cfl_regular.h

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00001 
00002 /** @file cfl_regular.h 
00003 
00004 Operations on regular languages.
00005 See [Cassandras and Lafortune. Introduction to Discrete Event Systems] for an
00006 introduction to regular language operations.
00007 Operations are always performed on language(s) marked by the passed generator(s),
00008 resulting in the language(s) marked by the resulting generator(s).
00009 Only if mentioned extra, the same is done for the involved generated (prefix-closed)
00010 languages.
00011 
00012 */
00013 
00014 /* FAU Discrete Event Systems Library (libfaudes)
00015 
00016    Copyright (C) 2006  Bernd Opitz
00017    Exclusive copyright is granted to Klaus Schmidt
00018 
00019    This library is free software; you can redistribute it and/or
00020    modify it under the terms of the GNU Lesser General Public
00021    License as published by the Free Software Foundation; either
00022    version 2.1 of the License, or (at your option) any later version.
00023 
00024    This library is distributed in the hope that it will be useful,
00025    but WITHOUT ANY WARRANTY; without even the implied warranty of
00026    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
00027    Lesser General Public License for more details.
00028 
00029    You should have received a copy of the GNU Lesser General Public
00030    License along with this library; if not, write to the Free Software
00031    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA */
00032 
00033 
00034 #ifndef FAUDES_REGULAR_H
00035 
00036 #include "cfl_definitions.h"
00037 #include "cfl_parallel.h"
00038 #include "cfl_project.h" 
00039 
00040 namespace faudes {
00041 
00042 /**
00043  * Language union, nondeterministic version.
00044  *
00045  * This function performs the union of two languages marked by two generators;
00046  * the resulting generator marks the resulting language.
00047  * Moreover, the same is done for the involved generated (prefix-closed) languages.
00048  * Method:
00049  * This function implements the textbook version in taking unions of all generator
00050  * entities (alphabets, initial states, ...) of rGen1 and rGen2. State sets are taken
00051  * as disjoint by definition and thus reindexed and renamed to achieve disjoint union.
00052  * The resulting language is defined over the union of the alphabets of the original
00053  * languages; original languages defined over different alphabets are treated as if
00054  * they were defined over the union of both alphabets.
00055  * 
00056  * Determinism:
00057  * Input parameters may be nondeterministic.
00058  * This function is more economical than the deterministic version, but likely to
00059  * produce a non-deterministic result; see also LanguageUnion().
00060  *
00061  * No restrictions on parameters.
00062  *
00063  * @param rGen1
00064  *   generator generating/marking L1/Lm1
00065  * @param rGen2
00066  *   generator generating/marking L2/Lm2
00067  * @param rResGen
00068  *   resulting generator generating/marking the language union of L1 and L2/of Lm1 and Lm2
00069  *
00070  *
00071  * @ingroup GeneratorFunctions
00072  */
00073 void LanguageUnionNonDet(const Generator& rGen1, const Generator& rGen2, 
00074     Generator& rResGen);
00075 
00076 /**
00077  * Language union, deterministic version.
00078  *
00079  * This function performs the union of two languages marked by two generators;
00080  * the resulting generator marks the resulting language.
00081  * Moreover, the same is done for the involved generated (prefix-closed) |languages.
00082  * Method:
00083  * This function implements the textbook version (which textbook??) in taking unions
00084  * of all generator entities (alphabets, initial states, ...). State sets are taken
00085  * as disjoint by definition and thus reindexed and renamed to achieve disjoint union.
00086  * The resulting language is defined over the union of the alphabets of the original
00087  * languages.
00088  *
00089  * Determinism:
00090  * Input parameters may be nondeterministic.
00091  * This function calls LanguageUnionNonDet() and then Deterministic() to convert the 
00092  * result into a deterministic generator. Note that this conversion is usually
00093  * straightforward, but there exist theoretical worst-case examples of exponential complexity.
00094  *
00095  * No restrictions on parameters.
00096  *
00097  * ToDo: a version similar to parallel composition that produces a deterministic result by construction. (?)
00098  *
00099  * @param rGen1
00100  *   generator generating/marking L1/Lm1
00101  * @param rGen2
00102  *   generator generating/marking L2/Lm2
00103  * @param rResGen
00104  *   resulting generator generating/marking the language union of L1 and L2/of Lm1 and Lm2
00105  * 
00106  * <h4>Example:</h4>
00107  * <table border=0> <tr> <td> <table>
00108  * <tr> <td> Generator G1 </td> <td> Generator G2 </td> </tr>
00109  * <tr>
00110  * <td> @image html tmp_boolean_g1.png </td>
00111  * <td> @image html tmp_boolean_g2.png </td>
00112  * </tr>
00113  * </table> </td> </tr> <tr> <td> <table width=100%>
00114  * <tr> <td> LanguageUnion(G1,G2,Result) </td> </tr>
00115  * <tr> <td> @image html tmp_union_g1g2.png </td> </tr>
00116  * </table> </td> </tr> </table>
00117  *
00118  * @ingroup GeneratorFunctions
00119  */
00120 void LanguageUnion(const Generator& rGen1, const Generator& rGen2,
00121     Generator& rResGen);
00122 
00123 /**
00124  * Language union.
