Sequential circuit design using synthesis and optimization

State assignment is the most critical step in the synthesis and optimization of sequential circuits as it significantly impacts sequential circuits area and power. Due to the high complexity of the state assignment problem and the ineffectiveness of existing deterministic algorithms in generating good solutions, evolutionary algorithms can be employed to obtain more effective state assignment solutions. In this paper, we propose a probabilistic tabu search (PTS) state assignment algorithm that is employed for the optimization of area and power of sequential circuits. The proposed algorithm is based on tabu search with the addition of exploiting code swap probabilities to prune the search space more effectively. Code swap probabilities are updated dynamically during the execution of the algorithm in such a way that code swaps that result in relatively inferior solutions will be assigned lower probabilities while those that result in good solutions will be assigned higher probabilities. In addition, tabu list size is changed dynamically during execution to help the algorithm get out of local minima. Based on experimental results, we show that the proposed PTS state assignment algorithm is more effective than all existing state assignment algorithms as it generates state assignment solutions with significantly lower area and power.

Many applications produce acceptable results when their underlying computations are executed in an approximate manner. For such applications, approximate circuits enable hardware implementations that exhibit improved efficiency for a given quality. Previous efforts have largely focused on the design of approximate combinational logic blocks such as adders and multipliers. In practice, however, designers are concerned with the quality of outputs generated by a sequential circuit after several cycles of computation, rather than an embedded combinational block. We propose ASLAN (Automatic methodology for Sequential Logic ApproximatioN), the first effort towards the synthesis of approximate sequential circuits. Given a sequential circuit and an output quality constraint, ASLAN creates an approximate version of the circuit that consumes lower energy, while meeting the specified quality bound. The key challenges in approximating sequential circuits are (i) to model how errors due to approximations are generated, re-circulate through the combinational logic over multiple cycles of operation, and eventually impact quality of the final output, and (ii) to select the most beneficial approximations, i.e., those that result in higher energy savings for smaller impact on quality. ASLAN addresses the first challenge by constructing a virtual Sequential Quality Constraint Circuit (SQCC) and utilizing formal verification techniques to ensure that the selected approximations meet the quality constraint. To address the second challenge, ASLAN identifies combinational blocks in the sequential circuit that are amenable to approximation, generates local quality-energy trade-off curves for them, and uses a gradient-descent approach to iteratively approximate the entire sequential circuit. We used ASLAN to automatically synthesize approximate versions of ten sequential benchmarks, resulting in energy reductions of 1.20X-2.44X for tight quality constraints, and 1.32X-4.42X for moderate quality constraints. We present case studies of using the approximate circuits generated by ASLAN in two popular applications - MPEG Encoding and K-Means Clustering - obtaining 1.32X energy savings with 0.5% PSNR degradation, and 1.26X energy savings with 0.8% increase in mean cluster radius, respectively.

The paper deals with synthesis of sequential circuits defined by their algorithmic state machine notation. Such circuits have a number of specific properties which enable efficient design of the circuits by utilizing so-called linearization techniques. A typical linearization technique includes calculation of autocorrelation values for a system of logic functions corresponding to the circuit. For the mentioned sequential circuits, the calculations which usually require massive computational recourses may be significantly reduced and thus low-overhead implementations of the circuits can be obtained relatively easy. The paper introduces a novel architecture of so-called linearized sequential circuits, and a piece-wise linearization approach for synthesis of sequential circuits. Results are evaluated both analytically and by using a number of standard benchmarks.

Logic circuits in digital electronics can generally be classified two categories-combinational and sequential logic circuits.There are several software-based applications and hardware description languages to describe the structure and behavior of electronic circuits.Although it is an easy to construct a state transition table from the state transition diagram,creating an excitation table according to the memory element type in the sequential circuit design is a very laborious and time-consuming task.After the logic functions extracted from the state transition tables are obtained,logic design verification can be carried out by a conventional simulator.This will require time and persistence much like learning any other skill.Computer science degrees include courses focused mainly on programming languages.There’s a strong case to be made for use of skills acquired in programming courses to shorten the learning curve.Thus, this work has proposed a method for the implementation of the circuit only the state equations of the sequential circuit without dealing with excitation tables.This eliminates the process of constructing the circuit schematically, since it does not require flip-flop selection.In this method, since the state equations can be expressed through buttonbox,checkbox,textbox etc.which are the basic elements of the programming language,the behavior of the circuit can be observed in a very short time.

