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## Details

Document Type: | Book |
---|---|

All Authors / Contributors: |
John D Lafferty; Alexander Vardy |

OCLC Number: | 40420767 |

Notes: | "July 30, 1998." |

Description: | 31 p. : ill. ; 28 cm. |

Series Title: | Research paper (Carnegie Mellon University. School of Computer Science), CMU-CS-98-162. |

Responsibility: | John Lafferty, Alexander Vardy. |

### Abstract:

Abstract: "Ordered binary decision diagrams (OBDDs) are graph-based data structures for representing Boolean functions. They have found widespread use in computer-aided design and in formal verification of digital circuits. Minimal trellises are graphical representations of error-correcting codes that play a prominent role in coding theory. This paper establishes a close connection between these two graphical models, as follows. Let C be a binary code of length n, and let f[subscript c](x₁, ..., x[subscript n]) be the Boolean function that takes the value 0 at x₁, ..., x[subscript n] if and only if (x₁, ..., x[subscript n]) [element of] C. Given this natural one-to-one correspondence between Boolean functions and binary codes, we prove that the minimal proper trellis for a code C with minimum distance d> 1 is isomorphic to the single-terminal OBDD for its Boolean indicator function f[subscript c](x₁, ..., x[subscript n]). Prior to this result, the extensive research during the past decade on binary decision diagrams -- in computer engineering -- and on minimal trellises -- in coding theory -- has been carried out independently. As outlined in this work, the realization that binary decision diagrams and minimal trellises are essentially the same data structure opens up a range of promising possibilities for transfer of ideas between these disciplines."

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