TL;DR: In this paper, a method for determining a minimum clock cycle that can be used to propagate a signal about the critical cycle in a circuit design is provided, wherein the critical cycles is a cycle in the design that has the highest proportionality of delay to number of registers.
Abstract: A method is provided that includes: determining a minimum clock cycle that can be used to propagate a signal about the critical cycle in a circuit design; wherein the critical cycle is a cycle in the design that has a highest proportionality of delay to number of registers; determining for a circuit element in the circuit design, sequential slack associated with the circuit element; wherein the sequential slack represents a minimum delay from among respective maximum delays that can be added to respective structural cycles of which the circuit element is a constituent, based upon the determined limit upon clock cycle duration; using the sequential slack to ascertain sequential optimization based design flexibility throughout multiple stages of a design flow.
TL;DR: Boost Logic, a charge- recovery circuit family that can operate efficiently at clock frequencies in excess of 1 GHz, relies on a combination of aggressive voltage scaling, gate overdrive, and charge-recovery techniques to achieve high energy efficiency.
Abstract: In this paper, we present Boost Logic, a charge- recovery circuit family that can operate efficiently at clock frequencies in excess of 1 GHz. To achieve high energy efficiency, Boost Logic relies on a combination of aggressive voltage scaling, gate overdrive, and charge-recovery techniques. In post-layout simulations of 16-bit multipliers with a 0.13-mum CMOS process at 1GHz, a Boost Logic implementation achieves 5 times higher energy efficiency than its minimum-energy pipelined, voltage-scaled, static CMOS counterpart at the expense of 3 times longer latency. In a fully integrated test chip implemented using a 0.13-mum bulk silicon process and on-chip inductors, chains of Boost Logic gates operate at clock frequencies up to 1.3 GHz with a 1.5-V supply. When resonating at 850 MHz with a 1.2-V supply, the Boost Logic test chip achieves 60% charge-recovery
TL;DR: See-tolerant configurations are shown and described for combinational logic circuits, state-holding logic circuits and SRAM memory circuits in this article, with a focus on single-event effects.
Abstract: New and improved methods and circuit designs for asynchronous circuits that are tolerant to transient faults, for example of the type introduced through radiation or, more broadly, single-event effects. SEE-tolerant configurations are shown and described for combinational logic circuits, state-holding logic circuits and SRAM memory circuits.
TL;DR: A new class of asynchronous pipelines is proposed, called lookahead pipelines (LP), which use dynamic logic and are capable of delivering multi-gigahertz throughputs and are characterized by low-cost control structures and the avoidance of explicit latches.
Abstract: A new class of asynchronous pipelines is proposed, called lookahead pipelines (LP), which use dynamic logic and are capable of delivering multi-gigahertz throughputs. Since they are asynchronous, these pipelines avoid problems related to high-speed clock distribution, such as clock power, management of clock skew, and inflexibility in handling varied environments. The designs are based on the well-known PSO style of Williams and Horowitz as a starting point, but achieve significant improvements through novel protocol optimizations: the pipeline communication is structured so that critical events can be detected and exploited earlier. A special focus of this work is to target extremely fine-grain or gate-level pipelines, where the datapath is sectioned into stages, each consisting of logic that is only a single level deep. Both dual-rail and single-rail pipeline implementations are proposed. All the implementations are characterized by low-cost control structures and the avoidance of explicit latches. Post-layout SPICE simulations, in 0.18-mum technology, indicate that the best dual-rail LP design has more than twice the throughput (1.04 giga data items/s) of Williams' PSO design, while the best single-rail LP design achieves even higher throughput (1.55 giga data items/s).
TL;DR: A new analytical modelling approach to evaluate the impact of single event transients (SETs) on CMOS circuits has been developed, which allows evaluation of transient pulse amplitude and width at the logic level, without the need to run circuit level (Spice-like) simulations.
