Elimination of static and dynamic hazards for multiple input changes in combinational switching circuits

We introduce a new design style called extended burst-mode. The extended burst-mode design style covers a wide spectrum of sequential circuits ranging from delay-insensitive to synchronous. We can synthesize multiple-input change asynchronous finite state machines and many circuits that fall in the gray area (hard to classify as synchronous or asynchronous) which are difficult or impossible to synthesize automatically using existing methods. Our implementation of extended burstmode machines uses standard CMOS logic, generates low-latency outputs, and guarantees freedom from hazards at the gate level. In Part I, we formally define the extended burst-mode specification, provide an overview of the synthesis methods, and describe the hazard-free synthesis requirements for two different next-state logic synthesis methods: two-level sums-of-products implementation and generalized C-elements implementation. We also present an extension to existing theories for hazard-free combinational synthesis to handle nonmonotonic input changes.

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“…1) Definitions: We summarize some definitions and concepts from [41]- [44] that are used in the following subsections.…”

Section: B Function Hazardmentioning

confidence: 99%

Automatic synthesis of extended burst-mode circuits. I. (Specification and hazard-free implementations)

Yun

Dill

1999

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

116

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“…In this paper, we ignore the electronic aspect of hazards, and stick on their idealized, mathematical model as, for example, in [5,8,30,14,16]. The classical Kleene's three-valued "strong logic of indeterminacy" [15] extends the Boolean operations AND, OR and NOT from the Boolean domain t0, 1u to the ternary domain t0, u, 1u, where the bits 0 and 1 are interpreted as stable, and the bit u as unstable:…”

Section: Ternary Logicmentioning

confidence: 99%

“…There are several types of hazards-we will only consider the so-called static logical hazards [5,8,30].…”

Section: 3mentioning

confidence: 99%

“…In 1965, Eichelberger [8,Theorem 2] extended this result: if a DNF D representing f contains no zero-terms, that is, terms with a variable together with its negation, then D is hazard-free if and only if D contains all prime implicants of f as terms. After these structural results, research mainly concentrated on developing algorithms for detecting hazards, and many important results were obtained [5,8,20,30], just to mention some of them.…”

Section: Introductionmentioning

confidence: 99%

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Notes on Hazard-Free Circuits

Jukna¹

2020

Preprint

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The problem of constructing hazard-free Boolean circuits (those avoiding electronic glitches) dates back to the 1940s and is an important problem in circuit design and even in cybersecurity. We show that a DeMorgan circuit is hazard-free if and only if the circuit produces (purely syntactically) all prime implicants as well as all prime implicates of the Boolean function it computes. This extends to arbitrary DeMorgan circuits a classical result of Eichelberger [IBM J. Res. Develop., 9 (1965)] showing this property for special depth-two circuits. Via an amazingly simple proof, we also strengthen a recent result Ikenmeyer et al. [J. ACM, 66:4 (2019)]: not only the complexities of hazard-free and monotone circuits for monotone Boolean functions do coincide, but every optimal hazard-free circuit for a monotone Boolean function must be monotone. Then we show that hazard-free circuit complexity of a very simple (non-monotone) Boolean function is super-polynomially larger than its unrestricted circuit complexity. This function accepts a Boolean n ˆn matrix iff every row and every column has exactly one 1-entry. Finally, we show that every Boolean function of n variables can be computed by a hazard-free circuit of size Op2 n {nq.

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“…[2] and [3], among others, extended earlier work to handle both static and dynamic hazard detection. The technique in [2] is particularly interesting since it is based on the definition of a unateness criterion for the appearance of static and dynamic hazards.…”

Section: Introductionmentioning

confidence: 99%