Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Automata
Automata supports computation with finite state machines, syntactic semigroups and one-dimensional cellular automata.
This listing includes the most important functions in the package. For more information and more examples, see .
Finite State Machines
— computes the complement automaton
— computes the concatenation automaton
— converts to a deterministic machine
— constructs a DFA testing divisilibility properties
— constructs a (partial) DFA for a finite language
— converts a frontier to a DFA
— generates a finite state machine using a closure operation
— determines the growth function of a DFA
— computes the intersection automaton
— computes the Kleene star automaton
— converts a finite automaton to a minimal DFA, may use DeterminizeFA
— minimizes a DFA
SemilinerFA
— constructs a DFA based on a transformation semigroup
— computes the union automaton
— adds a transition to a transition system
— the label and target of a transition
— the number of transitions in a transition system
— removes a transition to a transition system
— assigns to a symbol list the curried transition functions of a transition system
— the label of a transition
— the list of transitions in a transition system
— computes the transition matrix of a transition system
— apply a map to a list of transitions
— the source of a transition
— reverse all transitions in a transition system
— select some transition in a transition system
— sort transitions in lexicographic order
— the states of a transition
— classifies transitions and applies a map to the classes
— the source and label of a transition
— adds a transition to a transition system
— the alphabet of a transition system
— the labeled digraph of a transition system
— the type of a transition system
— returns the alphabet of a regular expression
— tests whether a regular expression is empty
— converts a regular expression to a begin/exit automaton
— converts a regular expression to a deterministic one
— converts a regular expression to a finite automaton
— converts a regular expression to a finite automaton
— converts a regular expression to a normal nondeterministic automaton
AlphabetBaseCount
— returns the number of symbols in the alphabet
— returns a list of the symbols in the alphabet
— returns various parameters of the alphabet
— returns the number of tracks in the alphabet
— concatenates words
— is a symbol representing the empty string
— replaces empty strings by Eps
EpsionFreeQ
— tests for the empty string or Eps
— replaces Eps by the empty string
— determines the number of scattered factors
— returns the length of a word, considers Eps empty
— tests lexicographic order between words
— tests whether an object is a string or Eps
— generates a random word
— generates all words over an alphabet of a certain length
— shuffles two words
— sorts lists of words in lexicographic order
Syntactic Semigroups
— constructs a transformation from its kernel and image
IdempotenQSGT
— returns the identity transformation of some degree
— the image of a transformation
— the kernel and image of a transformation
— checks whether the image is a selector for the kernel
— the kernel of a transformation
— converts a permutation to a transformation
— exponentiates a transformation
— generates a random transformation of some degree
— the rank of a transformation
— denotes an element of a transformation semigroup
TransformationDegree
— the integer list representing a transformation
— checks whether an integer list represents a transformation
— the diagrammatic product of two transformation
— replace terms according to a transformation
— simplifies the rewrite rules of a transformation semigroup
— rewrites a string according to a list of rewrite rules
— rewrite to an irreducible string according to a list of rewrite rules
— a transformation semigroup with generators
— computes the Cayley graph of a transformation semigroup
— computes the Cayley table of a transformation semigroup
— the degree of a semigroup
— the transformations of a semigroup
— the identities of a transformation semigroup as rewrite rules
— generates a transformation semigroup
— the generators of a semigroup
— the order of a semigroup
— checks whether an object is a semigroup
— adjoins a unit element to a semigroup if necessary
— the witnesses for a transformation semigroup
Cellular Automata
— determines whether the global map of a CA is surjective, open, or injective
— constructs a CA from various parameters
— constructs the global map of a CA
— constructs the local map of a CA
— computes an orbit of a CA
— constructs a seed configuration for a CA orbit
— constructs the reversible Fredkin automaton of a CA
— converts a CA to a de Bruijn semiautomaton
— constructs the Welch automata of a CA
Utilities
— determines transient and period of an orbit
— assign a finite function to a symbol
— generates the Cartesian product
— computes the function closure of an object
— returns the cycle decomposition of a set under a permutation
— returns the canonical cycle decomposition of a permutation
— flattens by one level
— convert a bitvector to a subset
— shuffles two lists
— generates non-decreasing sequences
— converts lists to pairs of objects
— computes the partitions of an integer
— returns the position of several objects
— generates the collection of all subsets
— computes the rank of elements of Cartesian products
— returns rewrite rules that replace an object by its rank
— converts a relation to a Boolean matrix
— convert a subset to a bitvector
— computes equivalence classes from different representations
— computes the canonical selector function for a list
— a mod function with a transient part
— unranks elements in a Cartesian product
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