Abstract: A new analytical modelling approach to evaluate the impact of single event transients (SETs) on CMOS circuits has been developed. The model allows evaluation of transient pulse amplitude and width (duration) at the logic level, without the need to run circuit level (Spice-like) simulations. The SET mechanism in MOS circuits is normally investigated by Spice-like circuit simulation. The problem is that electrical simulation is time-consuming and must be performed for each different circuit topology, incident particle and track. The availability of a simple model at the logic gate level may greatly improve circuit sensitivity analysis. The electrical response of a circuit to an ionising particle hit depends on many parameters, such as circuit topology, circuit geometry and waveform shape of the charge injection mechanism. The proposed analytical model, which is accurate and computer efficient, captures these transistor-level effects of ionising particle hits and models them to the logic level of abstraction. The key idea is to exploit a model that allows the rapid determination of the sensitivity of any logic gate in a CMOS circuit, without the need to run circuit simulations. The model predicts whether or not a particle hit generates a SET, which may propagate to the next logic gate or memory element, making possible to analyse the sensitivity of each node in a complex circuit. Model derivation is strongly related to circuit electrical behaviour, being consistent with technology scaling. The model is suitable for integration into CAD tools, intending to make automated evaluation of circuit sensitivity to SET possible, as well as automated estimation of soft error rate.
TL;DR: A new methodology to model and synthesize data path QDI circuits is presented and a digit-slice radix 4 ALU is used as an example to illustrate the methodology and show the results.
Abstract: Quasi delay insensitive circuits are functionally independent of delays in gates and wires (except for some particular wires). Such asynchronous circuits offer high robustness but do not perform well to automatically synthesize and optimize. This paper presents a new methodology to model and synthesize data path QDI circuits. The model used to represent circuits is based on Multi-valued Decision Diagrams and allows obtaining QDI circuits with two-input gates. Optimization is achieved by applying a technology mapping algorithm with a library of asynchronous standard cells called TAL. This work is a part of the back-end of our synthesis flow from high level language. Throughout the paper, a digit-slice radix 4 ALU is used as an example to illustrate the methodology and show the results.
TL;DR: Two 128-point 16-bit radix-2 FFT/IFFT processors based on synchronous-logic (sync) and asynchronous- logic (async) for low voltage (1.1-1.4 V) energy-critical low-speed hearing aids are described, with the emphasis is energy efficacy.
Abstract: Two 128-point 16-bit radix-2 FFT/IFFT processors based on synchronous-logic (sync) and asynchronous-logic (async) for low voltage (1.1-1.4 V) energy-critical low-speed hearing aids are described. The two processors herein are designed with the same function and similar architecture, and the emphasis is energy efficacy. The async approach, on average, features ~37% lower energy per FFT/IFFT computation than the sync approach but with ~10% larger IC area penalty and an inconsequential 1.4 times worse delay; the async design can be designed to be 0.24 times faster and with largely the same energy dissipation if the matched delay elements and the latch controllers therein are better optimized. In this low-speed application, the lower energy feature of the async design is not attributed to the absence of the clock infrastructure but instead due to the adoption of established and proposed async circuit designs, resulting in reduced redundant operations and reduced spurious/glitch switching, and to the use of latches. The prototype async FFT/IFFT processor (in a 0.35-mum CMOS process) can be operated at 1.0 V and dissipates 93 nJ.
TL;DR: A 90nm buck converter is intended for complex multi-core ICs and using the 3GHz system clock for switching reduces the area to 0.27mm2 and allows the output filter to be integrated.
Abstract: A 90nm buck converter is intended for complex multi-core ICs. Using the 3GHz system clock for switching reduces the area to 0.27mm2 and allows the output filter to be integrated. Efficiency is increased by recycling clock charge and delivering it to the load instead of ground. A dedicated 3GHz clock circuit driving 12pF consumes 39.9mW. In contrast, a combined clock and converter circuit consumes 56.2mW and delivers 25.7mW at the converter output. Regulation is achieved through PWM of the clock. The circuit converts 1.0V to between 0.5 to 0.7V at 40 to 100mA.
TL;DR: In this paper, the authors present an approach to convert a circuit design from a synchronous representation to an asynchronous representation without interaction or redesign without knowledge of the underlying asynchronous architecture and hardware.
Abstract: Methods (700, 800, 900) and systems (Fig. 1) automate an approach to convert a circuit design from a synchronous representation (Fig. 4A) to an asynchronous representation (Fig. 4B) without interaction or redesign. Conversion of representations of synchronous circuit designs (101) to and from representations of asynchronous circuit designs (104) enable traditional electronic design automation tools to process asynchronous designs while allowing synchronous designs to be implemented using asynchronous hardware solutions. Feedback to synchronous design tools (105) in synchronous representation enables optimization while minimizing the need for knowledge of the underlying asynchronous architecture and hardware.
TL;DR: An efficient algorithm (CNF2CKT) for extracting circuit information from CNF instances that is optimal in the sense that it extracts a maximum acyclic combinational circuit from any given CNF using the logic gates pre-specified in a library.
