### Abstract

We address the technology mapping problem for lookup table FPGAs. The area minimization problem, for mapping K-bounded networks, consisting of nodes with at most K inputs, using K-input lookup tables, is known to be NP-complete for K ≥ 5. The complexity was unknown for K = 2, 3, and 4. The corresponding delay minimization problem (under the constant delay model) was solved in polynomial time by the flow-map algorithm, for arbitrary values of K. We study the class of K-bounded networks, where all nodes have exactly K inputs. We call such networks K-exact. We give a characterization of mapping solutions for such networks. This leads to a polynomial time algorithm for computing the simultaneous area and delay minimum mapping for such networks using K-input lookup tables. We also show that the flow-map algorithm computes the same mapping solution as our algorithm. We then show that for K = 2 the mapping solution for a 2-bounded network, minimizing the area and delay simultaneously, can be easily obtained from that of a 2-exact network derived from it by eliminating single input nodes. Thus the area minimization problem for 2-input lookup tables can be solved in polynomial time, resolving an open problem.

Original language | English (US) |
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Pages (from-to) | 287-302 |

Number of pages | 16 |

Journal | Integration, the VLSI Journal |

Volume | 20 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1996 |

Externally published | Yes |

### ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Electrical and Electronic Engineering