Retiming is an effective technique to optimize the performance of synchronous sequential circuits. This paper proposes a method to improve the effectiveness of retiming by transforming the sequential circuit. Bottlenecks which prevent retiming to achieve a desired clock period are identified. Conditions to eliminate the retiming bottlenecks are derived. These conditions are satisfied by a process of identifying sub-circuits and satisfying a set of timing constraints on the sub-circuits. The transformed circuit, which satisfies the timing constraints, can be retimed to achieve the desired clock period. If the original circuit has its initial state specified, our method always generates the final circuit with an equivalentinitial state. Experimental results on a variety of sequential benchmark circuits demonstrate significant performance improvement.

A new approach to the state assignment problem for the synthesis of sequential switching circuits is applied to solve completely the synthesis problem of gateless counters. The necessary and sufficient condition that assures that the counter may be synthesised without gates is found. A method is developed to determine a priori if a given state table corresponds to a circuit that may be synthesised without gates.

This paper considers the general problem of the synthesis of asynchronous combinational and sequential circuits based on the assumption that gate delays may be unbounded and that line delays are suitably constrained. Certain problems inherent to circuit realizations with unbounded gate delays are discussed and methods of solving them are proposed. Specific synthesis techniques are presented for both combinational and sequential circuits. The use of completion detection necessitated by the assumption of unbounded gate delays also causes the circuits to stop operating for approximately half of all possible single faults, thus achieving a degree of self-checking.

An approach to logic synthesis of digital synchronous sequential circuits is presented. Algorithms are described for minimizing the area of synchronous combinational and/or sequential circuits under cycle time constraints and for minimizing the cycle time under area constraints. It is shown how to optimize concurrently the circuit equations and the register position by a set of algorithms based on logic transformations. An implementation of the algorithms in the program Minerva is described, and experimental results are reported.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new approach is presented to logic synthesis of digital synchronous sequential circuits. The authors describe algorithms for minimizing (i) the area of synchronous combinational and/or sequential circuits under cycle time constraints, and (ii) the cycle time under area constraints. Previous approaches attacked this problem by separating the combinational logic from the registers and by applying circuit transformations to the combinational component only. The authors show instead how to optimize concurrently the circuit equations and the register position. This method is novel and can achieve results that are at least as good as those obtained by previous methods. A computer implementation of the algorithms in the Minerva program is described. >

The advantage of Evolvable Hardware over the traditional circuit design approach is its capacity for dynamic and autonomous adaptation. EHW can reconfigure its structure according to changes in the task requirement or the environment in which the EHW is embedded. Focuses on the application of extrinsic evolution and their used for the design of small sequential circuits. At the foundation of evolvable hardware, a full-connected feed-forward circuit network model was constructed which is based on the character of sequential circuits. This model is imitating the structure of artificial neural network. It firstly using D flip-latch and logic gate as the basic element, and the one-to-one mapping existed in the mathematical encoding, circuit topology, and HDL file was established. Then, the method to obtain HDL file according to circuit encoding was designed, the circuit evaluation process was automated by using of batch processing technology. Designed the mutation rate dynamic adjust function to improve the performance of (1+λ)-ES. Experiment results of two types of Finite State Machine proved the feasibility and validity of the circuit evolution method.

Coupling Of Synthesis And Layout: Challenges And Solutions

The opportunities created by modern microelectronic technology cannot be effectively exploited, because of weaknesses of the traditional circuit synthesis methods used in today's CAD tools. In this paper, a new information-driven circuit synthesis method is discussed. It differs considerably from all other known methods. It is based on our original information-driven approach to circuit synthesis, bottom-up general functional decomposition and theory of information relationship measures. A special focus of the paper is on the role and usage of information trans-coders in the information-driven circuit synthesis. The experimental results from the automatic circuit synthesis tool that implements the method demonstrate that the information-driven general decomposition produces very fast and compact gate-based circuits, and the information trans-coders play an important role in achieving this aim.

