An efficient algorithm for deriving logic functions of asynchronous circuits

A signal transition graph (STG) embodies the causal relationships among signal transitions in a system, and provides a useful starting point for the synthesis of asynchronous circuits. The prevalent synthesis techniques require the input STG to possess the unique state coding (USC) property. This paper describes an algorithm to ascertain whether a given STG has the USC property. The algorithm is path-oriented, and has the advantage of operating directly on the STG rather than a state graph. This approach has the advantage of being easier to visually and intuitively correlate with the STG specification, and therefore suggest ways in which a designer (or tool) may modify the input STG if it does not satisfy the USC property. The technique can also be used to compute the input set of a signal. >

We present a procedure for synthesizing initializable asynchronous circuits from functionally uninitializable Signal Transition Graphs (STG). After characterizing the necessary conditions for functional uninitializability, we propose a technique that transforms the original STG into an equivalent, functionally initializable STG. It is shown that initializability can be achieved by sacrificing minimal concurrency without violating the syntactic properties of the STG required for a hazard-free implementation. The synthesis of a trigger module illustrates this procedure. >

Asynchronous circuits are a promising type of digital circuit that still see moderate usage in today’s commercial products, which has often been linked to the adaptation challenges that are posed within industry, e.g. time required to develop new tools and train designers versus using existing synchronous tools to quickly meet market demands. Several formal models were introduced to aid with the design of asynchronous circuits, including Burst-Mode (BM) Specifications and Signal Transition Graphs (STGs). BM specifications resemble synchronous Finite State Machines (FSMs) allowing circuit designers to easily adapt and use them, however their circuit implementations may be limited due to declining tool support. STGs have access to well-established tools that produce optimal hazard-free circuit implementations, but they are seen as too different by the industry. In this paper, we present a new ‘co-design’ methodology that bridges the gap between BM specifications and STGs by using a formal model called Burst Automaton (BA). BA is a generic FSM-like model that acts as a framework for enabling interoperability between many different formal models, and offers several benefits that BM specifications and STGs can leverage. Our ‘co-design’ methodology is implemented in Workcraft, and is evaluated on several benchmarks showing an improved synthesis flow.

We propose a novel method to eliminate dynamic hazards in asynchronous circuits synthesized from the signal transition graph (STG) specifications. We first review a relationship between syntactic constraints such as liveness and complete state coding at the STG level and the hazard properties at the gate level. Using this relationship, we identify the cause of dynamic hazards and remove them by an iterative factoring method. Each factoring entails augmenting the given STG with an internal signal. This method is applicable to both combinational and sequential circuits, and results in hazard-free multi-level implementations from STG specifications.

A method is presented for deriving a system of parallel extended-burst-mode (XBM) machines from a signal transition graph (STG) specifying required input-output behaviour. First, a primitive finite-state machine is derived as the most general, sequential solution, from which allowable concurrency can still be recognized. Output concurrency is dealt with by decomposition (output partitioning, omission of irrelevant inputs). The component FSMs, with input concurrency only, are tested for XBM feasibility and-if positive-their XBM specifications are constructed. The entire procedure is systematic and is illustrated by deriving two XBM machines from an STG with input and output concurrency. We propose to view the STG as the most general and most precise causal specification of any asynchronous design problem, above and beyond considerations of circuit models and delay assumptions.

Synthesis of asynchronous circuits from signal transition graphs (STGs) involves resolution of state encoding conflicts by means of refining the STG specification. The refinement process is generally done automatically using heuristics. It often produces suboptimal solutions or sometimes fails to solve the problem. Thus manual intervention by the designer may be required. A framework is presented for an interactive refinement process aimed to help the designer. It is based on the visualisation of conflict cores, i.e. sets of transitions causing encoding conflicts, which are represented at the level of finite and complete prefixes of STG unfoldings.

A constraint satisfaction framework is proposed that can guarantee necessary and sufficient conditions for a state graph assignment to result in a transformed state graph that is race-free. Performing transformations at the state graph level has the advantage that the requirements imposed on the initial signal transition graph (STG) are very weak. Unlike previous methods, the initial STG need not be a live, safe, free choice net. The only requirement is that the corresponding initial state graph should be finite and connected, and have a consistent state assignment. Hence, a very broad range of STGs can be synthesized. The transformation achievable using the proposed framework correspond to very complex transformations on STGs. Even transformations that convert a free choice net into a correct non-free choice net, and a 1-safe net into a correct 2-safe net are feasible. Addition of transitions that do not follow the Petri net firing rule is also possible. >

STGs (Signal Transition Graphs) give a formalism for the description of asynchronous circuits based on Petri nets. To overcome the state explosion problem one may encounter during circuit synthesis, a nondeterministic algorithm for decomposing STGs was suggested by Chu and improved by one of the present authors.We study how CSC solving (which is essential for circuit synthesis) can be combined with decomposition. For this purpose the correctness definition for decomposition is enhanced with internal signals and it is shown that speed-independent CSC solving preserves correctness. The latter uses a more general result about correctness of top-down decomposition. Furthermore, we apply our definition to give the first correctness proof for the decomposition method of Carmona and Cortadella.

