Complex systems exist in every aspect of society. From communication networks to the human body, complex systems exist in practically anything and everything. Understanding algorithms that govern complex systems can help scientists and other individuals better maintain and devise these systems in the future. A linear system, in addition, is a simple system that typically acts in a predictable sequence, such as with automatic controls. A complex linear system would be an intricate system that still follows a linear pattern.

Algorithms are used to understand complex linear systems. An algorithm is a specifically defined set of instructions that relates to a specific function. An algorithm determines the narrowed process that variables go through when a computation or action is performed. An example of an algorithm would be typing on a keyboard. Each key on a keyboard is associated with a language symbol. When the key is pressed, the computer will always (if it is working correctly) produce the corresponding symbol on the computer. This is a finite and defined algorithm for typing that particular letter.

In complex linear systems, algorithms guide everything. They keep systems from becoming chaotic by determining that every action or command execution has a finite path in which it can travel. Sometimes, that finite path can change to a slightly different path with the introduction of other variable. Pressing the ‘shift’ key, for example, will change the path of a typed letter. Instead of producing the original lowercase form, the algorithm now knows to produce a new symbol – an uppercase. Many computer programs are considered linear systems.

In some complex systems, algorithms must be used to determine reliability and other factors. This method includes assessing probable outcomes when taking all working states and possibilities of a system into account. To do so, studiers must observe a smaller scale example of the system they are hoping to assess. Complex systems are made of many parts, and even linear systems like this can be hard to navigate. Algorithms are needed to determine many aspects of complex, linear systems.