Abstract: Boolean satisfiability is seeing increasing use as a decision procedure in electronic design automation (EDA) and other domains. Most applications encode their domain specific constraints in conjunctive normal form (CNF), which is accepted as input by most efficient contemporary SAT solvers (Moskewicz et al., 2001). However, such translation may have information loss. For example, when a circuit is encoded into CNF, structural information such as gate orientation, logic paths, signal observability, etc. is lost. However, recent research (Li, 2000) shows that a substantial amount of the lost information can be restored in circuit form. This paper presents an efficient algorithm (CNF2CKT) for extracting circuit information from CNF instances. CNF2CKT is optimal in the sense that it extracts a maximum acyclic combinational circuit from any given CNF using the logic gates pre-specified in a library. The extracted circuit structure is valuable in various ways, particularly when the CNF is not encoded from the circuit, or the circuit description is not readily available. As an example, we show that the extracted circuit structure can be used to derive circuit observability don't cares (Bartlett et al., 1988) for speeding up CNF-SAT (Fu et al., 2005)
TL;DR: 1. Number Systems and Binary Codes, Fundamental Concepts of Digital Logic, and Sequential Circuit Design using VHDL.
Abstract: 1. Number Systems and Binary Codes. 2. Fundamental Concepts of Digital Logic. 3. Combinational Logic Design. 4. Fundamentals of Synchronous Sequential Circuits. 5. VHDL in Digital Design. 6. Combinational Logic Design using VHDL. 7. Synchronous Sequential Circuit Design. 8. Counter Design. 9. Sequential Circuit Design using VHDL. 10. Asynchronous Sequential Circuits. Appendix A. CMOS Logic. Index.
TL;DR: In this paper, the role of the mode and clock signals on the mode/clock and clock/mode signals, or their reversal, selects one or the other of the data communication circuits.
Abstract: Data is communicated through two separate circuits or circuit groups, each having clock and mode inputs, by sequentially reversing the role of the clock and mode inputs. The data communication circuits have data inputs, data outputs, a clock input for timing or synchronizing the data input and/or output communication, and a mode input for controlling the data input and/or output communication. A clock/mode signal connects to the clock input of one circuit and to the mode input of the other circuit. A mode/clock signal connects to the mode input of the one circuit and to the clock input of the other circuit. The role of the mode and clock signals on the mode/clock and clock/mode signals, or their reversal, selects one or the other of the data communication circuits.
TL;DR: In this paper, a method for determining a minimum clock cycle that can be used to propagate a signal about the critical cycle in a circuit design is provided, wherein the critical cycles is a cycle in the design that has the highest proportionality of delay to number of registers.
Abstract: A method is provided that includes: determining a minimum clock cycle that can be used to propagate a signal about the critical cycle in a circuit design; wherein the critical cycle is a cycle in the design that has a highest proportionality of delay to number of registers; determining for a circuit element in the circuit design, sequential slack associated with the circuit element; wherein the sequential slack represents a minimum delay from among respective maximum delays that can be added to respective structural cycles of which the circuit element is a constituent, based upon the determined limit upon clock cycle duration; using the sequential slack to ascertain sequential optimization based design flexibility throughout multiple stages of a design flow.
TL;DR: The SCRAM2 is an 8-bit bit-serial microprocessor with three-stage pipelining, with a basic microarchitecture similar to that of the previously designed synchronous microprocessor, CORE1alpha, with the estimated average performance of 577 MIPS.
Abstract: A microprocessor test vehicle was developed for the investigation of asynchronous design methodology for rapid- single-flux-quantum (RSFQ) circuits. We have designed and implemented a fully asynchronous RSFQ microprocessor, named SCRAM2. The data-driven self-timing (DDST) architecture is used for the design of circuit blocks of the SCRAM2. In order to ensure the logical ordering between the circuit blocks, bit-serial handshaking was adopted. The performance of the handshaking system was enhanced based on the scalable-delay-insensitive (SDI) model. The SCRAM2 is an 8-bit bit-serial microprocessor with three-stage pipelining, with a basic microarchitecture similar to that of our previously designed synchronous microprocessor, CORE1alpha. The estimated average performance of the SCRAM2 is 577 MIPS using a logic simulation. We have implemented all circuit components using the SRL 2.5 kA/cm2 Nb process and confirmed their correct operation. Several operations of the SCRAM2 have been successfully confirmed.
TL;DR: In this paper, the authors present a systematic, workable and repeatable process for evaluating synchronous circuit designs, converting the wires, switches/connections and logic functions to equivalent-function asynchronous circuit designs and hence implementing a functionally equivalent asynchronous circuit with all the benefits thereof.
