Complexity classifications for different equivalence and audit problems for Boolean circuits

We study Boolean circuits as a representation of Boolean functions and consider different equivalence, audit, and enumeration problems. For a number of restricted sets of gate types (bases) we obtain efficient algorithms, while for all other gate types we show these problems are at least NP-hard.Comment: 25 pages, 1 figur

Synchronization of Coupled Nonidentical Genetic Oscillators

The study on the collective dynamics of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic oscillators are biochemical networks, which can generally be modelled as nonlinear dynamic systems. We show in this paper that many genetic oscillators can be transformed into Lur'e form by exploiting the special structure of biological systems. By using control theory approach, we provide a theoretical method for analyzing the synchronization of coupled nonidentical genetic oscillators. Sufficient conditions for the synchronization as well as the estimation of the bound of the synchronization error are also obtained. To demonstrate the effectiveness of our theoretical results, a population of genetic oscillators based on the Goodwin model are adopted as numerical examples.Comment: 16 pages, 3 figure

Distributed classifier based on genetically engineered bacterial cell cultures

We describe a conceptual design of a distributed classifier formed by a population of genetically engineered microbial cells. The central idea is to create a complex classifier from a population of weak or simple classifiers. We create a master population of cells with randomized synthetic biosensor circuits that have a broad range of sensitivities towards chemical signals of interest that form the input vectors subject to classification. The randomized sensitivities are achieved by constructing a library of synthetic gene circuits with randomized control sequences (e.g. ribosome-binding sites) in the front element. The training procedure consists in re-shaping of the master population in such a way that it collectively responds to the "positive" patterns of input signals by producing above-threshold output (e.g. fluorescent signal), and below-threshold output in case of the "negative" patterns. The population re-shaping is achieved by presenting sequential examples and pruning the population using either graded selection/counterselection or by fluorescence-activated cell sorting (FACS). We demonstrate the feasibility of experimental implementation of such system computationally using a realistic model of the synthetic sensing gene circuits.Comment: 31 pages, 9 figure

Improving the Asymmetric TSP by Considering Graph Structure

Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally show that such implied propagators bring robustness to pathological instances and highlight the fact that graph structure can significantly improve search heuristics behavior. Finally, we show that our approach outperforms current state of the art results.Comment: Technical repor

Fuzzy Logic and VLSI Testing

A new application of Fuzzy logic (FL), in the context of test vector generation in VLSI testing is presented. Fuzzification of the threshold value simulation (TVS) approach and setting up of mathematical concepts are carried out in terms of a hierarchy of membership functions. The test-vectors are found by optimising a suitable membership function. The Fuzzy model besides giving a different mathematical basis, also helps in defining new and better optimising functions, thus provind its utility. The concepts outlined in this paper, though demonstrated on toy model of a circuit consisting of only AND gates, can easily be extended to circuits with other logic gates