On non-recursive trade-offs between finite-turn pushdown automata

It is shown that between one-turn pushdown automata (1-turn PDAs) and deterministic finite automata (DFAs) there will be savings concerning the size of description not bounded by any recursive function, so-called non-recursive tradeoffs. Considering the number of turns of the stack height as a consumable resource of PDAs, we can show the existence of non-recursive trade-offs between PDAs performing k+ 1 turns and k turns for k >= 1. Furthermore, non-recursive trade-offs are shown between arbitrary PDAs and PDAs which perform only a finite number of turns. Finally, several decidability questions are shown to be undecidable and not semidecidable

Approximating Language Edit Distance Beyond Fast Matrix Multiplication: Ultralinear Grammars Are Where Parsing Becomes Hard!

In 1975, a breakthrough result of L. Valiant showed that parsing context free grammars can be reduced to Boolean matrix multiplication, resulting in a running time of O(n^omega) for parsing where omega <= 2.373 is the exponent of fast matrix multiplication, and n is the string length. Recently, Abboud, Backurs and V. Williams (FOCS 2015) demonstrated that this is likely optimal; moreover, a combinatorial o(n^3) algorithm is unlikely to exist for the general parsing problem. The language edit distance problem is a significant generalization of the parsing problem, which computes the minimum edit distance of a given string (using insertions, deletions, and substitutions) to any valid string in the language, and has received significant attention both in theory and practice since the seminal work of Aho and Peterson in 1972. Clearly, the lower bound for parsing rules out any algorithm running in o(n^omega) time that can return a nontrivial multiplicative approximation of the language edit distance problem. Furthermore, combinatorial algorithms with cubic running time or algorithms that use fast matrix multiplication are often not desirable in practice. To break this n^omega hardness barrier, in this paper we study additive approximation algorithms for language edit distance. We provide two explicit combinatorial algorithms to obtain a string with minimum edit distance with performance dependencies on either the number of non-linear productions, k^*, or the number of nested non-linear production, k, used in the optimal derivation. Explicitly, we give an additive O(k^*gamma) approximation in time O(|G|(n^2 + (n/gamma)^3)) and an additive O(k gamma) approximation in time O(|G|(n^2 + (n^3/gamma^2))), where |G| is the grammar size and n is the string length. In particular, we obtain tight approximations for an important subclass of context free grammars known as ultralinear grammars, for which k and k^* are naturally bounded. Interestingly, we show that the same conditional lower bound for parsing context free grammars holds for the class of ultralinear grammars as well, clearly marking the boundary where parsing becomes hard

Streaming algorithms for language recognition problems

We study the complexity of the following problems in the streaming model. Membership testing for \DLIN We show that every language in \DLIN\ can be recognised by a randomized one-pass $O(\log n)$ space algorithm with inverse polynomial one-sided error, and by a deterministic p-pass $O(n/p)$ space algorithm. We show that these algorithms are optimal. Membership testing for \LL$(k)$ For languages generated by \LL$(k)$ grammars with a bound of $r$ on the number of nonterminals at any stage in the left-most derivation, we show that membership can be tested by a randomized one-pass $O(r\log n)$ space algorithm with inverse polynomial (in $n$) one-sided error. Membership testing for \DCFL We show that randomized algorithms as efficient as the ones described above for \DLIN\ and \LL(k) (which are subclasses of \DCFL) cannot exist for all of \DCFL: there is a language in \VPL\ (a subclass of \DCFL) for which any randomized p-pass algorithm with error bounded by $\epsilon < 1/2$ must use $\Omega(n/p)$ space. Degree sequence problem We study the problem of determining, given a sequence $d_1, d_2,..., d_n$ and a graph $G$, whether the degree sequence of $G$ is precisely $d_1, d_2,..., d_n$. We give a randomized one-pass $O(\log n)$ space algorithm with inverse polynomial one-sided error probability. We show that our algorithms are optimal. Our randomized algorithms are based on the recent work of Magniez et al. \cite{MMN09}; our lower bounds are obtained by considering related communication complexity problems

Kenyon Collegian - January 20, 1977

https://digital.kenyon.edu/collegian/1954/thumbnail.jp

Characteristics of UHF transistors using autoregistered structures

The basis of a novel bipolar transistor structure was proposed by Dr R. Aubusson of Middlesex Polytechnic in 1977. The novelty lies in replacing the conventional overlay transistor's P+ base grid with a refractory metal grid, in order (a) to lower the base resistance and (b) to autoregister the emitter. It was claimed that the linearity of the transistor would also be improved. A number of questions raised by this idea have been investigated, the methods and conclusions of which are presented here. Plausible structures, using the metal base grid, are proposed and compared with conventional structures. Some advantages are seen to be possible. The current understanding of distortion analysis applied to transistors is reviewed. The main ideas are presented in a unified manner and are extended to higher order. A number of the transistor's second order effects are analysed in a novel fashion. The metal base grid transistor is analysed and compared with conventional transistors, with favourable results. Practical aspects of fabricating the metal base grid transistor were investigated. A procedure for deposition has been determined and is presented here along with the film physical and electrical characteristics. Analysis of the tungsten-silicon interface shows the suitability of the metallization as a base grid. Suitable means of delineating the tungsten film have been assessed and a working procedure determined. Subsequent deposition of various insulators has been investigated and the problems associated with the readily oxidized tungsten film have been overcome. Formation of the emitter, requiring further high temperature processing, has been assessed in view of the limitations imposed by the preformed base metallization. In summary, it has been shown that the novel structure can be constructed and that significant performance improvement is to be expected, although a full realization was not possible within the resource constraints of the project

The Register, 1973-10-12

https://digital.library.ncat.edu/atregister/1477/thumbnail.jp

Optimization study of high power static inverters and converters Final report

Optimization study and basic performance characteristics for conceptual designs for high power static inverter