In daviddoret/haricot: Algorithm Composition, Manipulation And Analysis

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Definition

In the context of the haricot package, we define a binary switch transformation that takes two iso-dimensional algorithms and returns a new iso-output-dimensional algorithm that contains the two original algorithms with a supplementary input bit that discriminates between these two.

Class

Transformation

Notation

$$ \mathcal{T}_{switch} $$

Application with truthtable algorithms

Viewed from the perspective of truthtables, it is the same as putting the truthtables of the two input algorithms on top of each other.

Application with NAND-based DAG algorithms

Viewed from the perspective of a NAND-based DAG algorithm, it is the same as creating a new algorithm that contains the graphs of the two input algorithms and adding an input bit $b$ with some graph circuitry such that:
if $b$ = 0, the output of the first input algorithm is used, if $b$ = 1, the output of the second input algorithm is used.

Example truthtable algorithms

$$ Let A_{a} \in \mathbb{A}^{\mathbb{B}^2 \rightarrow \mathbb{B}^3} = \left [ \begin{array}{lll} 010\ 101\ 111\ 000\ \end{array} \right ] $$

$$ Let A_{b} \in \mathbb{A}^{\mathbb{B}^2 \rightarrow \mathbb{B}^3} = \left [ \begin{array}{lll} 110\ 011\ 001\ 100\ \end{array} \right ] $$

$$Then, \mathcal{T}{switch}(A{a},A_{b}) \in \mathbb{A}^{\mathbb{B}^3 \rightarrow \mathbb{B}^3} = \left [ \begin{array}{lll} 010\ 101\ 111\ 000\ 110\ 011\ 001\ 100\ \end{array} \right ] $$

See also

• commutate
• unswitching_algorithms

daviddoret/haricot documentation built on May 21, 2019, 1:42 a.m.