Safety-critical systems used in applications that demand high levels of dependability, efficiency, and fault-tolerance often use sequential logic circuits in its design and implementation. The safety-critical digital system typically uses latches, flip-flops, and other memory elements, which are prone to the effects of natural faults and single event upsets (SEUs) caused by radiation-induced effects. The faults can lead to subsystem failures due to the continuous advancement in the realization of the small size transistor. To design a reliable digital-based system, it is essential to develop new fault-tolerance approaches that are integrated into the design of sequential logic circuits. This work proposes a novel fault-tolerant approach based on the redundancy of sequential logic circuit, which consists of a variety of design components, D flip-flop storage elements linked to a fault injection unit, a duplicate modular redundancy, and data monitoring units with a switching circuit. The experimental simulation results using a five-state Markov chain analysis model prove that the proposed fault-tolerant system can achieve 0.99999998 for reliability of the fault detection coverage (C) which equal to 0.99999. Finally, we believe that using this new approach of fault-tolerance and redundancy would improve the dependability and reliability of next generation safety-critical applications.

Boolean formula minimization is a notoriously hard problem. Circuit minimization, typically studied in the context of a much broader subject known as synthesis and optimization of circuits, introduces another layer of complexity since ultimately those technology-independent representations (e.g., Boolean formulas and truth tables) has to be transformed into a netlist of cells of the target technology library. To manage those complexities, the industrial community typically separates the synthesis process into two steps: technology-independent optimization and technology mapping. In each step, this approach only tries to find the local optimal solution and relies heavily on heuristics rather than a systematic search. However, for small S-boxes, a more systematic exploration of the design space is possible. Aiming at the global optimum, we propose a method which can synthesize a truth table for a small S-box directly into a netlist of the cells of a given technology library. Compared with existing technology-dependent synthesis tools like LIGHTER and PEIGEN, our method produces improved results for many S-boxes with respect to circuit area. In particular, by applying our method to the GF(2^4)-inverter involved in the tower field implementation of the AES S-box, we obtain the currently known lightest implementation of the AES S-box. The search framework can be tweaked to take circuit delay into account. As a result, we find implementations for certain S-boxes with both latency and area improved.

Carbon nanotube field-effect transistors (CNFETs) show great potential to build digital systems on advanced technology nodes with big benefits in terms of power, performance, and area (PPA). However, CNFET-specific additional features such as the number of tubes, pitch (spacing between tubes), tube position, and diameter in array of tubes play a significant role in accurate PPA evaluation. Furthermore, count and density variations in carbon nanotubes (CNTs) due to manufacturing limitations, like the presence of metallic tubes in the CNFET channel, degrade the anticipated PPA benefits. Moreover, modeling the CNFET parameters, CNT variations and etching techniques for CNTs create additional complexity during performance optimization. Hence, for realistic optimization of CNFET circuit’s performance, it is imperative to incorporate the impact of these parameters and variations. In this paper, we propose delay models [pitch-aware logical effort (PALE) and position-aware pitch factor (PAPF)] for fast and accurate performance evaluation by including the impact due to CNFET-specific parameters and CNT variations. These models are developed based on industry standard logical effort framework. Furthermore, we present an optimization tool using PALE and PAPF to minimize the delay and area of CNFET circuits. We deploy several circuit-level techniques prior to optimizing the tubes (CNTs) in the logic gates to achieve globally optimum solution. For better optimization of the circuits, we also include the impact of wire parasitic in estimating the delay of the individual gates. Our optimization tool results in the maximum and average delay improvement by 27% and 17%, respectively, and $2.5\times $ reduction in area for standard ISCAS and OpenSPARC benchmark circuits. Fast and fairly accurate delay computation in our optimization framework offers great runtime benefits as compared to state-of-the-art simulation and statistical-based methods.