00125  *
00126  * See also LanguageUnion(const Generator&, const Generator&, Generator&);
00127  * This version takes a vector of generators as argument to perform
00128  * the union for multiple languages. The implementation
00129  * calls the std union multiple times, future implementations may
00130  * do better.
00131  *
00132  * @param rGenVec
00133  *   Vector of input generators
00134  * @param rResGen
00135  *   Reference to resulting generator
00136  *
00137  */
00138 void LanguageUnion(const GeneratorVector& rGenVec, Generator& rResGen);
00139 
00140 
00141 /**
00142  * Language intersection.
00143  *
00144  * This function performs the intersection of two languages marked by two generators;
00145  * the resulting generator marks the resulting language.
00146  * Moreover, the same is done for the involved generated (prefix-closed) languages.
00147  * The resulting languages are defined over the intersection of the involved alphabets.
00148  * Method:
00149  * This function calls Product(). In the product of two automata, an event occurs if
00150  * and only if it occurs in both automata rGen1 and rGen2. The result generates/marks
00151  * the intersection of the involved languages, see e.g.
00152  * [Cassandras, Lafortune. Introduction to Discrete Event Systems, p.84]
00153  *
00154  * Determinism:
00155  * Input parameters may be nondeterministic.
00156  * Result can be nondeterministic only if input parameters are nondeterministic.
00157  *
00158  * No restrictions on parameters.
00159  *
00160  * @param rGen1
00161  *   generator generating/marking L1/Lm1
00162  * @param rGen2
00163  *   generator generating/marking L2/Lm2
00164  * @param rResGen
00165  *   resulting generator generating/marking the language intersection of L1 and L2/of Lm1 and Lm2
00166  *
00167  * <h4>Example:</h4>
00168  *
00169  * <table border=0> <tr> <td> <table>
00170  * <tr> <td> Generator G1 </td> <td> Generator G2 </td> </tr>
00171  * <tr>
00172  * <td> @image html tmp_boolean_g1.png </td>
00173  * <td> @image html tmp_boolean_g2.png </td>
00174  * </tr>
00175  * </table> </td> </tr> <tr> <td> <table width=100%>
00176  * <tr> <td> LanguageIntersection(G1,G2,Result) </td> </tr>
00177  * <tr> <td> @image html tmp_intersection_g1g2.png </td> </tr>
00178  * </table> </td> </tr> </table>
00179  *
00180  * @ingroup GeneratorFunctions
00181  */
00182 void LanguageIntersection(const Generator& rGen1, const Generator& rGen2, 
00183     Generator& rResGen);
00184         
00185 /**
00186  * Language intersection.
00187  *
00188  * See also LanguageUnion(const Generator&, const Generator&, Generator&);
00189  * This version takes a vector of generators as argument to perform
00190  * the intersection for multiple languages. The implementation
00191  * calls the std intersection multiple times, future implementations may
00192  * do better.
00193  *
00194  * @param rGenVec
00195  *   Vector of input generators
00196  * @param rResGen
00197  *   Reference to resulting generator
00198  *
00199  */
00200 void LanguageIntersection(const GeneratorVector& rGenVec, Generator& rResGen);
00201 
00202 
00203 /**
00204  * Test for empty language intersection  (same as Disjoind()).
00205  *
00206  * This function checks if the intersection of two languages marked by two generators
00207  * is empty that is the two languages are disjoint.
00208  * The involved generated (prefix-closed) languages are not considered. This function
00209  * is identical to Disjoint().
00210  *
00211  * No restrictions on parameters.
00212  *
00213  * @param rGen1
00214  *   generator marking Lm1
00215  * @param rGen2
00216  *   generator marking Lm2
00217  *
00218  * @return
00219  *   true if language intersection is empty, false if not.
00220  *
00221  * @ingroup GeneratorFunctions
00222  */  
00223 bool EmptyLanguageIntersection(const Generator& rGen1, const Generator& rGen2);
00224 
00225 /**
00226  * Test whether two languages are disjoint.
00227  *
00228  * This function tests whether the intersection of two languages marked by two generators
00229  * is empty, ie the two languages are disjoint.
00230  * The involved generated (prefix-closed) languages are not considered. This function
00231  * is identical to EmptyLanguageIntersection().
00232  *
00233  * No restrictions on parameters.
00234  *
00235  * @param rGen1
00236  *   generator marking Lm1
00237  * @param rGen2
00238  *   generator marking Lm2
00239  *
00240  * @return
00241  *   true if language intersection is empty, false if not.
00242  *
00243  * @ingroup GeneratorFunctions
00244  */  
00245 bool LanguageDisjoint(const Generator& rGen1, const Generator& rGen2);
00246 
00247 /**
00248  * Convert generator to automaton.
00249  *
00250  * Convert a generator marking the language Lm into a formal automaton recognizing Lm
00251  * with a dump state representing Sigma*-PrefixClosure(Lm). In this function, Sigma is
00252  * given by the alphabet of rGen; see also Automaton(rGen,rAlphabet).
00253  * For information about automata, see [Wonham. Supervisory Control of Discrete Event
00254  * Systems].
00255  * The original generated language is ignored.
