A survey of modeling techniques used in compiler design and implementation

Compiler design is a complex and a mathematically precise activity. As such, mathematical modeling plays a crucial part, in the compiler design process. Traditionally, compiler design has used mathematical abstractions, such as Regular Expressions and Context-Free Grammars to represent the syntax of programming languages. Compiler Optimization has utilized several mathematical models such as, Data Flow Graphs, Control Flow Graphs and Single Static Assignment, to model computation, at various stages of compilation. Program Parallelization, has employed models such as, Program Dependent Graphs, Integer Linear Programming to extract parallel threads of computation. This survey aims to study the mathematical abstractions in use today to solve problems encountered in the design and optimization of compilers.