Class Ops

Provides operations for finite automata.

Inheritance

object

Ops

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Namespace: Automata.Core.Operations

Assembly: Automata.Core.dll

Syntax

public static class Ops

Methods

Complement(Mfa)

Complement of a given MFA.

Declaration

public static Dfa Complement(this Mfa mfa)

Parameters

Type	Name	Description
Mfa	mfa	A Mfa to complement.

Returns

Type	Description
Dfa	A new deterministic finite automaton (DFA) representing the complement of the input MFA.

Concatenation(Fsa, FsaDet)

Concatenates two finite state automata.

Declaration

public static FsaDet Concatenation(Fsa left, FsaDet right)

Parameters

Type	Name	Description
Fsa	left	The left finite state automaton.
FsaDet	right	The right finite automaton.

Returns

Type	Description
FsaDet	A new deterministic finite automaton representing a concatenation of the two automata.

Remarks

Creates a new automaton. For optimal performance, use ConcatenationWith(Nfa, FsaDet) when possible to reduce overhead.

The resulting alphabet will be the union of both alphabets, irrespective of whether all symbols were referenced by right.

ConcatenationWith(Nfa, FsaDet)

Mutating concatenation: Appends another automaton to the source automaton.

Declaration

public static Nfa ConcatenationWith(this Nfa source, FsaDet right)

Parameters

Type	Name	Description
Nfa	source	Source automaton to append to.
FsaDet	right	Automaton to append.

Returns

Type	Description
Nfa	Source automaton source

Remarks

This operation mutates source.

Resulting alphabet of source will be the union of both alphabets, irrespective of whether all symbols were referenced by right.

Difference(FsaDet, Mfa)

Computes the difference between two deterministic finite automata.

Declaration

public static FsaDet Difference(this FsaDet minuend, Mfa subtrahend)

Parameters

Type	Name	Description
FsaDet	minuend	The automaton from which to subtract.
Mfa	subtrahend	The automaton whose language will be subtracted from the minuend.

Returns

Type	Description
FsaDet	A new FsaDet representing the language of the minuend except the language of the subtrahend.

Intersection(FsaDet, FsaDet)

Intersection of two deterministic finite automata. The resulting automaton accepts only the strings that are accepted by both input automata.

Declaration

public static Mfa Intersection(this FsaDet a, FsaDet b)

Parameters

Type	Name	Description
FsaDet	a	The first finite automaton.
FsaDet	b	The second finite automaton.

Returns

Type	Description
Mfa	An new Mfa representing the intersection of the two input automata.

KleenePlusWith(Nfa)

Adds a Kleene plus closure (one or many) to the specified automaton.

Declaration

public static Nfa KleenePlusWith(this Nfa source)

Parameters

Type	Name	Description
Nfa	source	Automaton to modify

Returns

Type	Description
Nfa	Modified source with Kleene Plus

KleeneStarWith(Nfa)

Adds a Kleene star closure to the specified automaton.

Declaration

public static Nfa KleeneStarWith(this Nfa source)

Parameters

Type	Name	Description
Nfa	source	Automaton to modify

Returns

Type	Description
Nfa	Modified source with Kleene Star

OptionWith(Nfa)

Applying Optional closure (?). Ensures the NFA accepts the empty string (ε), modifying it to represent L? = L ∪ {ε}. If the NFA already accepts ε, it is returned unmodified.

Declaration

public static Nfa OptionWith(this Nfa source)

Parameters

Type	Name	Description
Nfa	source	The source NFA to modify in place.

Returns

Type	Description
Nfa	The same automaton, with potential modification.

Overlaps(FsaDet, FsaDet)

Indicates whether the languages of two deterministic finite automata overlap. The resulting value is trueiff there exists at least one string accepted by both input automata.

Declaration

public static bool Overlaps(this FsaDet fsa, FsaDet other)

Parameters

Type	Name	Description
FsaDet	fsa	The first finite automaton.
FsaDet	other	The second finite automaton.

Returns

Type	Description
bool	true iff there exists at least one string accepted by both input automata.

PrefixClosure(Mfa)

Prefix closure of a given automaton, making all states final.

Declaration

public static Dfa PrefixClosure(this Mfa mfa)

Parameters

Type	Name	Description
Mfa	mfa	The Mfa to transform.

Returns

Type	Description
Dfa	A new Dfa representing the prefix closure of the input Mfa.

Remarks

The prefix closure is an automaton that accepts all prefixes (including ε) of the language recognized by the original automaton. This transformation makes every state in the original MFA a final state in the resulting DFA.

Properties of the prefix closure:

• All states are final.
• Retains graphical identity: the same alphabet, transitions, and state IDs as the original MFA.
• Retains determinism but not necessarily minimalism. For example, the prefix closure of a+ is a*, which can be represented with a single-state MFA.

Reversal(FsaDet)

Creates a new NFA that recognizes the reversal of the language accepted by the given automaton.

Declaration

public static Nfa Reversal(this FsaDet source)

Parameters

Type	Name	Description
FsaDet	source

Returns

Type	Description
Nfa	A new NFA representing the reversed automaton.

Union(Fsa, FsaDet)

Creates union of two finite state automata.

Declaration

public static FsaDet Union(Fsa left, FsaDet right)

Parameters

Type	Name	Description
Fsa	left	First automaton.
FsaDet	right	Second automaton.

Returns

Type	Description
FsaDet	A new deterministic finite automaton representing a union of the two automata.

Remarks

Creates a new automaton. For optimal performance, use UnionWith(Nfa, FsaDet) when possible to reduce overhead.

Resulting alphabet of left will be the union of both alphabets, irrespective of whether all symbols were referenced by right.

UnionWith(Nfa, FsaDet)

Unites the source automaton with another automaton (in-place union).

Declaration

public static Nfa UnionWith(this Nfa source, FsaDet other)

Parameters

Type	Name	Description
Nfa	source	Source automaton to mutate.
FsaDet	other	Automaton to union with.

Returns

Type	Description
Nfa	Source automaton source

Remarks

This operation mutates source to represent the union of the two automata.

Resulting alphabet of source will be the union of both alphabets, irrespective of whether all symbols were referenced by other.