00256  * Note: An automaton is a deterministic transition structure according to the formal
00257  *       definition; see also "Determinism" below.
00258  * Method:
00259  * Uncoaccessible states are erased, as the language generated by rGen is not examined
00260  * in this function. A dump state representing "Sigma*-PrefixClosure(Lm)" is created.
00261  * Then, the transition relation is completed such that it is fully defined for each
00262  * state and each event. Formerly undefined transitions lead to the dump state.
00263  *
00264  * Determinism:
00265  * Input parameter has to be deterministic for correct result. If not, then the 
00266  * (also nondeterministic) result recognizes the correct language, but the dump state
00267  * does not represent "Sigma*-PrefixClosure(Lm)" as it should;
00268  * see also example ExAutomaton_basic().
00269  * If FAUDES_CHECKED is defined a warning on non-deterministic input is issued.
00270  * 
00271  * No further restrictions on parameter.
00272  * 
00273  * @param rGen
00274  *   generator that is converted to automaton
00275  *
00276  * <h4>Example:</h4>
00277  * <table>
00278  * <tr> <td> Generator G </td> <td> Automaton(G) </td> </tr>
00279  * <tr>
00280  * <td> @image html tmp_automaton_g.png </td>
00281  * <td> @image html tmp_automaton_gRes.png </td>
00282  * </tr>
00283  * </table> 
00284  *
00285  * @ingroup GeneratorFunctions
00286  */
00287 void Automaton(Generator& rGen);
00288 
00289 /**
00290  * Convert generator to automaton wrt specified alphabet.
00291  *
00292  * Convert a generator marking the language Lm into a formal automaton recognizing Lm
00293  * with a dump state representing Sigma*-PrefixClosure(Lm(rGen)). In this function,
00294  * Sigma is given by the parameter rAlphabet.
00295  * For information about automata, see [Wonham. Supervisory Control of Discrete Event
00296  * Systems].
00297  * The original generated language is ignored.
00298  * Note: An automaton is a deterministic transition structure according to the formal
00299  *       definition; see also "Determinism" below.
00300  * Method:
00301  * Uncoaccessible states are erased, as the language generated by rGen is not examined
00302  * in this function. A dump state representing "Sigma*-PrefixClosure(Lm)" is created.
00303  * Then, the transition relation is completed such that it is fully defined for each
00304  * state of rGen and each event of rAlphabet. Formerly undefined transitions lead to
00305  * the dump state.
00306  *
00307  * Determinism:
00308  * Input parameter has to be deterministic for correct result. If not, then the 
00309  * (also nondeterministic) result recognizes the correct language, but the dump state
00310  * does not represent "Sigma*-PrefixClosure(Lm)" as it should;
00311  * see also example ExAutomaton_basic().
00312  * If FAUDES_CHECKED is defined a warning on non-deterministic input is issued.
00313  * 
00314  * No further restrictions on parameters.
00315  * 
00316  * @param rGen
00317  *   generator that is converted to automaton
00318  *
00319  * @param rAlphabet
00320  *   the dump state of the resulting automaton represents the
00321  *   language L_dump=rAlphabet*-PrefixClosure(Lm(rGen))
00322  *
00323  * @ingroup GeneratorFunctions
00324  */
00325 void Automaton(Generator& rGen, const EventSet& rAlphabet);
00326 
00327 /**
00328  * Language complement.
00329  *
00330  * Convert generator marking the language Lm into generator marking the language
00331  * complement of Lm which is defined as Sigma*-Lm. In this function, Sigma is
00332  * given by the alphabet of rGen; see also LanguageComplement(rGen,rAlphabet).
00333  * The original generated language is ignored.
00334  * Method:
00335  * This function calls Automaton() first and then inverts the marking of the states
00336  * of the result.
00337  *
00338  * Determinism:
00339  * Input parameter has to be deterministic for correct result, see Automaton() for
00340  * explanations.
00341  * If FAUDES_CHECKED is defined a warning on non-deterministic input is issued.
00342  * (by function Automaton()).
00343  *
00344  * No further restrictions on parameter.
00345  *
00346  * @param rGen
00347  *   generator on which the language complement is performed
00348  *
00349  * <h4>Example:</h4>
00350  * <table>
00351  * <tr> <td> Generator G </td> <td> LanguageComplement(G) </td> </tr>
00352  * <tr>
00353  * <td> @image html tmp_boolean_g1.png </td>
00354  * <td> @image html tmp_complement_g1.png </td>
00355  * </tr>
00356  * </table> 
00357  *
00358  *
00359  * @ingroup GeneratorFunctions
00360  */
00361 void LanguageComplement(Generator& rGen);
00362 
00363 /**
00364  * Language complement wrt specified alphabet.
00365  *
00366  * Convert generator marking the language Lm into generator marking the language
00367  * complement of Lm which is defined as Sigma*-Lm. In this function, Sigma is
00368  * given by the parameter rAlphabet.
00369  * The original generated language is ignored.
00370  * Method:
00371  * This function calls Automaton() first and then inverts the marking of the states
00372  * of the result.
00373  *
00374  * Determinism:
00375  * Input parameter has to be deterministic for correct result, see Automaton() for
00376  * explanations.
