In these notes, we explore the space of processes (real or mental) from a natural or synthetic origin in order to explore ways to map them to representations in a given model of computation, adding some techniques on how to do this.

Computation is the process of performing mathematical, logical, or data-processing operations using algorithms and hardware to solve problems or perform tasks.

Note (Meta): Given a process $p$, what is the “Model of Computation” that best represents $p$? Formally $p$ $\in \text{Process Space} \rightarrow \text{Model of Computation(p)}$.

Note: $\text{Model of Computation}$: $\text{Process Space}$ → $\text{Computation Space}$.

A model of computation (computation model) (or computational formalism) is a formal system that defines how computations are represented and executed. How is this process represented? And what are the semantics of this representation?

A computation model is associated with a set of techniques and methods to articulate computations for the model of computation.

Goals:

• Study Models of Computation & Express Computation With Them.
• Learn how to design new abstractions within a given model of computation to facilitate the representation of processes.

Guide:

• Note: The word programming language is synonymous with a model of computation.
• Note: Many Concurrency Models are basically models of Computation.
• Key Questions:
  • (Problem - Process → Model of Computation) In which model of computation is this process most naturally or easily expressed?
  • (Model of Computation → Process) What kinds of processes can be naturally represented in this computational model?
  • Which programming paradigms does this model of computation enable?

Note: A model of computation formalizes the informal concept of programming paradigms.

Index

Computation