In this article, we explore a new approach to analyzing timing properties in computer systems. Timing properties are important for understanding how a system will behave under different conditions, such as when it is handling multiple tasks or responding to external events. Our approach uses abstraction techniques to simplify the analysis process, making it easier to understand and reason about timing properties.
Abstraction Techniques
In computer science, abstraction refers to the process of simplifying complex systems by hiding irrelevant details and highlighting the essential features. In the context of timing analysis, we use abstraction techniques to model a system as a set of simpler components, each with its own timing properties. By combining these components in various ways, we can analyze the overall timing behavior of the system.
Indexed Predicates
One key technique we use is indexed predicates. These are atomic formulas (i.e., simple statements) that contain a variable 𝑖 and relate to a particular position in an array. For example, 𝑎[𝑖] ≤ 𝑎[𝑛] means that the value at position 𝑖 is less than or equal to the value at position 𝑛. By mapping these formulas into words over a set of positions (e.g., {0, 1}𝑚), we can analyze the truth values of the predicates for each position and summarize the results in a single word.
Synchronized Automata
Another important concept is synchronized automata. These are models that run on tuples of words (i.e., sequences of bits) and capture the behavior of systems with multiple tasks or processes. By using synchronized automata, we can analyze the timing properties of a system by simulating its behavior over time.
Summary
In summary, this article presents a new approach to analyzing timing properties in computer systems using abstraction techniques. We introduce indexed predicates and synchronized automata as key concepts for simplifying the analysis process. By combining these techniques, we can better understand how a system will behave under different conditions and design more efficient and reliable systems.