00377  * If FAUDES_CHECKED is defined a warning on non-deterministic input is issued.
00378  * (by function Automaton()).
00379  *
00380  * No further restrictions on parameter.
00381  *
00382  * @param rGen
00383  *   generator on which the language complement is performed
00384  *
00385  * @param rAlphabet
00386  *   reference alphabet to build the complement
00387  *
00388  * @ingroup GeneratorFunctions
00389  */
00390 void LanguageComplement(Generator& rGen, const EventSet& rAlphabet);
00391 
00392 
00393 /** 
00394  * Language Complement (uniform API wrapper). 
00395  *
00396  * @param rGen
00397  *   generator on which the language complement is performed
00398  *
00399  * @param rRes
00400  *   resulting generator
00401  *
00402  * @ingroup GeneratorFunctions
00403  */
00404 void LanguageComplement(const Generator& rGen, Generator& rRes);
00405 
00406 /** 
00407  * Language Complement (uniform API wrapper).
00408  *
00409  * @param rGen
00410  *   generator on which the language complement is performed
00411  *
00412  * @param rSigma
00413  *   reference alphabet to build the complement
00414  *
00415  * @param rRes
00416  *   resulting generator
00417  *
00418  * @ingroup GeneratorFunctions
00419  */
00420 void LanguageComplement(const Generator& rGen, const EventSet& rSigma, Generator& rRes);
00421 
00422 
00423 
00424 /**
00425  * Language difference (set-theoretic difference).
00426  *
00427  * This function calculates Lm1-Lm2 (sometimes also denoted by Lm1\\Lm2), that is the
00428  * set of all strings included in Lm1 but not in Lm2.
00429  * Method:
00430  * The language difference is computed by taking the intersection of Lm1 with the
00431  * complement of Lm2.
00432  * 
00433  * Determinism:
00434  * Due to the use of LanguageComplement(), rGen2 has to be deterministic.
00435  * Result can be nondeterministic only if rGen1 is nondeterministic.
00436  *
00437  * Restrictions on prameters:
00438  * rGen2 has to be deterministic.
00439  *
00440  * @param rGen1 
00441  *  generator marking the language Lm1
00442  * @param rGen2
00443  *  generator marking the language Lm2 
00444  * @param rResGen
00445  *  generator marking the language difference Lm1-Lm2 
00446  *
00447  * @exception Exception
00448  *   - nondeterministic parameter rGen2 (id 101). 
00449  *
00450   * <h4>Example:</h4>
00451  * <table border=0> <tr> <td> <table>
00452  * <tr> <td> Generator G1 </td> <td> Generator G2 </td> </tr>
00453  * <tr>
00454  * <td> @image html tmp_difference_g1.png </td>
00455  * <td> @image html tmp_difference_g2.png </td>
00456  * </tr>
00457  * </table> </td> </tr> <tr> <td> <table width=100%>
00458  * <tr> <td> LanguageDifference(G1,G2,Result) </td> </tr>
00459  * <tr> <td> @image html tmp_difference_g1minusg2.png </td> </tr>
00460  * </table> </td> </tr> </table>
00461  *
00462  * @ingroup GeneratorFunctions
00463  */
00464 void LanguageDifference(const Generator& rGen1, const Generator& rGen2,
00465                  Generator& rResGen);
00466 
00467 /**
00468  * Language concatenation, nondeterministic version.
00469  *
00470  * With the languages Lm1 and Lm2 marked by rGen1 and rGen2, respectively, the result
00471  * rResGen marks the concatenation LmRes=Lm1Lm2.
00472  * The languages generated by rGen1 and rGen2 are ignored. It would be possible to let
00473  * the result also generate the concatenation of the generated languages; however, this can
00474  * produce disproportionate computational overhead, if only the marked languages shall be
00475  * concatenated.
00476  * Method:
00477  * rGen2 is appended to rGen1: first, the initial states of rGen2 are erased. Then,
00478  * transitions, that formerly started from the initial state(s) of rGen2, are redirected 
00479  * and multiplied such that they start from each marked state of rGen1. The marked states
00480  * corresponding to rGen2 remain marked. The marked states of rGen1 remain marked only if
00481  * rGen2 has at least one marked initial state (i.e. if epsilon is concatenated to Lm1.)
00482  * 
00483  * Determinism:
00484  * Input parameters may be nondeterministic. Result can be nondeterministic even if input
00485  * parameters are deterministic; see also LanguageConcatenate().
00486  *
00487  * No restrictions on parameters.
00488  * 
00489  * @param rGen1
00490  *   generator marking Lm1
00491  * @param rGen2
00492  *   generator marking Lm2
00493  * @param rResGen
00494  *   resulting generator marking the language concatenation Lm1Lm2
00495  *
00496  * @ingroup GeneratorFunctions
00497  */
00498 void LanguageConcatenateNonDet(const Generator& rGen1, const Generator& rGen2,
00499     Generator& rResGen);
00500 
00501 /**
00502  * Language concatenation, deterministic version.
00503  *
00504  * With the languages Lm1 and Lm2 marked by rGen1 and rGen2, respectively, the result
00505  * rResGen marks the concatenation LmRes=Lm1Lm2.
