit simulation of the system is almost certainly necessary. We also show that the...

Evolution is applied to the development of parallel digital computer programs. The environment is a shared memory virtual computer containing a population of parallel computer programs. Although the digital computer is a very different environment than the ecology of the Earth, evolution is...

We exhibit some simple gadgets useful in designing shallow parallel circuits for quantum algorithms. We prove that any quantum circuit composed entirely of controlled-not gates or of diagonal gates can be parallelized to logarithmic depth, while circuits composed of both cannot. Finally, while...

We propose a definition of QNC, the quantum analog of the efficient parallel class NC. We exhibit several useful gadgets and prove that various classes of circuits can be parallelized to logarithmic depth, including circuits for encoding and decoding standard quantum error-correcting codes, or...

We exhibit a quantum circuit that performs the Quantum Fourier Transform on $n$ qubits in $ (n)$ depth. Thus, a parallel quantum computer can carry out the QFT in linear time. We conjecture that this can, in fact, be reduced to $ ({\rm log} n)$ depth, which would place the QFT in the class {\bf...

We show that predicting the HPP or FHP III lattice gas for finite time is equivalent to calculating the output of an arbitrary Boolean circuit, and is therefore P-complete: that is, it is just as hard as any other problem solvable by a serial computer in polynomial time. <p> It is widely believed...</p>