shell_morprops.h File Reference

Shell functions testing properties of automata. More...

#include "alloc.h"
#include "shell_languages.h"
#include "monoid_props.h"

Go to the source code of this file.

Functions
bool	shell_morprop_htgentriv (int, char *, FILE *)
	Checks if the H-classes of 1 and all generators are trivial.
bool	shell_morprop_monotriv (int, char *, FILE *)
	Checks if a monoid is trivial.
bool	shell_morprop_semitriv (int, char *, FILE *)
	Checks if a semigroup is trivial.
bool	shell_morprop_orbtriv (int, orbits_type, char *, char *, FILE *)
	Checks if a set of orbits is trivial.
bool	shell_morprop_letterind (int, char *, FILE *)
	Checks if a morphism maps all letters to the same element.
bool	shell_morprop_monogroup (int, char *, FILE *)
	Checks if a monoid is a group.
bool	shell_morprop_semigroup (int, char *, FILE *)
	Checks if a semigroup is a group.
bool	shell_morprop_monocom (int j, char *name, FILE *out)
	Checks if a monoid is a group.
bool	shell_morprop_kercom (int j, kernel_type type, char *ker, char *name, FILE *out)
	Checks if a kernel is commutative.
bool	shell_morprop_orbcom (int j, orbits_type type, char *orbs, char *name, FILE *out)
	Checks if orbits are commutative.
bool	shell_morprop_semigencom (int j, char *name, FILE *out)
	Checks if a semigroup is commutative.
bool	shell_morprop_monoidem (int j, char *name, FILE *out)
	Checks if a monoid is idempotent.
bool	shell_morprop_keridem (int j, kernel_type type, char *ker, char *name, FILE *out)
	Checks if a kernel is idempotent.
bool	shell_morprop_orbidem (int j, orbits_type type, char *orbs, char *name, FILE *out)
	Checks if orbits are idempotent.
bool	shell_morprop_monogreen (int j, green_relation R, char *name, FILE *out)
	Checks if a Green relation is trivial in a monoid.
bool	shell_morprop_kergreen (int j, green_relation R, kernel_type type, char *ker, char *name, FILE *out)
	Checks if a Green relation is trivial in a kernel.
bool	shell_morprop_orbgreen (int j, green_relation R, orbits_type type, char *orbs, char *name, FILE *out)
	Checks if a Green relation is trivial in a set of orbits.
bool	shell_morprop_monoda (int j, char *name, FILE *out)
	Checks if a monoid is in DA.
bool	shell_morprop_kerda (int j, kernel_type type, char *ker, char *name, FILE *out)
	Checks if a kernel is in DA.
bool	shell_morprop_orbda (int j, orbits_type type, char *orbs, char *name, FILE *out)
	Checks if orbits are in DA.
bool	shell_morprop_monojsat (int j, char *name, FILE *out)
	Checks if a monoid satisfies the J-saturation property.
bool	shell_morprop_monoejsat (int j, char *name, FILE *out)
	Checks if a monoid satisfies J-saturation property restricted to idempotents.
bool	shell_morprop_kerjsat (int j, kernel_type type, char *ker, char *name, FILE *out)
	Checks if a kernel satisfies the J-saturation property.
bool	shell_morprop_orbjsat (int j, orbits_type type, char *orbs, char *name, FILE *out)
	Checks if orbits satisfy the J-saturation property.
bool	shell_morprop_bpgroupeq (int j, kernel_type type, char *ker, char *name, FILE *out)
	Checks if a morphism satisfies the BPol(G)-equation.
bool	shell_morprop_blockg (int j, char *name, FILE *out)
	Checks if a monoid satisfies the block-group property.
bool	shell_mprop_semiknast (int j, char *name, FILE *out)
	Checks if a semigroup satisfies Knast's equation.
bool	shell_morprop_kerknast (int j, kernel_type type, char *ker, char *name, FILE *out)
	Checks if a strict kernel satisfies Knast's equation.
bool	shell_morprop_knastat (int j, char *name, FILE *out)
	Checks if a monoid satisfies Knast's equation for AT sets.
bool	shell_morprop_bpgroupeqplus (int j, orbits_type type, char *orbs, char *name, FILE *out)
	Checks if a kernel satisfies the BPol(G⁺)-equation.
bool	shell_morprop_ubp2eq (int j, orbits_type type, char *orbs, char *name, FILE *out)
	Checks if orbits satisfy the UBP2 equality property.

Detailed Description

Shell functions testing properties of automata.

Shell functions testing properties of morphisms.

Attention

All functions must be called on indices of the objects array that refer to automata.ACCESSX_MAX_TABLESIZE This is not checked in the functions.

All functions must be called on indices of the objects array that refer to morphisms. This is not checked in the functions.