00506  * The languages generated by rGen1 and rGen2 are ignored. It would be possible to let
00507  * the result also generate the concatenation of the generated languages; however, this can
00508  * produce disproportionate computational overhead, if only the marked languages shall be
00509  * concatenated.
00510  * Method:
00511  * rGen2 is appended to rGen1: first, the initial states of rGen2 are erased. Then,
00512  * transitions, that formerly started from the initial state(s) of rGen2, are redirected 
00513  * and multiplied such that they start from each marked state of rGen1. The marked states
00514  * corresponding to rGen2 remain marked. The marked states of rGen1 remain marked only if
00515  * rGen2 has at least one marked initial state (i.e. if epsilon is concatenated to Lm1.)
00516  * 
00517  * Determinism:
00518  * Input parameters may be nondeterministic.
00519  * This function calls LanguageUnionNonDet() and then Deterministic() to convert the 
00520  * result into a deterministic generator. Note that this conversion is usually
00521  * straightforward, but there exist theoretical worst-case examples of exponential complexity.
00522  *
00523  * No restrictions on parameters.
00524  * 
00525  * @param rGen1
00526  *   generator marking Lm1
00527  * @param rGen2
00528  *   generator marking Lm2
00529  * @param rResGen
00530  *   Resulting generator marking the language concatenation Lm1Lm2
00531  *
00532  * <h4>Example:</h4>
00533  * <table border=0> <tr> <td> <table>
00534  * <tr> <td> Generator G1 </td> <td> </td> <td> LanguageConcatenate(G1,G3,Result) </td> </tr>
00535  * <tr>
00536  * <td> @image html tmp_concat_g1.png </td>
00537  * <td> </td>
00538  * <td> @image html tmp_concat_g1g3.png </td>
00539  * </tr>
00540  * <tr> <td> Generator G2 </td> <td> </td> <td> LanguageConcatenate(G1,G4,Result) </td> </tr>
00541  * <tr>
00542  * <td> @image html tmp_concat_g2.png </td>
00543  * <td> </td> 
00544  * <td> @image html tmp_concat_g1g4.png </td>
00545  * </tr>
00546  * </tr>
00547  * <tr> <td> Generator G3 </td> <td> </td> <td> LanguageConcatenate(G2,G3,Result) </td> </tr>
00548  * <tr>
00549  * <td> @image html tmp_concat_g3.png </td>
00550  * <td> </td> 
00551  * <td> @image html tmp_concat_g2g3.png </td>
00552  * </tr>
00553  * </tr>
00554  * <tr> <td> Generator G4 </td> <td> </td> <td> LanguageConcatenate(G2,G4,Result) </td> </tr>
00555  * <tr>
00556  * <td> @image html tmp_concat_g4.png </td>
00557  * <td> </td> 
00558  * <td> @image html tmp_concat_g2g4.png </td>
00559  * </tr>
00560  * </table> </td> </tr> </table>
00561  *
00562  * @ingroup GeneratorFunctions
00563  */
00564 void LanguageConcatenate(const Generator& rGen1, const Generator& rGen2,
00565     Generator& rResGen);
00566 
00567 /**
00568  * Full Language, L(G)=Lm(G)=Sigma*.
00569  *
00570  * Construct generator generating and marking full language Sigma* from alphabet Sigma.
00571  * Method: this function creates a generator with one state that is marked and init state. This
00572  * state is selflooped with all events from rAlphabet.
00573  *
00574  * @param rAlphabet
00575  *   Alphabet Sigma from which full language Sigma* is built
00576  * @param rResGen
00577  *   Generator generating and marking full language Sigma*
00578  *
00579  * <h4>Example:</h4>
00580  * <table>
00581  * <tr> <td> FullLanguage(Sigma={a,b},Result) </td> </tr>
00582  * <tr>
00583  * <td> @image html tmp_languagesFull_result.png </td>
00584  * </tr>
00585  * </table> 
00586  *
00587  * @ingroup GeneratorFunctions
00588  */
00589 void FullLanguage(const EventSet& rAlphabet, Generator& rResGen);
00590 
00591 /**
00592  * Alphabet Language, L(G)=Lm(G)=Sigma
00593  *
00594  * Construct generator generating and marking an alphabet as languages, that is L(G)=Lm(G)=Sigma.
00595  * Method: this function creates a generator with one init state and one marked state. For each
00596  * event from rAlphabet, a transition is inserted leading from the init state to the marked state.
00597  *
00598  * No restrictions on parameters.
00599  * 
00600  * @param rAlphabet
00601  *   alphabet from which alphabet language is built
00602  * @param rResGen
00603  *   generator with languages Lm(G)=Sigma
00604  *
00605  * <h4>Example:</h4>
00606  * <table>
00607  * <tr> <td> AlphabetLanguage(Sigma={a,b},Result) </td> </tr>
00608  * <tr>
00609  * <td> @image html tmp_languagesAlphabet_result.png </td>
00610  * </tr>
00611  * </table> 
00612  *
00613  * @ingroup GeneratorFunctions
00614  */
00615 void AlphabetLanguage(const EventSet& rAlphabet, Generator& rResGen);
00616 
00617 /**
00618  * Empty string language, L(G)=Lm(G)={epsilon}.
