Computational Structure of Human Language

The central thesis of this report is that human language is NP-complete. That is, the process of comprehending and producing utterances is bounded above by the class NP, and below by NP-hardness. This constructive complexity thesis has two empirical consequences. The first is to predict that a linguistic theory outside NP is unnaturally powerful. The second is to predict that a linguistic theory easier than NP-hard is descriptively inadequate. To prove the lower bound, I show that the following three subproblems of language comprehension are all NP-hard: decide whether a given sound is possible sound of a given language; disambiguate a sequence of words; and compute the antecedents of pronouns. The proofs are based directly on the empirical facts of the language user's knowledge, under an appropriate idealization. Therefore, they are invariant across linguistic theories. (For this reason, no knowledge of linguistic theory is needed to understand the proofs, only knowledge of English.) To illustrate the usefulness of the upper bound, I show that two widely-accepted analyses of the language user's knowledge (of syntactic ellipsis and phonological dependencies) lead to complexity outside of NP (PSPACE-hard and Undecidable, respectively). Next, guided by the complexity proofs, I construct alternate linguisitic analyses that are strictly superior on descriptive grounds, as well as being less complex computationally (in NP). The report also presents a new framework for linguistic theorizing, that resolves important puzzles in generative linguistics, and guides the mathematical investigation of human language.

Strained Silicon on Silicon by Wafer Bonding and Layer Transfer from Relaxed SiGe Buffer

We report the creation of strained silicon on silicon (SSOS) substrate technology. The method uses a relaxed SiGe buffer as a template for inducing tensile strain in a Si layer, which is then bonded to another Si handle wafer. The original Si wafer and the relaxed SiGe buffer are subsequently removed, thereby transferring a strained-Si layer directly to Si substrate without intermediate SiGe or oxide layers. Complete removal of Ge from the structure was confirmed by cross-sectional transmission electron microscopy as well as secondary ion mass spectrometry. A plan-view transmission electron microscopy study of the strained-Si/Si interface reveals that the lattice-mismatch between the layers is accommodated by an orthogonal array of edge dislocations. This misfit dislocation array, which forms upon bonding, is geometrically necessary and has an average spacing of approximately 40nm, in excellent agreement with established dislocation theory. To our knowledge, this is the first study of a chemically homogeneous, yet lattice-mismatched, interface.