## Representation and Symbolic Manipulation of Linearly Inductive Boolean Functions (1993)

Venue: | In Proceedings of the IEEE International Conference on Computer-Aided Design. IEEE Computer |

Citations: | 10 - 1 self |

### BibTeX

@INPROCEEDINGS{Gupta93representationand,

author = {Aarti Gupta and Allan L. Fisher},

title = {Representation and Symbolic Manipulation of Linearly Inductive Boolean Functions},

booktitle = {In Proceedings of the IEEE International Conference on Computer-Aided Design. IEEE Computer},

year = {1993},

pages = {192--199},

publisher = {Society Press}

}

### OpenURL

### Abstract

We consider a class of practically useful Boolean functions, called Linearly Inductive Functions (LIFs), and present a canonical representation as well as algorithms for their automatic symbolic manipulation. LIFs can be used to capture structural induction in parameterized circuit descriptions, whereby our LIF representation provides a fixed-sized representation for all size instances of a circuit. Furthermore, since LIFs can naturally capture the temporal induction inherent in sequential system descriptions, our representation also provides a canonical form for sequential functions. This allows for a wide range of applications of symbolic LIF manipulation in the verification and synthesis of digital systems. We also present practical results from a preliminary implementation of a general purpose LIF package. 1 Introduction Symbolic manipulation of Boolean functions has found numerous applications in the area of VLSI design automation [5]. These applications are greatly facilitated ...

### Citations

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Citation Context ...greatly facilitated by the availability of a canonical Boolean function representation -- Bryant's Binary Decision Diagram (BDD) -- and symbolic manipulation algorithms that are efficient in practice =-=[4]-=-. In this paper, we focus on automatic symbolic manipulation for a class of inductive Boolean functions, i.e. Boolean functions that are defined in terms of induction parameters, called Linearly Induc... |

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Citation Context ...lts from a preliminary implementation of a general purpose LIF package. 1 Introduction Symbolic manipulation of Boolean functions has found numerous applications in the area of VLSI design automation =-=[5]-=-. These applications are greatly facilitated by the availability of a canonical Boolean function representation -- Bryant's Binary Decision Diagram (BDD) -- and symbolic manipulation algorithms that a... |

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Citation Context ...(the parameter of inductive description), and depends instead on the number of FDs in the system. On the other hand, previous results for functions similar to our LIFs --- with bounded circuit widths =-=[1, 15]-=-, and iterative systems [16] --- indicate that size complexity of the corresponding BDD representations is linear in i. 3 Applications Since the inductive characterization of LIFs can be used to captu... |

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Citation Context ...r an LIF, we need to ensure canonicity of both the Basis BDD and the LIBDD. Since the Basis BDD is a standard BDD, it can be made canonical by construction (with respect to a given variable ordering) =-=[3]-=-. The canonicity of the LIBDD can also be maintained by extending the standard Reduce operation [4], with the modification that leaf nodes are taken to be isomorphic if and only if either they denote ... |

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Citation Context ...ction and symbolic tautology-checking in a way that would incorporate the advantages of both. Though reasoning by induction is a popular proof method, successfully employed by several research groups =-=[7, 12, 13, 17, 18]-=-, most available techniques are semi-automated at best. A complete proof typically requires user interaction and heuristic search. On the other hand, symbolic tautology-checking has been very successf... |

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Citation Context ...tice, we have explored additional parametric circuit representation mechanisms, which allow us to represent common practical circuits as LIFs. These mechanisms have been described in detail elsewhere =-=[11]-=-, along with examples that include serial adders, decoders, register files etc. In the same paper, we also describe a verification example for checking the mutual exclusion property of decoder outputs... |

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de Geus. High level design: A design vision for the 90's
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Citation Context ...erties. This has practical application in the representation and verification of standard libraries of parameterized designs, which are becoming increasingly important due to emphasis on design reuse =-=[9]-=-. In the second category, LIFs naturally capture the temporal induction inherent in sequential system descriptions, where functions at time t are defined in terms of inputs at time t and functions at ... |

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