From STG to extended-burst-mode machines

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.

Signal Transition Graphs (STGs) are Petri nets, which were introduced to represent a behavior of asynchronous circuits. To derive logic functions from an STG, the reachability graph should be constructed. In the verification of STGs some method based on Occurrence nets (OCN) and its prefix, called unfolding, has been proposed. OCNs can represent both causality and concurrency between two nodes by net structure. In this paper, we propose a method to derive a logic function by generating substate space of a given STG using the structural properties of OCN. The proposed method can be seen as a parallel algorithm for deriving a logic function.

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.

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. >

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.

A new asynchronous wrapper circuit is proposed based on standard cells for the realization of point to point high speed seamless data transmission. The wrapper is realized from the Signal Transition Graph (STG) by Petrify based on the fundamental GALS system structure. The asynchronous circuit includes the design of synchronous/asynchronous interface and local clock which can be suspended. The traditional EDA tools are merged together with asynchronous circuit design, and the wrapper only has standard cells but not special asynchronous logic gates. The simulation and verification were made by Modelsim and Quartus respectively, and the results have shown that the GALS system works properly and has a preferable performance.

This paper presents a novel design method for asynchronous control logic targeting successive approximation register (SAR) analog-to-digital converters (ADCs). This work is based on modeling the control logic for SAR ADCs using signal transition graphs (STGs). Different from conventional synchronous controllers, the proposed method results in asynchronous controllers driven by the causality of signals rather than relying on clocks to control the conversion process. Moreover, the proposed asynchronous control logic can be modularized through the handshake protocol, making it possible to build ADCs of arbitrary precision based on single-bit control units. This work results in a formal, model-based asynchronous design flow for SAR ADC control, which is shown to produce resulting circuits of similar speeds but great power efficiency improvements.

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.