Abstract: Methods and systems for converting synchronous circuit designs to asynchronous circuit designs, and particularly programmable asynchronous circuit designs. Provide is a systematic, workable and repeatable process for evaluating synchronous circuit designs, converting the wires, switches/connections and logic functions to equivalent-function asynchronous circuit designs and hence implementing a functionally equivalent asynchronous circuit with all the benefits thereof. Further provided are a process for systematically doing the conversion and hardware equivalents (in form or functional description) for the asynchronous components. Using the present invention, any synchronous circuit design can be converted to an asynchronous equivalent, typically with no change to the original design implementation.
TL;DR: In this paper, an integrated circuit device includes a programmable logic block, a monitoring input, a condition sensing circuit coupled to the monitoring input and configured to generate a condition-sensed signal at an output in response to sensing a condition at the monitor input.
Abstract: An integrated circuit device includes a programmable logic block, a monitoring input, a condition-sensing circuit coupled to the monitoring input and configured to generate a condition-sensed signal at an output in response to sensing a condition at the monitoring input, a first digital input, a first digital output, and a gating circuit configured in the programmable logic block and coupled between the first digital input and the first digital output. The gating circuit has a gating input coupled to the condition-sensing circuit and generates an output. The output is related to an input state of the first digital input in the absence of the condition-sensed signal and assumes an override state in the presence of the condition-sensed signal.
TL;DR: In this article, an integrated receiver with multiple independently synchronized clock signals for multiple channel transport stream decoding and delivery substantially implemented on a single CMOS integrated circuit is described, where the output of the clock circuit is distributed to the various processing blocks within the integrated circuit that operate upon channel content received and processed by the transport block.
Abstract: An integrated receiver with multiple, independently synchronized clock signals for multiple channel transport stream decoding and delivery substantially implemented on a single CMOS integrated circuit is described. An integrated circuit that services two satellite programs must generate and distribute corresponding time domain clocks to the various components of the integrated circuit. The transport block that receives one or more satellite signals from a demodulating block will extract program clock recover values from each signal being decoded and use these values to produce an error signal or control word that serves as an input to a clock generator. Based upon this input, the clock circuit will produce a corresponding time domain clock for each channel serviced by the integrated circuit. The output of the clock circuit is distributed to the various processing blocks within the integrated circuit that operate upon channel content received and processed by the transport block.
TL;DR: In this paper, a low-power clock gating circuit using a Multi-Threshold CMOS (MTCMOS) technique is presented, in which a latch circuit of an input stage and an AND gate of an output stage is used to reduce power consumption caused by leakage current in the clock gate.
Abstract: Provided is a low-power clock gating circuit using a Multi-Threshold CMOS (MTCMOS) technique. The low-power clock gating circuit includes a latch circuit of an input stage and an AND gate circuit of an output stage, in which power consumption caused by leakage current in the clock gating circuit is reduced in a sleep mode, and supply of a clock to a unused device of a targeted logic circuit is prevented by the control of a clock enable signal in an active mode, thereby reducing power consumption. The low-power clock gating circuit using an MTCMOS technique uses devices having a low threshold voltage and devices having a high threshold voltage, which makes it possible to implement a high-speed, low-power circuit, unlike a conventional clock gating circuit using a single threshold voltage.
TL;DR: In this paper, two versions of a reconfigurable logic element are developed for use in constructing a field-programmable gate array (FPGA): one with extra embedded registration capability, which requires additional area, and one without.
Abstract: Two versions of a reconfigurable logic element are developed for use in constructing afield-programmable gate array NULL convention logic (NCL) field-programmable gate array (FPGA): one with extra embedded registration capability, which requires additional area, and one without. Both versions can be configured as any of the 27 fundamental NCL gates, including resettable and inverting variations, and both can utilize embedded registration for gates with three or fewer inputs; however, only the version with the additional embedded registration capability can utilize embedded registration with four-input gates. These two approaches are compared with each other and with an existing approach, showing that both versions developed herein yield a more area efficient NCL circuit implementation, compared to the previous work. The two FPGA logic elements are simulated at the transistor level using the 1.8-V, 180-nm TSMC CMOS process.
TL;DR: A clock gating solution for energy recovery clocking by gating the flip-flops is proposed and it is proposed that this solution reduces their power by 1000times in the idle mode with negligible power and delay overhead in the active mode.
