# Cora Documentation – WeightSets Ib¶

(version 21/02/2019 - Awali 1.0.2)

Awali deals with weighted automata. The weights are taken in sets that are called internally WeightSets and that are, in a first approximation, semirings. This first document presents the numerical semirings that are available in the current version of Awali. A next document will present more complex WeightSets , and another one how a user can define its own WeightSet and integrate it in Awali.

The list of numerical semirings that are available is given at the end of the output of the command cora help:

B, Z, Q, R, C, F2, Z-min-plus, Z-max-plus, R-max-prod, Z/<int>Z



The name are explicit. Besides for the last one which is peculiar as it depends from a parameter given by the user, the above writing is the way the semiring is denoted in the -W option.

Boolean automata have been described in the document GettingStartedWithCora, those with weights in the semirings Z, Q, R and C in CoraDoc-WeightsIA. We review here the commands for the remaining semirings.

TO BE WRITTEN

## 1. Weights in $\mathbb{F}2$¶

There is no preloaded $\mathbb{F}2$-automaton in Awali so far.

## 2. Weights in $\mathbb{Z}\mathsf{-min}\mathsf{-plus}$¶

There are several preloaded $\mathbb{Z}\mathsf{-min-plus}$-automata in Awali:

minab, minblocka, slowgrow

## 3. Weights in $\mathbb{Z}\mathsf{-max}\mathsf{-plus}$¶

There is only one preloaded $\mathbb{Z}\mathsf{-max}\mathsf{-plus}$-automaton in Awali: heapmodel

## 4. Weights in $\mathbb{R}\mathsf{-max}\mathsf{-prod}$¶

There is no preloaded $\mathbb{R}\mathsf{-max}\mathsf{-prod}$-automata in Awali.

## 5. Weights in $\mathbb{Z}/\mathtt{<\!int\!>}\mathbb{Z}$¶

There is no preloaded $\mathbb{Z}/\mathtt{<\!int\!>}\mathbb{Z}$-automata in Awali.

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