Power languages and density

AbstractThe class of all languages can be seen as a distributive lattice with respect to a preorder defined by letter-to-letter morphisms. Maximal dense intervals in the lattice are investigated. The results are based on a construction that builds a new language, so-called power language, from subsets of a given language. Applications to grammar form theory and graph theory are also presented

Language competition with bilinguals in social networks

Several models have been proposed to study the dynamics of competition between languages. Among them, and starting from the dynamics of endangered languages, recent approaches have addressed the issue of bilingualism. Along these lines we consider the dynamics of language use, allowing for bilingualism, within a social network in the case where the two languages are equivalent. Understanding this case is a first step to describe the case of an endangered language competing against a language with higher status. Local effects are analyzed, studying interface dynamics and growth laws of the system. Power laws for the decay of interface density and bilingual population density are obtained. A final state is reached, where one of the languages disappears. We also study the stability of bilingual communities, which suggests possible explanations for the difficulty of coexistence of languages in the long term.Complex systems, Language competition, social networks

FPGA-Based Bandwidth Selection for Kernel Density Estimation Using High Level Synthesis Approach

FPGA technology can offer significantly hi\-gher performance at much lower power consumption than is available from CPUs and GPUs in many computational problems. Unfortunately, programming for FPGA (using ha\-rdware description languages, HDL) is a difficult and not-trivial task and is not intuitive for C/C++/Java programmers. To bring the gap between programming effectiveness and difficulty the High Level Synthesis (HLS) approach is promoting by main FPGA vendors. Nowadays, time-intensive calculations are mainly performed on GPU/CPU architectures, but can also be successfully performed using HLS approach. In the paper we implement a bandwidth selection algorithm for kernel density estimation (KDE) using HLS and show techniques which were used to optimize the final FPGA implementation. We are also going to show that FPGA speedups, comparing to highly optimized CPU and GPU implementations, are quite substantial. Moreover, power consumption for FPGA devices is usually much less than typical power consumption of the present CPUs and GPUs.Comment: 23 pages, 6 figures, extended version of initial pape

Unbounded-error quantum computation with small space bounds

We prove the following facts about the language recognition power of quantum Turing machines (QTMs) in the unbounded error setting: QTMs are strictly more powerful than probabilistic Turing machines for any common space bound $s$ satisfying $s(n)=o(\log \log n)$. For "one-way" Turing machines, where the input tape head is not allowed to move left, the above result holds for $s(n)=o(\log n)$. We also give a characterization for the class of languages recognized with unbounded error by real-time quantum finite automata (QFAs) with restricted measurements. It turns out that these automata are equal in power to their probabilistic counterparts, and this fact does not change when the QFA model is augmented to allow general measurements and mixed states. Unlike the case with classical finite automata, when the QFA tape head is allowed to remain stationary in some steps, more languages become recognizable. We define and use a QTM model that generalizes the other variants introduced earlier in the study of quantum space complexity.Comment: A preliminary version of this paper appeared in the Proceedings of the Fourth International Computer Science Symposium in Russia, pages 356--367, 200

Physics of randomness and regularities for cities, languages, and their lifetimes and family trees

Time evolution of the cities and of the languages is considered in terms of multiplicative noise and fragmentation processes; where power law (Pareto-Zipf law) and slightly asymmetric log-normal (Gauss) distribution result for the size distribution of the cities and for that of the languages, respectively. The cities and the languages are treated differently (and as connected; for example, the languages split in terms of splitting the cities, etc.) and thus two distributions are obtained in the same computation at the same time. Evolutions of lifetimes and families for the cities and the languages are also studied. We suggest that the regularities may be evolving out of randomness, in terms of the relevant processes.Comment: 22 pages including all figures; for Int. J. Mod. Phys. C 18 (2007

Scaling relations for diversity of languages

The distribution of living languages is investigated and scaling relations are found for the diversity of languages as a function of the country area and population. These results are compared with data from Ecology and from computer simulations of fragmentation dynamics where similar scalings appear. The language size distribution is also studied and shown to display two scaling regions: (i) one for the largest (in population) languages and (ii) another one for intermediate-size languages. It is then argued that these two classes of languages may have distinct growth dynamics, being distributed on the sets of different fractal dimensions.Comment: 10 pages, 4 figure