Abstract: Energy recovery clocking has been demonstrated as an effective method for reducing the clock power. In this method the conventional square wave clock signal is replaced by a sinusoidal clock generated by a resonant circuit. Such a modification in clock signal prevents application of existing clock gating solutions. In this paper, we propose a clock gating solution for energy recovery clocking by gating the flip-flops. Applying our clock gating to the energy recovery clocked flip-flops reduces their power by 1000times in the idle mode with negligible power and delay overhead in the active mode. Applying the proposed clock gating technique to a system of 1000 flip-flops with idle mode probability and data switching activity of 50%, reduces the total power by 47%. We also propose a negative edge triggering solution for the energy recovery clocked flip-flops.
TL;DR: In this paper, an improved built-in self-test (BIST) circuit and an associated method for measuring phase and/or cycle-to-cycle jitter of a clock signal are described.
Abstract: Disclosed herein are embodiments of an improved built-in self-test (BIST) circuit and an associated method for measuring phase and/or cycle-to-cycle jitter of a clock signal. The embodiments of the BIST circuit implement a Variable Vernier Digital Delay Locked Line method. Specifically, the embodiments of the BIST circuit incorporate both a digital delay locked loop and a Vernier delay line, for respectively coarse tuning and fine tuning portions of the circuit. Additionally, the BIST circuit is variable, as the resolution of the circuit changes from chip to chip, and digital, as it is implemented with standard digital logic elements.
TL;DR: In this article, a multi-phase converter comprising a plurality of switching circuits each controlled by a phase controller and each providing a switched output voltage to an output node of the converter and where each switching circuit under control of the phase controller sequentially provides a switch voltage to the output node at which an output voltage of a converter is developed is developed.
Abstract: A multi-phase converter comprising a plurality of switching circuits each controlled by a phase controller and each providing a switched output voltage to an output node of the converter and wherein each switching circuit under control of the phase controller sequentially provides a switched output voltage to the output node at which an output voltage of the converter is developed; and a main control circuit including a clock circuit for providing a first clock signal to each of the switching circuits and a second lower frequency clock signal to a first of the phase controllers, each phase controller having a delay circuit controlled by the first clock signal to provide a delayed second clock signal for coupling to a next one of the phase controllers and in the case of a last one of the phase controllers, back to the main control circuit, whereby a plurality of sequentially delayed second clock signals is provided, one to each of the remaining phase controllers after the first phase controller to determine when each switching circuit provides the switched output voltage to the output node.
TL;DR: In this paper, a method for determining a minimum clock cycle that can be used to propagate a signal about the critical cycle in a circuit design is provided, wherein the critical cycles is a cycle in the design that has the highest proportionality of delay to number of registers.
Abstract: A method is provided that includes: determining a minimum clock cycle that can be used to propagate a signal about the critical cycle in a circuit design; wherein the critical cycle is a cycle in the design that has a highest proportionality of delay to number of registers; determining for a circuit element in the circuit design, sequential slack associated with the circuit element; wherein the sequential slack represents a minimum delay from among respective maximum delays that can be added to respective structural cycles of which the circuit element is a constituent, based upon the determined limit upon clock cycle duration; using the sequential slack to ascertain sequential optimization based design flexibility throughout multiple stages of a design flow.
TL;DR: In this paper, a high-speed receiver includes multiple receiver components, including sampling latches for receiving data, phase rotators for controlling timing of sampling of data, and a clock-tracking logic stage for providing clock and data recovery.
Abstract: A high-speed receiver includes multiple receiver components. Each receiver component includes sampling latches for receiving data, phase rotators for controlling timing of sampling of data by the sampling latches, and a clock-tracking logic stage for providing clock and data recovery. The clock-tracking logic stage is divided into a high-speed early/late (E/L) logic and aggregation counter section and a low-speed logic section, separated by a synchronization logic block. The receiver also includes a delay locked loop (DLL) for receiving an input clock signal corresponding to a data rate of the received data, providing coarse delay adjustment of the clock signal and outputting multiple clock phase vectors corresponding to the adjusted clock signal to the phase rotators on each receiver component. The phase rotators control sampling of the data based on the clock phase vectors received from the DLL. A single regulated power supply regulator regulates power supplied to the DLL and the phase rotators.
TL;DR: In this article, a method of converting a Boolean logic circuit into an asynchronous multi-rail circuit using at least Shannon's expansion is provided. Butler et al. presented a method to convert a Boolean Logic Circuit into an Asynchronous Multi-Rail Circuit using Shannon's Expansion.
