Verification and synthesis of asynchronous control circuits using petri net unfoldings

PhD ThesisDesign of asynchronous control circuits has traditionally been associated with application of formal methods. Event-based models, such as Petri nets, provide a compact and easy to understand way of specifying asynchronous behaviour. However, analysis of their behavioural properties is often hindered by the problem of exponential growth of reachable state space. This work proposes a new method for analysis of asynchronous circuit models based on Petri nets. The new approach is called PN-unfolding segment. It extends and improves existing Petri nets unfolding approaches. In addition, this thesis proposes a new analysis technique for Signal Transition Graphs along with an efficient verification technique which is also based on the Petri net unfolding. The former is called Full State Graph, the latter - STG-unfolding segment. The boolean logic synthesis is an integral part of the asynchronous circuit design process. In many cases, even if the verification of an asynchronous circuit specification has been performed successfully, it is impossible to obtain its implementation using existing methods because they are based on the reachability analysis. A new approach is proposed here for automated synthesis of speed-independent circuits based on the STG-unfolding segment constructed during the verification of the circuit's specification. Finally, this work presents experimental results showing the need for the new Petri net unfolding techniques and confirming the advantages of application of partial order approach to analysis, verification and synthesis of asynchronous circuits.The Research Committee, Newcastle University: Overseas Research Studentship Award

Synthesis of asynchronous controllers using integer linear programming

A novel strategy for the logic synthesis of asynchronous control circuits is presented. It is based on the structural theory of Petri nets and integer linear programming. Techniques that are capable of checking implementability conditions, such as complete state coding, and deriving a gate netlist to implement the specified behavior are presented. These techniques can handle Petri net specifications consisting of several thousands of transitions and provide a significant speed-up compared with techniques that have previously been proposed.Peer ReviewedPostprint (published version

State-based encoding of large asynchronous controllers

State encoding is one of the fundamental problems in the synthesis of asynchronous controllers. The requirement for a correct hazard-free implementation imposes severe constraints on the way encoding signals can be inserted in the specification of a controller. Even though some specification formalisms, such as Burst-mode machines or Signal Transition Graphs, enable to specify behaviors at the event level, the state encoding methods that provide the best good-quality solutions work at the state level. This imposes a severe limitation on the size of the controllers that can be handled by these methods. This paper proposes a method to solve the encoding problem for large asynchronous controllers using statebased methods. It is based on an iterative process of projection and re-composition that reduces the size specification by hiding signals, partially solves the encoding problem at the state level and re-composes the original specification using a synchronous product. The process iterates until all encoding conflicts have been solved. The method is proved to preserve the behavior of the specification (branching bisimilarity) and shown to be capable of providing good-quality solutions for controllers of more than 100 signals and 106 states.Peer ReviewedPostprint (published version

Exploiting robustness in asynchronous circuits to design fine-tunable systems

PhD ThesisRobustness property in a circuit defines its tolerance to the effects of process, voltage and temperature variations. The mode signaling and event communication between computing units in a asynchronous circuits makes them inherently robust. The level of robustness depends on the type of delay assumptions used in the design and specification process. In this thesis, two approaches to exploiting robustness in asynchronous circuits to design self-adapting and fine-tunable systems are investigated. In the first investigation, a Digitally Controllable Oscillator (DCO) and a computing unit are integrated such that the operating conditions of the computing unit modulated the operation of the DCO. In this investigation, the computing unit which is a self-timed counter interacts with the DCO in a four-phase handshake protocol. This mode of interaction ensures a DCO and computing unit system that can fine-tune its operation to adapt to the effects of variations. In this investigation, it is shown that such a system will operate correctly in wide range of voltage supply. In the second investigation, a Digital Pulse-Width Modulator (DPWM) with coarse and fine-tune controls is designed using two Kessels counters. The coarse control of the DPWM tuned the pulse ratio and pulse frequency while the fine-tune control exploited the robustness property of asynchronous circuits in an addition-based delay system to add or subtract delay(s) to the pulse width while maintaining a constant pulse frequency. The DPWM realized gave constant duty ratio regardless of the operating voltage. This type of DPWM has practical application in a DC-DC converter circuit to tune the output voltage of the converter in high resolution. The Kessels counter is a loadable self-timed modulo−n counter, which is realized by decomposition using Horner’s method, specified and verified using formal asynchronous design techniques. The decomposition method used introduced parallelism in the system by dividing the counter into a systolic array of cells, with each cell further decomposed into two parts that have distinct defined operations. Specification of the decomposed counter cell parts operation was in three stages. The first stage employed high-level specification using Labelled Petri nets (LPN). In this form, functional correctness of the decomposed counter is modelled and verified. In the second stage, a cell part is specified by combing all possible operations for that cell part in high-level form. With this approach, a combination of inputs from a defined control block activated the correct operation for a cell part. In the final stage, the LPNs were converted to Signal Transition Graphs, from which the logic circuits of the cells were synthesized using the WorkCraft Tool. In this thesis, the Kessels counter was implemented and fabricated in 350 nm CMOS Technology.Niger Delta Development Commission (NDD

State encoding of asynchronous controllers using pseudo-boolean optimization

State encoding of asynchronous controllers is a challenging problem that faces a vast space of solutions. Subtle differences in the insertion of signals may result in significant variations in the complexity of the logic. This paper proposes a novel approach that models the encoding problem as Pseudo-Boolean formula. A cost function that estimates the complexity of the logic is incorporated, where the estimator of essential literals becomes one of the most important terms of the function. The new approach has been tested in 175 benchmarks with encoding conflicts, including 127 four-phase latch controllers. The presence of logic estimators in the formula contributes to an average reduction of 43% in literals when compared to a plain SAT version of the problem, at the expense of a longer runtime. When comparing to the region-based approach in petrify, an average reduction of 14% in literals is obtained.Peer ReviewedPostprint (author's final draft

On Computational Small Steps and Big Steps: Refocusing for Outermost Reduction

We study the relationship between small-step semantics, big-step semantics and abstract machines, for programming languages that employ an outermost reduction strategy, i.e., languages where reductions near the root of the abstract syntax tree are performed before reductions near the leaves.In particular, we investigate how Biernacka and Danvy's syntactic correspondence and Reynolds's functional correspondence can be applied to inter-derive semantic specifications for such languages.The main contribution of this dissertation is three-fold:First, we identify that backward overlapping reduction rules in the small-step semantics cause the refocusing step of the syntactic correspondence to be inapplicable.Second, we propose two solutions to overcome this in-applicability: backtracking and rule generalization.Third, we show how these solutions affect the other transformations of the two correspondences.Other contributions include the application of the syntactic and functional correspondences to Boolean normalization.In particular, we show how to systematically derive a spectrum of normalization functions for negational and conjunctive normalization