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Concept
And-inverter graph
Summary
An and-inverter graph (AIG) is a directed, acyclic graph that represents a structural implementation of the logical functionality of a circuit or network. An AIG consists of two-input nodes representing logical conjunction, terminal nodes labeled with variable names, and edges optionally containing markers indicating logical negation. This representation of a logic function is rarely structurally efficient for large circuits, but is an efficient representation for manipulation of boolean functions. Typically, the abstract graph is represented as a data structure in software.
Conversion from the network of logic gates to AIGs is fast and scalable. It only requires that every gate be expressed in terms of AND gates and inverters. This conversion does not lead to unpredictable increase in memory use and runtime. This makes the AIG an efficient representation in comparison with either the binary decision diagram (BDD) or the "sum-of-product" (ΣoΠ) form, that is, the canonical form in Boolean algebra known as the disjunctive normal form (DNF). The BDD and DNF may also be viewed as circuits, but they involve formal constraints that deprive them of scalability. For example, ΣoΠs are circuits with at most two levels while BDDs are canonical, that is, they require that input variables be evaluated in the same order on all paths.
Circuits composed of simple gates, including AIGs, are an "ancient" research topic. The interest in AIGs started with Alan Turing's seminal 1948 paper on neural networks, in which he described a randomized trainable network of NAND gates. Interest continued through the late 1950s and continued in the 1970s when various local transformations have been developed. These transformations were implemented in several
logic synthesis and verification systems, such as Darringer et al. and Smith et al., which reduce circuits to improve area and delay during synthesis, or to speed up formal equivalence checking. Several important techniques were discovered early at IBM, such as combining and reusing multi-input logic expressions and subexpressions, now known as structural hashing.
Official source
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