Abstract: A method of converting a Boolean logic circuit into an asynchronous multi-rail circuit is provided. A Boolean logic circuit is converted into a first multi-rail circuit using at least Shannon's expansion. The first multi-rail circuit is technology mapped into a second multi-rail circuit. Completion detection circuitry is added which receives the primary outputs of the second multi-rail circuit.
TL;DR: In this article, a configurable time-borrowing flip-flops are provided for circuits such as programmable logic devices, where a clock signal is delayed using configurable delay circuits.
Abstract: Configurable time-borrowing flip-flops are provided for circuits such as programmable logic devices. The flip-flops may be based on a configurable delay circuit and two latches or may be based on a configurable pulse generation circuit and a single latch. In designs based on two latches, a first and a second latch are arranged in series. A clock signal is delayed using a configurable delay circuit. Programmable memory elements that have been loaded with configuration data may be used to adjust how much delay is produced by the configurable delay circuit. The delayed version of the clock signal is provided to a clock input associated with the first latch. The second latch has a clock input that receives the clock signal without delay. In designs based on a single latch, a configurable pulse generation circuit receives a clock signal for the flip-flop and generates a corresponding clock pulse for the latch.
TL;DR: In this paper, a weighted averager circuit coupled to a multiplexer and a digital-to-analog converter (DAC) is proposed to output a phase interpolated clock signal.
Abstract: A phase interpolator circuit may comprise a multiplexer circuit (MUX) to receive a plurality of clock signals at MUX inputs and to output a first clock signal and a second clock signal that are out of phase with each other, a digital to analog converter circuit (DAC) to convert a digital input to first and second DAC output currents such that a sum of the first and second DAC output currents comprises a substantially constant current value, and a weighted averager circuit coupled to the MUX and the DAC. The weighted averager circuit may operate to sum weighted first and second clock signals and to output a phase interpolated clock signal. The first clock signal may be weighted according to the first DAC output current and the second clock signal may be weighted according to the second DAC output current. Other apparatus, systems, and methods are disclosed.
TL;DR: In this paper, a flip-flop circuit with low power consumption was proposed, where a sensing circuit senses a change in an input signal and an output signal of the flip flop, and a clock generating circuit generates a pseudo clock signal with a sharp rise and fall based upon an external clock signal.
Abstract: A flip-flop circuit having low power consumption includes a sensing circuit, and a clock generating circuit. The flip-flop is leading edge triggered and operates on an internally generated pseudo clock signal. The sensing circuit senses a change in an input signal and an output signal of the flip-flop. The clock generating circuit generates a pseudo clock signal with a sharp rise and fall based upon an external clock signal.
TL;DR: This paper presents two designs that are logically equivalent to a Muller C-element, however, Mathematical analysis and stochastic simulation show that only one functions reliably.
Abstract: Synthetic biology uses engineering principles to design circuits out of genetic materials that are inserted into bacteria to perform various tasks. While synthetic combinational Boolean logic gates have been constructed, there are many open issues in the design of sequential logic gates. One such gate common in most asynchronous circuits is the Muller C-element, which is used to synchronize multiple independent processes. This paper proposes a novel design for a genetic Muller C-element using transcriptional regulatory elements. The design of a genetic Muller C-element enables the construction of virtually any asynchronous circuit from genetic material. There are, however, many issues that complicate designs with genetic materials. These complications result in modifications being required to the normal digital design procedure. This paper presents two designs that are logically equivalent to a Muller C-element. Mathematical analysis and stochastic simulation, however, show that only one functions reliably.
TL;DR: To avoid dynamic auto-conflicts, the previous paper insisted on avoiding structural autoconflicts, which is too restrictive; as a main contribution, this extension makes it necessary to restructure presentation and correctness proof of the decomposition algorithm.
Abstract: Signal Transition Graphs (STGs) are a version of Petri nets for the specification of asynchronous circuit behaviour. It has been suggested to decompose such a specification as a first step; this leads to a modular implementation, which can support circuit synthesis by possibly avoiding state explosion or allowing the use of library elements.
In a previous paper, the originalmethod was extended and shown to bemuchmore generally applicable than known before. But further extensions are necessary, and some are presented in this paper. In particular, to avoid dynamic auto-conflicts, the previous paper insisted on avoiding structural autoconflicts, which is too restrictive; as a main contribution, we show how to work with the latter type of auto-conflicts. This extension makes it necessary to restructure presentation and correctness proof of the decomposition algorithm.