Defining the Delays of Asynchronous Circuits

Title: Defining the Delays of Asynchronous Circuits

Research Question: How can we define and measure the delays in asynchronous circuits, and what are the implications of these delays?

Methodology: The study proposes a semi-formalization of digital electrical engineering by defining delays, order, time invariance, constancy, symmetry, and the serial connection in asynchronous circuits. It uses Boolean functions and the order and laws of B (a set with elements 0 and 1) to model logical gates and wires.

Results: The research provides several key results:

1. Definition of delays: The study defines delays as the real-time mode of the circuit that computes the identity function 1{0, 1}. 2. Stability condition (SC): The research introduces the stability condition (SC), which states that if a certain condition is true for input 'a' at a specific time, then it must also be true for the output at the same time. 3. Rising and falling transmission delays for transitions: The study defines rising and falling transmission delays for transitions, which indicate how long it takes for a change in input to be reflected in the output. 4. Delay conditions (DCs): DCs are functions that define the set of solutions for stable systems of equations and inequalities modeling the real-time computation of the identity function. The research presents examples of DCs. 5. Determinism: The study discusses deterministic and non-deterministic DCs, with deterministic DCs indicating the uniqueness of the solution for all inputs.

Implications: The research has several implications, including the ability to define and measure delays in asynchronous circuits, which is crucial for understanding and improving the performance of these circuits. Additionally, the study's methodology and results provide a foundation for further research in the field.

Link to Article: https://arxiv.org/abs/0402040v1 Authors: arXiv ID: 0402040v1