00619  *
00620  * Construct generator generating and marking the empty string, that is L(G)=Lm(G)={epsilon}.
00621  * Method: this function creates a generator with one marked init state and the alphabet rAlphabet.
00622  *
00623  * No restrictions on parameters.
00624  * 
00625  * @param rAlphabet
00626  *   alphabet of the resulting generator
00627  * @param rResGen
00628  *   generator with languages L(G)=Lm(G)={epsilon} and alphabet rAlphabet
00629  *
00630  * <h4>Example:</h4>
00631  * <table>
00632  * <tr> <td> EmptyStringLanguage(Sigma={a,b},Result) </td> </tr>
00633  * <tr>
00634  * <td> @image html tmp_languagesEmptyString_result.png </td>
00635  * </tr>
00636  * </table> 
00637  *
00638  * @ingroup GeneratorFunctions
00639  */
00640 void EmptyStringLanguage(const EventSet& rAlphabet, Generator& rResGen);
00641 
00642 /**
00643  * Empty language Lm(G)={}.
00644  *
00645  * Construct generator and marking the empty language, that is Lm(G)={}.
00646  * Method: this function creates a deterministic generator with one initial state that is not marked. 
00647  * The alphabet is set as specified. 
00648  *
00649  * No restrictions on parameters.
00650  * 
00651  * @param rAlphabet
00652  *   Alphabet of the resulting generator
00653  * @param rResGen
00654  *   Generator with language Lm(G)={}
00655  *
00656  * @ingroup GeneratorFunctions
00657  */
00658 void EmptyLanguage(const EventSet& rAlphabet, Generator& rResGen);
00659 
00660 /**
00661  * Test for Empty language Lm(G)=={}.
00662  *
00663  * Tests if the language marked by rGen is empty, that is if Lm(G)=={}. The generated
00664  * language L(G) is not considered.
00665  * Method:
00666  * This function tests if 
00667  * a) the set of marked states is empty or else
00668  * b) the intersection of the set of accessible states and the set of marked states
00669  * is empty, i.e. if there is no marked state or if no marked state is accessible (reachable).
00670  *
00671  * No restrictions on parameter.
00672  *
00673  * @param rGen
00674  *   generator to be tested for empty marked language
00675  *
00676  * @return
00677  *   true on empty marked language, false on nonempty marked language
00678  *
00679  * @ingroup GeneratorFunctions
00680  */
00681 bool IsEmptyLanguage(const Generator& rGen);
00682 
00683 /**
00684  * Test language inclusion, Lm1<=Lm2.
00685  *
00686  * Test if language Lm1 marked by rGen1 is included in language Lm2 marked by rGen2. The
00687  * generated languages are not considered.
00688  * Method:
00689  * This function checks if there is no string in Lm1 that is not in Lm2 by testing if
00690  * the intersection of Lm1 and the language complement of Lm2 is empty.
00691  *
00692  * Restrictions on parameters: rGen2 has to be deterministic!
00693  * If FAUDES_CHECKED is defined a warning on non-deterministic input is issued.
00694  * (by function Automaton()).
00695  *
00696  * Determinism: correctness in case of nondeterministic parameter rGen1 has been tested with an
00697  *              example (see ExInclusion_simple), but not proven.
00698  *
00699  * ToDo: implement faster version using a variant of Product():
00700  * compute product without storing result, return false as soon as some event is
00701  * possible in Lm2 but not in Lm1.
00702  *
00703  * @param rGen1
00704  *   generator marking Lm1
00705  * @param rGen2
00706  *   generator marking Lm2
00707  *
00708  * @return
00709  *   true if language marked by rGen1 is included in language marked by rGen2
00710  *
00711  * @ingroup GeneratorFunctions
00712  */
00713 bool LanguageInclusion(const Generator& rGen1, const Generator& rGen2);
00714 
00715 /**
00716  * Language equality, Lm1==Lm2.
00717  *
00718  * Test if the language Lm1 marked by rGen1 equals the language Lm2 marked by rGen2. The
00719  * generated languages are not considered.
00720  * Method:
00721  * This function checks mutual inclusion of Lm1 in Lm2 and of Lm2 in Lm1 using the
00722  * function LanguageInclusion().
00723  *
00724  * Restrictions on parameters: rGen1 and rGen2 have to be deterministic!
00725  * If FAUDES_CHECKED is defined a warning on non-deterministic input is issued.
00726  * (by function Automaton()).
00727  *
00728  * ToDo: implement faster, version using a variant of Product():
00729  * compute product without storing result, return false as soon as rGen1 and rGen2
00730  * "disagree" on the occurrence of some event.
00731  *
00732  * @param rGen1
00733  *   generator marking Lm1
00734  * @param rGen2
00735  *   generator marking Lm2
00736  *
00737  * @return
00738  *   true if the language marked by rGen1 equals the language marked by rGen2
00739  *
00740  * @ingroup GeneratorFunctions
00741  */
00742 bool LanguageEquality(const Generator& rGen1, const Generator& rGen2);
00743 
00744 /**
00745  * Kleene Closure.
00746  *
00747  * This function computes the Kleene Closure ( ()* - operator) of the
00748  * language marked by rGen. The generated language is not considered.
