Abstract
We investigate a formal verification problem (mathematically rigorous correctness checking) for digital waveforms used in practical development of digital microelectronic devices (digital circuits) at early design stages. According to modern methodologies, a digital circuit design starts at high abstraction levels provided by hardware description languages (HDLs). One of essential steps of an HDLbased circuit design is an HDL code debug, similar to the same step of program development in means and importance. A popular way of an HDL code debug is based on extraction and analysis of a waveform, which is a collection of plots for digital signals: functional descriptions of value changes related to selected circuit places in real time. We propose mathematical means for automation of correctness checking for such waveforms based on notions and methods of formal verification against temporal logic formulae, and focus on such typical featues of HDL-related digital signals and corresponding (informal) properties, such as real time, three-valuededness, and presence of signal edges. The three-valuededness means that at any given time, besides basic logical values 0 and 1, a signal may have a special undefined value: one of the values 0 and 1, but which one of them is either not known, or not important. An edge point of a signal is a time point at which the signal changes its value. The main results are mathematical notions, propositions, and algorithms which allow to formalize and solve a formal verification problem for considered waveforms, including: definitions for signals and waveforms which the mentioned typical digital signal features; a temporal logic suitable for formalization of waveform correctness properties, and a related verification problem statement; a solution technique for the verification problem, which is based on reduction to signal transfromation and analysis; a corresponding verification algorithm together with its correctness proof and “reasonable” complexity bounds.
Highlights
We investigate a formal verification problem (mathematically rigorous correctness checking) for digital waveforms used in practical development of digital microelectronic devices (digital circuits) at early design stages
We propose mathematical means for automation of correctness checking for such waveforms based on notions and methods of formal verification against temporal logic formulae, and focus on such typical featues of hardware description languages (HDLs)-related digital signals and corresponding (informal) properties, such as real time, three-valuededness, and presence of signal edges
V., "Formal Verification of Three-Valued Digital Waveforms", Modeling and Analysis of Information Systems, 26:3 (2019), 332–350
Summary
Записями N, N0 и R обозначим соответственно множества всех натуральных чисел, всех целых неотрицательных чисел и всех действительных чисел. Также в работе используются диапазоны целых неотрицательных чисел: [x..y] = {z | z ∈ N0, x ≤ z ≤ y}. Записью f ⟨Z⟩ ∼ v, где Z ⊆ X и ∼ равенство (=) или неравенство (̸=), обозначим следующий факт: для каждого элемента z множества Z верно f (z) ∼ y. Записью T обозначим множество {0, 1, *}. В широком смысле, T множество значений, которыми оперируют троичные функции [9]. В узком смысле, T множество истинностных значений троичной логики Клини [10, 11], согласно которой 0 трактуется как ложь, 1 как истина, и * как неопределённое значение: либо истина, либо ложь, но неизвестно или неважно, что именно.
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