We show that ACC0 is precisely what can be computed with constant-width circuits of polynomial size and polylogarithmic genus. This extends a characterization given by Hansen, showing that planar constant-width circuits also characterize ACC0. Thus polylogarithmic genus provides no additional computational power in this model. We consider other generalizations of planarity, including crossing n...

STEP (STandard for the Exchange of Product model data, ISO 10303) data for numerical control, or STEP-NC, is intended to provide full product and process data interoperability between computer-aided manufacturing systems and machine tool controllers. Numerous prototype and several commercial implementations of STEP-NC are currently being developed. Testing is an essential step toward ensuring c...

We give a recursion-theoretic characterization of the complexity classes NC for k ≥ 1. In the spirit of implicit computational complexity, it uses no explicit bounds in the recursion and also no separation of variables is needed. It is based on three recursion schemes, one corresponds to time (time iteration), one to space allocation (explicit structural recursion) and one to internal computati...

We derive an effective Lagrangian for meson fields. This is done in the light-cone gauge for two-dimensional large-Nc QCD by using the bilocal auxiliary field method. The auxiliary fields are bilocal on light-cone space and their Fourier transformation determines the parton momentum distribution. As the first test of our method, the ’t Hooft equation is derived from the effective Lagrangian. E-...

Based on gauge invariance, we show that the new threshold phenomenon is discovered in the φ radiative decays φ → γa0 → γπη and φ → γf0 → γππ. This enables to conclude that production of the lightest scalar mesons a0(980) and f0(980) in these decays is caused by the four-quark transitions, resulting in strong restrictions on the large NC expansions of the decay amplitudes. The analysis shows tha...

In this paper a level-based geometric representation for a real-time material removal simulator is presented. It will be embedded into a commercial NC machine. The representation and its accompanying architecture have been used for the generation of an interactive simulation of a part being machined, taking the NC machine feedback as input. The simulator complies with the following restrictions...

The effect of severely tightening the uniformity of Boolean circuit families is investigated. The impact on NC and its subclasses is shown to depend on the characterization chosen for the class, while classes such as P appear to be more robust. Tightly uniform subclasses of NC whose separation may be within reach of current techniques emerge.