00749  * Method: KleeneClosureNonDet() is called, which, for all transitions
00750  * leading from a state x to a marked state, inserts a transition with the
00751  * same event starting from x and leading to (one of) the initial state(s).
00752  * As this step causes nondeterminism, the function Deterministic() is called.
00753  * See also KleeneClosureNonDet().
00754  *
00755  * No restrictions on parameter.
00756  *
00757  * @param rGen
00758  *   generator marking the language Lm to which the Kleene Closure is applied
00759  *
00760  * <h4>Example:</h4>
00761  * <table>
00762  * <tr> <td> Generator G </td> <td> KleeneClosure(G) </td> </tr>
00763  * <tr>
00764  * <td> @image html tmp_kleene_g.png </td>
00765  * <td> @image html tmp_kleene_gRes.png </td>
00766  * </tr>
00767  * </table> 
00768  *
00769  * @ingroup GeneratorFunctions
00770  */
00771 void KleeneClosure(Generator& rGen);
00772 
00773 /**
00774  * Kleene Closure.
00775  *
00776  * This function is a convenience wrapper for KleeneClosure(Generator&).
00777  *
00778  *
00779  * @ingroup GeneratorFunctions
00780  */
00781 void KleeneClosure(const Generator& rGen, Generator& rResGen);
00782 
00783 /**
00784  * Kleene Closure, nondeterministic version.
00785  *
00786  * This function computes the Kleene Closure ( ()* - operator) of the
00787  * language marked by rGen. The generated language is not considered.
00788  * Method: KleeneClosureNonDet() is called, which, for all transitions
00789  * leading from a state x to a marked state, inserts a transition with the
00790  * same event starting from x and leading to (one of) the initial state(s).
00791  *
00792  * @param rGen
00793  *   generator marking the language Lm to which Kleene Closure is applied
00794  *
00795  * @ingroup GeneratorFunctions
00796  */
00797 void KleeneClosureNonDet(Generator& rGen);
00798 
00799 /**
00800  * Prefix Closure.
00801  *
00802  * This function computes the prefix closure the language Lm marked by rGen. A
00803  * language Lm is prefix closed if each string of Lm implies that all its
00804  * prefixes are also element of Lm. The prefix closure of a language marked by
00805  * a generator is always a subset of the generated language and is represented
00806  * by the set of coaccessible states of the generator.
00807  * Method:
00808  * First, Coaccessible() is called to erase all states of rGen that do not
00809  * represent prefixes of marked strings. Then, all remaining states are marked.
00810  *
00811  * No restrictions on parameter.
00812  *
00813  * ToDo: (slightly) more efficient version: implement generator function
00814  * CoAccessibleSet() similar to AccessibleSet() and call
00815  * InjectMarkedStates(AccessibleSet()).
00816  *
00817  * @param rGen
00818  *   generator marking the language Lm to which prefix closure is applied
00819  *
00820  * <h4>Example:</h4>
00821  * <table>
00822  * <tr> <td> Generator G </td> <td> PrefixClosure(G) </td> </tr>
00823  * <tr>
00824  * <td> @image html tmp_prefixclosure_g.png </td>
00825  * <td> @image html tmp_prefixclosure_gRes.png </td>
00826  * </tr>
00827  * </table>
00828  *
00829  * @ingroup GeneratorFunctions
00830  */
00831 void PrefixClosure(Generator& rGen);
00832 
00833 
00834 /**
00835  * Test for prefix closed marked language.
00836  *
00837  * This function tests whether the language Lm(G) marked by the specified generator G
00838  * is prefix closed. It does so by testing whether all accessible and coaccessible
00839  * states are marked. 
00840  *
00841  * The specified generator must be deterministic.
00842  *
00843  * @param rGen
00844  *   generator G marking the Lm(G) to test
00845  * @return
00846  *   True <> Lm(G) is prefix closed
00847  *
00848  * @ingroup GeneratorFunctions
00849  */
00850 bool IsPrefixClosed(const Generator& rGen);
00851 
00852 
00853 /**
00854  * Test for nonblocking generator
00855  *
00856  * A generator G is nonblocking if closure(Lm(G)) = L(G), i.e.
00857  * if every accessible state is coacessile.
00858  *
00859  * The specified generator must be deterministic.
00860  *
00861  * @param rGen
00862  *   generator G marking to test
00863  * @return
00864  *   True <> G is nonblocking
00865  *
00866  * @ingroup GeneratorFunctions
00867  */
00868 bool IsNonblocking(const Generator& rGen);
00869 
00870 /**
00871  * Test for nonblocking marked languages.
00872  *
00873  * Two languages L1 and L2 are nonblocking, if
00874  * closure(L1 || L2) == closure(L1) || closure(L2).
00875  *
00876  * This function performs the parallel composition of the two
00877  * specified generators and tests it for nonblockingness. Provided
00878  * that both generators are trim, this is equivalent to the
00879  * respective marked languages being nonblocking.
00880  *
00881  * The specified generators must be trim.
00882  *
00883  * @param rGen1
00884  *   Generator G1
00885  * @param rGen2
00886  *   Generator G2
00887  * @return
00888  *   True <> Lm(G1) and Lm(G2) are nonblocking
00889  *
00890  * @ingroup GeneratorFunctions
00891  */
00892 bool IsNonblocking(const Generator& rGen1, const Generator& rGen2);
00893 
00894 
00895 /**
00896  * Self-loop all states.