Verifying the correctness of asynchronous sequential circuits is one of the most important tasks in asynchronous design. However, the absence of the global clock and the variation of gate delays in asynchronous circuits make the verification a formidable task. In this paper, a method that can perform efficient timing analysis of gate-level implementation of asynchronous circuits is presented. The method is based on specific behavior given by the Signal Transition Graph (STG). By modifying the STG into the STG control graph, the circuit can be simulated correctly with automatic test generation. The ternary logic is introduced in order to describe the behaviors of gates with bounded inertial delays. The program is written in VHDL. Lastly in this paper, one of the many simulation results to detect hazards is presented.

Switched Capacitor DC-DC converters play an important role in low power technologies such as energy harvesting systems as they can provide step-up voltage outputs with lower inputs. This paper models and analyses Switched Capacitor DC-DC converters with Signal Transition Graphs, which are originally used for modelling asynchronous circuits. With this new approach, the causality relations between phases, capacitors and internal signals in Switched-Capacitor DC-DC converter can be described distinctly, especially for some complicated converters. This is the first attempt at generating formal models for these types of components, which previously have been described by natural language and waveforms.

The synthesis of asynchronous circuits is difficult in VLSI design. Transition based specification such as signal transition graphs (STGs) are simple and powerful in specifying and synthesizing asynchronous behavior. A relationship is established between the signal transition graph syntactic constraints, i.e., persistency and complete state coding (CSC). A direct proof is presented which shows that a persistency violation either does not affect hazards or, if it does, there results a complete state coding violation. The authors' results give the conditions under which a persistency violation may lead to a complete state coding violation. >

This paper presents a time-efficient method for the decomposition and resynthesis of speed-independent (SI) circuits. Given the specification of an SI circuit, our method first generates its standard C implementation. Then, the combinational decomposition is performed to decompose each high-fanin gate that does not exist in the gate library into some available low-fanin gates. The time efficiency of our method is achieved in two ways. First, the signal transition graph (STG), whose complexity is polynomial in the worst case, is adopted as our input specification. Second, to reduce the resynthesis cycles, which constitute a major part of the run time, our method first investigates the hazard-free decomposition of each high-fanin gate without adding any signals. Then, for those gates that cannot be decomposed hazard free, two signal-adding methods constructed at the STG level are developed for resynthesis. This decomposition and resynthesis process is iterated until all high-fanin gates are successfully decomposed or no solution can be found. Several experiments on asynchronous benchmarks show that our method largely reduces run time with only a little more area expense when compared with previous work.

Communications to, or between, low-end microprocessors within a product always comes at a cost. This paper develops a new, economic solution that will be useful in a variety of cost-sensitive applications. This paper starts by identifying the properties of an inter-microprocessor communications system that adds minimal cost to a product and enables the use of lower price microprocessors. This leads us to introduce a new category of communications called time independent asynchronous (TIA) communications. An economic 2-wire TIA communications protocol is developed and described using timing diagrams. The protocol is modeled using signal transition graphs (STGs), which are found to have some limitations, and so a modification is developed called STG for threads (STG-FT). Two-wire TIA is simulated to confirm livelock and deadlock properties. An implementation is created that verifies the simulation results, and the performance is reported. Finally, a novel application of 2-wire TIA is discussed.

We present a hardware design for the learning datapath of the Tsetlin machine algorithm, along with a latency analysis of the inference datapath. In order to generate a low energy hardware which is suitable for pervasive artificial intelligence applications, we use a mixture of asynchronous design techniques—including Petri nets, signal transition graphs, dualrail and bundled-data. The work builds on previous design of the inference hardware, and includes an in-depth breakdown of the automaton feedback, probability generation and Tsetlin automata. Results illustrate the advantages of asynchronous design in applications such as personalized healthcare and battery-powered internet of things devices, where energy is limited and latency is an important figure of merit. Challenges of static timing analysis in asynchronous circuits are also addressed.

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 original method was extended and shown to be much more generally applicable than known before. But further extensions are necessary, and some are presented here, e.g.: to avoid dynamic auto-conflicts, the previous paper insisted on avoiding structural auto-conflicts, which is too restrictive; we show how to work with the latter type of auto-conflicts. This and another simple extension makes it necessary to restructure presentation and correctness proof of the decomposition algorithm.