-expression denoted by expression.examples::Thompson – set of Thompson automata
examples::Thompson(A,S) creates a domain for Thompson automata with multiplicities over the alphabet A to which we add a new letter called "epsilon" and the component semi-ring S.
The domain element examples::Thompson(A,S)(expression) represents the Thompson automaton built from a rational -expression denoted by expression.
Creating the Type
examples::Thompson(A, S)
Thompson(A,S)(expression)
Parameters:
|
A: |
an alphabet, i.e., a list of letters |
|
S: |
a semiring, i.e., a domain of category Cat::SemiRing |
|
expression: |
a string. |
Superdomain
Related Domains:
Dom::BooleanSemiRing, Dom::MaxMinSemiRing, Dom::MaxPlusSemiRing, Dom::MinMaxSemiRing, Dom::MinPlusSemiRing, Dom::RationalExpression, Dom::SemiRing, Dom::WeightedAutomaton
Let us consider the set of Thompson automata defined over the alphabet {a,b} and whose scalars are taken in the set of integer numbers. First, we define the set of scalars and the alphabet:
Z:=Dom::Integer:
alphabet:=[a,b]:
Then the set of Z-Thompson automata is introduced:
TZ:=examples::Thompson(alphabet,Z):
Now we show how to create a Z-Thompson automaton corresponding to a rational Z-expression. Here, we distinguish between rational Z-expressions as objects of Dom::RationalExpression and their writings as strings because we do not need to create them:
TZ("2*star(a)+b")
+- -+
| 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |,
+- -+
+- -+
| 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 |
| |
| 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 |
| |
epsilon = | 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0 |,
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
+- -+
+- -+
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
a = | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |,
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
+- -+
+- -+ +- -+
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | | 2 |
| | | |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | | 0 |
| | | |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | | 0 |
| | | |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | | 0 |
| | | |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | | 0 |
| | | |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | | 0 |
| | | |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | | 0 |
| | | |
b = | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |, | 0 |
| | | |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | | 0 |
| | | |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | | 0 |
| | | |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | | 0 |
| | | |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | | 0 |
| | | |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 | | 0 |
| | | |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | | 0 |
| | | |
| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | | 1 |
+- -+ +- -+
Changes in MuPAD 4.0
New Function.