00897  *
00898  * This function selfoops all states of rGen with the events from rAlphabet.
00899  * Method:
00900  * The alphabet of rGen is extended by rAlphabet. For each state x of rGen
00901  * and each event alpha of rAlphabet, a transition (x,alpha,x) is inserted,
00902  * irrespective of whether this event was already active in x before.
00903  * See also SelfLoop(rGen,rAlphabet,rStates) and SelfLoopMarkedStates(rGen,rAlphabet).
00904  *
00905  * No restrictions on parameter.
00906  *
00907  * Determinism: resulting generator is nondeterministic, if it was nondeterministic
00908  * before, or if rGen already contains one or more (non selfloop) transitions with
00909  * events from rAlphabet.
00910  *
00911  * @param rGen
00912  *   generator to be selflooped with events from rAlphabet
00913  * @param rAlphabet
00914  *   alphabet with selfloop events
00915  *
00916  * <h4>Example:</h4>
00917  * <table>
00918  * <tr> <td> Generator G </td> <td> SelfLoop(G,Sigma={e,f}) </td> </tr>
00919  * <tr>
00920  * <td> @image html tmp_selfloop_g.png </td>
00921  * <td> @image html tmp_selfloop_gRes.png </td>
00922  * </tr>
00923  * </table>
00924  *
00925  * @ingroup GeneratorFunctions
00926  */
00927 void SelfLoop(Generator& rGen,const EventSet& rAlphabet);
00928 
00929 /**
00930  * Self-loop all marked states.
00931  *
00932  * This function selfoops all marked states of rGen with the events from rAlphabet.
00933  * Method:
00934  * The alphabet of rGen is extended by rAlphabet. For each marked state x of rGen
00935  * and each event alpha of rAlphabet, a transition (x,alpha,x) is inserted,
00936  * irrespective of whether this event was already active in x before.
00937  * See also SelfLoop(rGen,rAlphabet) and SelfLoop(rGen,rAlphabet,rStates).
00938  *
00939  * No restrictions on parameter.
00940  *
00941  * Determinism: resulting generator is nondeterministic, if it was nondeterministic
00942  * before, or if rGen already contains one or more (non selfloop) transitions
00943  * starting from a marked state with events from rAlphabet.
00944  *
00945  * @param rGen
00946  *   generator with marked states to be selflooped with events from rAlphabet
00947  * @param rAlphabet
00948  *   alphabet with selfloop events
00949  *
00950  * <h4>Example:</h4>
00951  * <table>
00952  * <tr> <td> Generator G </td> <td> SelfLoopMarkedStates(G,Sigma={e,f}) </td> </tr>
00953  * <tr>
00954  * <td> @image html tmp_selfloop_g.png </td>
00955  * <td> @image html tmp_selfloopMarked_gRes.png </td>
00956  * </tr>
00957  * </table>
00958  *
00959  * @ingroup GeneratorFunctions
00960  */
00961 void SelfLoopMarkedStates(Generator& rGen,const EventSet& rAlphabet);
00962 
00963 /**
00964  * Self-loop specified states.
00965  *
00966  * This function selfoops the states rStates of rGen with the events from rAlphabet.
00967  * Method:
00968  * The alphabet of rGen is extended by rAlphabet. For each state x of rStates
00969  * and each event alpha of rAlphabet, a transition (x,alpha,x) is inserted,
00970  * irrespective of whether this event was already active in x before.
00971  * See also SelfLoop(rGen,rAlphabet) and SelfLoopMarkedStates(rGen,rAlphabet).
00972  *
00973  * No restrictions on parameter.
00974  *
00975  * Determinism: resulting generator is nondeterministic, if it was nondeterministic
00976  * before, or if rGen already contains one or more (non selfloop) transitions
00977  * starting from a state of rState with events from rAlphabet.
00978  *
00979  * @param rGen
00980  *   generator with marked states to be selflooped with events from rAlphabet
00981  * @param rAlphabet
00982  *   alphabet with selfloop events
00983  * @param rStates
00984  *   states to apply selfloop
00985  *
00986  * @exception Exception
00987  *   - rStates is not a subset of rGen.States() (id 100). 
00988  *
00989  * <h4>Example:</h4>
00990  * <table>
00991  * <tr> <td> Generator G </td> <td> SelfLoop(G,Sigma={e,f},G.InitStates()) </td> </tr>
00992  * <tr>
00993  * <td> @image html tmp_selfloop_g.png </td>
00994  * <td> @image html tmp_selfloopInit_gRes.png </td>
00995  * </tr>
00996  * </table>
00997  *
00998  * @ingroup GeneratorFunctions
00999  */
01000 void SelfLoop(Generator& rGen,const EventSet& rAlphabet,const StateSet& rStates);
01001 
01002 
01003 
01004 
01005 } // namespace faudes
01006 
01007 #define FAUDES_REGULAR_H
01008 #endif 
01009 

libFAUDES 2.23h --- 2014.04.03 --- c++ api documentaion by doxygen