Probabilistic and Stochastic Computational Models: from Nanoelectronic to Biological Applications

Abstract

A finite state machine (FSM) is a classical abstract model for sequential circuits that are at the core of any digital system. Due to fabrication defects and transient faults, the reliable operation of sequential circuits is greatly desired. In this thesis, computational models are initially constructed using state transition matrices (STMs) and binary decision diagrams (BDDs) of an FSM; a phenomenon called error masking and the restoring properties of sequential circuits are then analyzed in detail. This analysis provides a basis for further devising efficient and robust implementation when designing FSMs. Arithmetic circuits play an important role in many digital systems and have fundamentally critical applications in signal processing. Addition is perhaps the most important and basic arithmetic operation for many applications. Recent research has focused on probabilistic and approximate adders that trade off accuracy for energy saving. Since there was a lack of appropriate metrics to evaluate the efficacy of these inexact designs, several new metrics are proposed in this work for evaluating the reliability as well as the power efficiency of an adder. These new metrics can be used in future designs for a better assessment of the power and precision tradeoff. Although current digital systems are based on complementary metal–oxide–semiconductor (CMOS) technology and employ binary values in the representation of signals, multiple valued logic (MVL) circuits using novel nano-devices have been investigated due to their advantages in information density and operating speed. In this thesis, pseudo-complementary MVL circuits are further proposed for implementations using carbon nanotube field effect transistors (CNTFETs). Because of the fabrication non-idealities, reliability evaluation of these MVL circuits becomes important. Subsequently, stochastic computational models (SCMs) are developed to analyze the reliability of CNT MVL circuits. Finally, the stochastic computational model is applied in the modeling of biological networks. Specifically, stochastic Boolean networks (SBNs) are proposed for an efficient modeling of genetic regulatory networks (GRNs). The proposed SBN can accurately and efficiently simulate a GRN without and with random gene perturbation, which will help to reveal biologically meaningful insights for a better understanding of the dynamics of GRNs.