monoid_props.h

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#ifndef MONO_PROPS_H
#define MONO_PROPS_H
 
#include <stdbool.h>
#include <stdlib.h>
#include "nfa.h"
#include "monoid.h"
#include "monoid_orbits.h"
#include "monoid_kernels.h"
#include "sep_group.h"
 
 /*  __  __                   _     _         ____                            _   _            */
 /* |  \/  | ___  _ __   ___ (_) __| |___ _  |  _ \ _ __ ___  _ __   ___ _ __| |_(_) ___  ___  */
 /* | |\/| |/ _ \| '_ \ / _ \| |/ _` / __(_) | |_) | '__/ _ \| '_ \ / _ \ '__| __| |/ _ \/ __| */
 /* | |  | | (_) | | | | (_) | | (_| \__ \_  |  __/| | | (_) | |_) |  __/ |  | |_| |  __/\__ \ */
 /* |_|  |_|\___/|_| |_|\___/|_|\__,_|___(_) |_|   |_|  \___/| .__/ \___|_|   \__|_|\___||___/ */
 /*                                                          |_|                               */

typedef enum
{
    H_GREEN,
    L_GREEN,
    R_GREEN,
    J_GREEN,
} green_relation;
 
extern char green_rel_array[4];
 
 
/***********/
/* Trivial */
/***********/

bool is_trivial_monoid(morphism*,    
    uint* 
);

bool is_trivial_semigroup(morphism*, 
    uint* 
);

bool is_trivial_subsemi(subsemi*, 
    uint* 
);

bool is_trivial_orbmono(orbits*,   
    uint* 
);
 
 
 
 
/**********/
/* Groups */
/**********/

bool is_group_mono(morphism*, 
    uint* 
);

bool is_group_semigroup(morphism*, 
    uint* 
);

bool is_group_subsemi(subsemi*, 
    uint* 
);

bool is_group_orbmono(orbits*,    
    uint* 
);
 

bool is_letterind_mono(morphism*,    
    uint* 
);
 
 
 
/*****************/
/* Commutativity */
/*****************/

bool is_comm_mono(morphism*, 
    uint* 
);
 

bool is_comm_subsemi(subsemi*, 
    uint* 
);

bool is_com_orbmono(orbits*,        
    uint* 
);

bool is_comm_ltt_mono(orbits*,     
    uint* 
);
 
 
/***************/
/* Idempotence */
/***************/

bool is_idem_mono(morphism*, 
    uint* 
);

bool is_idem_subsemi(subsemi*, 
    uint* 
);
 

bool is_idem_orbmono(orbits*,    
    uint* 
);
 
/*******************/
/* H,R,L,J-trivial */
/*******************/
parti* grel_to_parti(green* G, green_relation P);

bool is_gtrivial_mono(morphism*, 
    green_relation,            
    uint* 
);

bool is_gtrivial_subsemi(subsemi*, 
    green_relation,                
    uint* 
);

bool is_gtrivial_orbmono(orbits*,    
    green_relation,                
    uint* 
);
 

bool is_htrivial_generators(morphism*, 
    uint* 
);
 
 
/******/
/* DA */
/******/
 

bool is_da_mono(morphism*,       
    uint* 
);

bool is_da_subsemi(subsemi*,      
    uint* 
);

bool is_da_orbmono(orbits*,    
    uint* 
);
 
/****************/
/* J-saturated  */
/****************/

bool is_jsat_mono(morphism*, 
    uint* 
);

bool is_ejsat_mono(morphism*, 
    uint* 
);

bool is_jsat_subsemi(subsemi*,  
    uint, 
    uint* 
);
 

bool is_jsat_orbmono(orbits*,   
    uint* 
);
 
 
 
 
 
/*********/
/* Knast */
/*********/

bool is_blockg_mono(morphism*,   
    uint* 
);

bool is_bpolmod_mono(morphism*,  
    uint* 
);
 

bool is_bpolamt_mono(morphism*,  
    uint* 
);

bool is_knast_mono(orbits*, 
    uint* 
);

bool is_knast_ker(orbits*, 
    subsemi*,          
    uint* 
);
 

bool is_bpolamtp_mono(orbits*, 
    uint* 
);

bool is_bpolgrp_mono(orbits*, 
    uint* 
);
 
 
 

bool is_knast_at_mono(morphism* M,   
    uint* cexa 
);
 
 
/*********************/
/* UPolBPol Equation */
/*********************/

bool is_upbp_mono(orbits*, 
    uint* 
);
 
 
#endif