Function Documentation

shell_morprop_blockg()

bool shell_morprop_blockg	(	int	j,
		char *	name,
		FILE *	out )

Checks if a monoid satisfies the block-group property.

Returns

True if the monoid satisfies the block-group property, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_bpgroupeq()

bool shell_morprop_bpgroupeq	(	int	j,
		kernel_type	type,
		char *	ker,
		char *	name,
		FILE *	out )

Checks if a morphism satisfies the BPol(G)-equation.

Returns

True if the morphism satisfies the BPol(G)-equation, false otherwise.

Parameters

j	Index of the morphism in the objects array.
type	The type of kernel to check.
ker	The name of the kernel (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_bpgroupeqplus()

bool shell_morprop_bpgroupeqplus	(	int	j,
		orbits_type	type,
		char *	orbs,
		char *	name,
		FILE *	out )

Checks if a kernel satisfies the BPol(G⁺)-equation.

Returns

True if the kernel satisfies the BPol(G⁺)-equation, false otherwise.

Parameters

j	Index of the morphism in the objects array.
type	The type of orbits to check.
orbs	The name of the orbits (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_htgentriv()

bool shell_morprop_htgentriv	(	int	j,
		char *	name,
		FILE *	out )

Checks if the H-classes of 1 and all generators are trivial.

Returns

True if the H-classes of 1 and all generators are trivial, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_kercom()

bool shell_morprop_kercom	(	int	j,
		kernel_type	type,
		char *	ker,
		char *	name,
		FILE *	out )

Checks if a kernel is commutative.

Returns

True if the kernel is commutative, false otherwise.

Parameters

j	Index of the morphism in the objects array.
type	The type of kernel to check.
ker	The name of the kernel (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_kerda()

bool shell_morprop_kerda	(	int	j,
		kernel_type	type,
		char *	ker,
		char *	name,
		FILE *	out )

Checks if a kernel is in DA.

Returns

True if the kernelis in DA, false otherwise.

Parameters

j	Index of the morphism in the objects array.
type	The type of kernel to check.
ker	The name of the kernel (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_kergreen()

bool shell_morprop_kergreen	(	int	j,
		green_relation	R,
		kernel_type	type,
		char *	ker,
		char *	name,
		FILE *	out )

Checks if a Green relation is trivial in a kernel.

Returns

True if the relation is trivial, false otherwise.

Parameters

j	Index of the morphism in the objects array.
R	The relation that needs to be checked.
type	The type of kernel to check.
ker	The name of the kernel (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_keridem()

bool shell_morprop_keridem	(	int	j,
		kernel_type	type,
		char *	ker,
		char *	name,
		FILE *	out )

Checks if a kernel is idempotent.

Returns

True if the kernel is idempotent, false otherwise.

Parameters

j	Index of the morphism in the objects array.
type	The type of kernel to check.
ker	The name of the kernel (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_kerjsat()

bool shell_morprop_kerjsat	(	int	j,
		kernel_type	type,
		char *	ker,
		char *	name,
		FILE *	out )

Checks if a kernel satisfies the J-saturation property.

Returns

True if the kernel satisfies the J-saturation property, false otherwise.

Parameters

j	Index of the morphism in the objects array.
type	The type of kernel to check.
ker	The name of the kernel (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_kerknast()

bool shell_morprop_kerknast	(	int	j,
		kernel_type	type,
		char *	ker,
		char *	name,
		FILE *	out )

Checks if a strict kernel satisfies Knast's equation.

Returns

True if the strict kernel satisfies Knast's equation, false otherwise.

Parameters

j	Index of the morphism in the objects array.
type	The type of kernel to check.
ker	The name of the kernel (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_knastat()

bool shell_morprop_knastat	(	int	j,
		char *	name,
		FILE *	out )

Checks if a monoid satisfies Knast's equation for AT sets.

Returns

True if the monoid satisfies Knast's equation for AT-sets, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_letterind()

bool shell_morprop_letterind	(	int	j,
		char *	name,
		FILE *	out )

Checks if a morphism maps all letters to the same element.

Returns

True if the morphism maps all letters to the same element, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_monocom()

bool shell_morprop_monocom	(	int	j,
		char *	name,
		FILE *	out )

Checks if a monoid is a group.

Returns

True if the monoid is a group, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_monoda()

bool shell_morprop_monoda	(	int	j,
		char *	name,
		FILE *	out )

Checks if a monoid is in DA.

Returns

True if the monoid is in DA, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_monoejsat()

bool shell_morprop_monoejsat	(	int	j,
		char *	name,
		FILE *	out )

Checks if a monoid satisfies J-saturation property restricted to idempotents.

Returns

True if the monoid satisfies the property, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_monogreen()

bool shell_morprop_monogreen	(	int	j,
		green_relation	R,
		char *	name,
		FILE *	out )

Checks if a Green relation is trivial in a monoid.

