# Semantical Equivalence of the Control Flow Graph and the Program Dependence Graph

## TL;DR

This paper establishes an equivalence between control flow graphs and a new class of deterministic program dependence graphs, providing a more general operational semantics that applies beyond well-structured programs.

## Contribution

It introduces deterministic PDGs with unique execution outcomes and proves their operational semantics are equivalent to control flow graphs, extending existing semantics.

## Key findings

- Deterministic PDGs have unique final states.
- Operational semantics of control flow graphs and deterministic PDGs are equivalent.
- Deterministic PDGs include those from well-structured programs.

## Abstract

The program dependence graph (PDG) represents data and control dependence between statements in a program. This paper presents an operational semantics of program dependence graphs. Since PDGs exclude artificial order of statements that resides in sequential programs, executions of PDGs are not unique. However, we identified a class of PDGs that have unique final states of executions, called deterministic PDGs. We prove that the operational semantics of control flow graphs is equivalent to that of deterministic PDGs. The class of deterministic PDGs properly include PDGs obtained from well-structured programs. Thus, our operational semantics of PDGs is more general than that of PDGs for well-structured programs, which are already established in literature.