Returns

True if the relation is trivial, false otherwise.

Parameters

j	Index of the morphism in the objects array.
R	The relation that needs to be checked.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_monogroup()

bool shell_morprop_monogroup	(	int	j,
		char *	name,
		FILE *	out )

Checks if a monoid is a group.

Returns

True if the monoid is a group, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_monoidem()

bool shell_morprop_monoidem	(	int	j,
		char *	name,
		FILE *	out )

Checks if a monoid is idempotent.

Returns

True if the monoid is idempotent, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_monojsat()

bool shell_morprop_monojsat	(	int	j,
		char *	name,
		FILE *	out )

Checks if a monoid satisfies the J-saturation property.

Returns

True if the monoid satisfies the J-saturation property, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_monotriv()

bool shell_morprop_monotriv	(	int	j,
		char *	name,
		FILE *	out )

Checks if a monoid is trivial.

Returns

True if the monoid is trivial, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_orbcom()

bool shell_morprop_orbcom	(	int	j,
		orbits_type	type,
		char *	orbs,
		char *	name,
		FILE *	out )

Checks if orbits are commutative.

Returns

True if the orbits are commutative, false otherwise.

Parameters

j	Index of the morphism in the objects array.
type	The type of orbits to check.
orbs	The name of the orbits (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_orbda()

bool shell_morprop_orbda	(	int	j,
		orbits_type	type,
		char *	orbs,
		char *	name,
		FILE *	out )

Checks if orbits are in DA.

Returns

True if the orbits are all in DA, false otherwise.

Parameters

j	Index of the morphism in the objects array.
type	The type of orbits to check.
orbs	The name of the orbits (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_orbgreen()

bool shell_morprop_orbgreen	(	int	j,
		green_relation	R,
		orbits_type	type,
		char *	orbs,
		char *	name,
		FILE *	out )

Checks if a Green relation is trivial in a set of orbits.

Returns

True if the relation is trivial for all orbits, false otherwise.

Parameters

j	Index of the morphism in the objects array.
R	The relation that needs to be checked.
type	The type of orbits to check.
orbs	The name of the orbits (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_orbidem()

bool shell_morprop_orbidem	(	int	j,
		orbits_type	type,
		char *	orbs,
		char *	name,
		FILE *	out )

Checks if orbits are idempotent.

Returns

True if the orbits are idempotent, false otherwise.

Parameters

j	Index of the morphism in the objects array.
type	The type of orbits to check.
orbs	The name of the orbits (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_orbjsat()

bool shell_morprop_orbjsat	(	int	j,
		orbits_type	type,
		char *	orbs,
		char *	name,
		FILE *	out )

Checks if orbits satisfy the J-saturation property.

Returns

True if the orbits satisfy the J-saturation property, false otherwise.

Parameters

j	Index of the morphism in the objects array.
type	The type of orbits to check.
orbs	The name of the orbits (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_orbtriv()

bool shell_morprop_orbtriv	(	int	j,
		orbits_type	type,
		char *	orbs,
		char *	name,
		FILE *	out )

Checks if a set of orbits is trivial.

Returns

True if the orbits are trivial, false otherwise.

Parameters

j	Index of the morphism in the objects array.
type	The orbits that need to be checked.
orbs	Name of the orbits (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_semigencom()

bool shell_morprop_semigencom	(	int	j,
		char *	name,
		FILE *	out )

Checks if a semigroup is commutative.

Returns

True if the semigroup is commutative, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_semigroup()

bool shell_morprop_semigroup	(	int	j,
		char *	name,
		FILE *	out )

Checks if a semigroup is a group.

Returns

True if the msemigroup is a group, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_semitriv()

bool shell_morprop_semitriv	(	int	j,
		char *	name,
		FILE *	out )

Checks if a semigroup is trivial.

Returns

True if the semigroup is trivial, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_morprop_ubp2eq()

bool shell_morprop_ubp2eq	(	int	j,
		orbits_type	type,
		char *	orbs,
		char *	name,
		FILE *	out )

Checks if orbits satisfy the UBP2 equality property.

Returns

True if the orbits satisfy the UBP2 equality property, false otherwise.

Parameters

j	Index of the morphism in the objects array.
type	The type of orbits to check.
orbs	The name of the orbits (for the display).
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).

shell_mprop_semiknast()

bool shell_mprop_semiknast	(	int	j,
		char *	name,
		FILE *	out )

Checks if a semigroup satisfies Knast's equation.

Returns

True if the semigroup satisfies Knast's equation, false otherwise.

Parameters

j	Index of the morphism in the objects array.
name	Name of the object (for the display)
out	Output stream (NULL is no output is desired).